Test Bank for Statistics for Business and Economics, 14th edition by Ace Test Banks

Test Bank for Statistics for Business and Economics, 14th edition

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McClave Statistics for Business and Economics 14e Chapter 1 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Which of the following is not the job of a statistician? A) determining what information is relevant in a given problem B) implementing new procedures based on the results of a study C) collecting numerical information in the form of data D) determining whether the conclusions drawn from a study are to be trusted Objective: (1.1) Define Statistics

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 2) What is statistics? Objective: (1.1) Define Statistics

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 3) A recent report stated "Based on a sample of 120 truck drivers, there is evidence to indicate that, on average, independent truck drivers earn more than company-hired truck drivers." Does this statement describe descriptive or inferential statistics? A) Descriptive statistics B) Inferential statistics Objective: (1.2) Define Descriptive and Inferential Statistics

4) A survey of high school teenagers reported that 82% of those sampled are interested in pursuing a college education. Does this statement describe descriptive or inferential statistics? A) Inferential statistics B) Descriptive statistics Objective: (1.2) Define Descriptive and Inferential Statistics

5) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics? A) Inferential statistics B) Descriptive statistics Objective: (1.2) Define Descriptive and Inferential Statistics

6) From past figures, it is predicted that 45% of the registered voters will vote in the March primary. Does this statement describe descriptive or inferential statistics? A) Inferential statistics B) Descriptive statistics Objective: (1.2) Define Descriptive and Inferential Statistics

7) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. The university is interested in using the information from the sample of 250 students collected to learn information about the entire student parking population. Would this be an application of descriptive or inferential statistics? A) Inferential statistics B) Descriptive statistics Objective: (1.2) Define Descriptive and Inferential Statistics

8) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Would this be an application of descriptive or inferential statistics? A) Inferential statistics B) Descriptive statistics Objective: (1.2) Define Descriptive and Inferential Statistics

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 9) In a survey of 5000 high school students, 17% of those surveyed read at least one best-seller each month. Give an example of a descriptive statement and an inferential statement that could be made based on this information. Objective: (1.2) Define Descriptive and Inferential Statistics

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) Which of the following is not an element of descriptive statistical problems? A) data are displayed visually in graphs B) patterns in a data set are identified C) information revealed in a data set is summarized D) predictions are made about a larger set of data Objective: (1.2) Define Descriptive and Inferential Statistics

Answer the question True or False. 11) When we take data obtained from a sample and make generalizations or predictions about the entire population, we are utilizing inferential statistics. A) True B) False Objective: (1.2) Define Descriptive and Inferential Statistics

12) Statistics involves two different processes, describing sets of data and drawing conclusions about the sets of data on the basis of sampling. A) True B) False Objective: (1.2) Define Descriptive and Inferential Statistics

Solve the problem. 13) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 240 students and recorded how long it took each of them to find a parking spot. Identify the population of interest to the university administration. A) the entire set of students who park at the university B) the entire set of faculty, staff, and students who park at the university C) the students who park at the university between 9 and 10 AM on Wednesdays D) the 240 students about whom the data were collected Objective: (1.3) Identify Elements of Statistics

14) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 140 students and recorded how long it took each of them to find a parking spot. Identify the variable of interest to the university administration. A) time to find a parking spot B) number of empty parking spots C) students who drive cars on campus D) number of students who cannot find a spot Objective: (1.3) Identify Elements of Statistics

15) An assembly line is operating satisfactorily if fewer than 5% of the phones produced per day are defective. To check the quality of a day's production, the company randomly samples 30 phones from a day's production to test for defects. Define the population of interest to the manufacturer. A) the 30 responses: defective or not defective B) all the phones produced during the day in question C) the 5% of the phones that are defective D) the 30 phones sampled and tested Objective: (1.3) Identify Elements of Statistics

16) An insurance company conducted a study to determine the percentage of cardiologists who had been sued for malpractice in the previous seven years. The sample was randomly chosen from a national directory of doctors. What is the variable of interest in this study? A) all cardiologists in the directory B) the doctor's area of expertise (i.e., cardiology, pediatrics, etc.) C) the responses: have been sued/have not been sued for malpractice in the last seven years D) the number of doctors who are cardiologists Objective: (1.3) Identify Elements of Statistics

17) A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida coastline from environmental disasters. Twenty-four hundred Florida residents were surveyed.Which of the following is the population used in the study? A) the 2,400 Florida residents who were surveyed B) all Florida residents who lived along the coastline C) Florida residents willing to spend more tax dollars protecting the coastline from environmental disasters D) all Florida residents Objective: (1.3) Identify Elements of Statistics

18) A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Forty-nine hundred Florida residents were surveyed.Which of the following describes the variable of interest in the study? A) the response to the question "Do you use the beach?" B) the response to the question, "Are you willing to spend more tax dollars on protecting the Florida beaches from environmental disasters?" C) the response to the question "Do you live along the beach?" D) the 4,900 Florida residents surveyed Objective: (1.3) Identify Elements of Statistics

19) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the population of interest to the university administration. A) the 250 students that data was collected from B) the entire set of students that park at the university C) the parking time, defined to be the amount of time the student spent finding a parking spot D) a single student that parks at the university Objective: (1.3) Identify Elements of Statistics

20) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the sample of interest to the university administration. A) the parking time, defined to be the amount of time the student spent finding a parking spot B) the 250 students that data was collected from C) a single student that parks at the university D) the entire set of students that park at the university Objective: (1.3) Identify Elements of Statistics

21) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the experimental unit of interest to the university administration. A) a single student that parks at the university B) the parking time, defined to be the amount of time the student spent finding a parking spot C) the 250 students that data was collected from D) the entire set of students that park at the university Objective: (1.3) Identify Elements of Statistics

22) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the variable of interest to the university administration. A) the parking time, defined to be the amount of time the student spent finding a parking spot B) the 250 students that data was collected from C) a single student that parks at the university D) the entire set of students that park at the university Objective: (1.3) Identify Elements of Statistics

23) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the population of interest for this study. A) the entire set of stocks that are traded on the NYSE B) the current price (or closing price) of a NYSE stock C) the 500 NYSE stocks that current prices were collected from D) a single stock traded on the NYSE Objective: (1.3) Identify Elements of Statistics

24) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the sample of interest for this study. A) a single stock traded on the NYSE B) the entire set of stocks that are traded on the NYSE C) the current price (or closing price) of a NYSE stock D) the 500 NYSE stocks that current prices were collected from Objective: (1.3) Identify Elements of Statistics

25) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the experimental unit of interest for this study. A) a single stock traded on the NYSE B) the current price (or closing price) of a NYSE stock C) the entire set of stocks that are traded on the NYSE D) the 500 NYSE stocks that current prices were collected from Objective: (1.3) Identify Elements of Statistics

26) As part of an economics class project, students were asked to randomly select 500 New Your Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the variable of interest for this study. A) the entire set of stocks that are traded on the NYSE B) a single stock traded on the NYSE C) the 500 NYSE stocks that current prices were collected from D) the current price (or closing price) of a NYSE stock Objective: (1.3) Identify Elements of Statistics

27) A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. Identify the population of interest in this study. A) all community college students in the state of Georgia B) the 1500 community college students contacted C) the response (Yes/No) to the question, "Have you taken at least one online class?" D) the number of online classes a student has taken Objective: (1.3) Identify Elements of Statistics

28) A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. Identify the variable of interest in this study. A) the 1500 community college students contacted B) the number of online classes a student has taken C) all community college students in the state of Georgia D) the response (Yes/No) to the question, "Have you taken at least one online class?" Objective: (1.3) Identify Elements of Statistics

29) Which of the following is not typically an element of inferential statistical problems? A) sample B) measure of reliability C) census D) variable of interest Objective: (1.3) Identify Elements of Statistics

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 30) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 140 students and recorded how long it took each of them to find a parking spot. Identify the population, sample, and variable of interest to the administrators. Objective: (1.3) Identify Elements of Statistics

31) A quality inspector tested 67 copiers in an attempt to estimate the average failure rate of the copier model. His study indicated that the number of failures decreased from two years ago, indicating an increase in the reliability of the copiers. Describe the variable of interest to the inspector. Objective: (1.3) Identify Elements of Statistics

32) A high school guidance counselor analyzed data from a sample of 900 community colleges throughout the United States. One of his goals was to estimate the annual tuition costs of community colleges in the United States. Describe the population and variable of interest to the guidance counselor. Objective: (1.3) Identify Elements of Statistics

33) Explain why it is not necessary to provide a measure of reliability when a census is used rather than a sample. Objective: (1.3) Identify Elements of Statistics

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 34) A variable is a characteristic or property of a population. A) True

B) False

Objective: (1.3) Identify Elements of Statistics

35) Measurement is the process of assigning numbers to variables of individual population units. A) True B) False Objective: (1.3) Identify Elements of Statistics

36) A census is feasible when the population of interest is small. A) True B) False Objective: (1.3) Identify Elements of Statistics

37) The process of using information from a sample to make generalizations about the larger population is called statistical inference. A) True B) False Objective: (1.3) Identify Elements of Statistics

38) A measure of reliability is an important element of a descriptive statistical problem. A) True B) False Objective: (1.3) Identify Elements of Statistics

Solve the problem. 39) When we study a process, what is generally the focus? A) the output B) the black box Objective: (1.4) Describe Processes

C) the input

D) the subprocesses

40) In the context of processes, what is a sample? A) any set of input C) any set of output

B) any set of subprocesses D) any subset of the population

Objective: (1.4) Describe Processes

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 41) What do we call a process whose operations are unknown or unspecified? Objective: (1.4) Describe Processes

42) A chain of coffee shops has 45 stores in one metropolitan area. For liability reasons, the chain is interested in the average temperature of hot drinks served at the stores. Three stores were chosen and the temperature of every fifth hot drink served at each of these stores was recorded during a two-week period. At the end of the two-week period, the temperatures of 10,571 hot drinks had been recorded. a. b. c. d.

Identify the process of interest. Identify the variable of interest. Describe the sample. Describe the inference of interest.

Objective: (1.4) Describe Processes

43) A department store receives customer orders through its call center and website. These orders as well as any special orders received in the stores are forwarded to a distribution center where workers pull the items on the orders from inventory, pack the items, and prepare the necessary paperwork for the shipping company that will pick the orders up and deliver them to the customers. In order to monitor the subprocess of pulling the items from inventory, every 15 minutes one order is checked to determine whether the worker has pulled the correct item. a. b. c. d.

Identify the process of interest. Identify the variable of interest. Describe the sample. Describe the inference of interest.

Objective: (1.4) Describe Processes

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 44) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 250 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. Identify the type of data collected by PAWT. A) qualitative B) quantitative Objective: (1.5) Classify Data as Quantitative or Qualitative

45) The manager of a car dealership records the colors of automobiles on a used car lot. Identify the type of data collected. A) quantitative B) qualitative Objective: (1.5) Classify Data as Quantitative or Qualitative

46) A postal worker counts the number of complaint letters received by the United States Postal Service in a given day. Identify the type of data collected. A) quantitative B) qualitative Objective: (1.5) Classify Data as Quantitative or Qualitative

47) An usher records the number of unoccupied seats in a movie theater during each viewing of a film. Identify the type of data collected. A) quantitative B) qualitative Objective: (1.5) Classify Data as Quantitative or Qualitative

48) A fan observes the numbers on the shirts of a girl's soccer team. Identify the type of data collected. A) qualitative B) quantitative Objective: (1.5) Classify Data as Quantitative or Qualitative

49) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. What type of variable is the administration interested in collecting? A) qualitative data B) quantitative data Objective: (1.5) Classify Data as Quantitative or Qualitative

50) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. What type of variable is being collected? A) qualitative data B) quantitative data Objective: (1.5) Classify Data as Quantitative or Qualitative

51) A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. What type of variable is being collected? A) qualitative data B) quantitative data Objective: (1.5) Classify Data as Quantitative or Qualitative

52) Which data about paintings would not be qualitative? A) the value B) the style

C) the theme

D) the artist

Objective: (1.5) Classify Data as Quantitative or Qualitative

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 53) Gender is one variable of interest in a study of the effectiveness of a new medication. For data entry purposes, the researcher conducting the study assigns 1 for Male and 2 for Female. Is the gender data quantitative or qualitative? Objective: (1.5) Classify Data as Quantitative or Qualitative

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 54) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 330 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. Identify how the data were collected in this study. A) observationally B) from a designed experiment C) from a survey D) from a published source Objective: (1.6) Identify Data Collection Method

55) A personnel director studied the eating habits of a company's employees. The director noted whether employees brought their own lunch to work, ate at the company cafeteria, or went out to eat lunch. This type of data collection would best be considered as a(n) __________. A) observational study B) designed experiment Objective: (1.6) Identify Data Collection Method

56) A student worked on her statistics project in the library and found a reference book that contained the median family incomes for all 50 states. On her project, she would report her data as being collected __________. A) from a designed experiment B) from a published source C) observationally D) from a survey Objective: (1.6) Identify Data Collection Method

57) What method of data collection would you use to collect data for a study where a drug was given to 30 patients and a placebo to another group of 30 patients to determine if the drug has an effect on a patient's illness? A) published source B) designed experiment C) observational study D) survey Objective: (1.6) Identify Data Collection Method

58) What method of data collection would you use to collect data for a study where a political pollster wishes to determine if his candidate is leading in the polls? A) published source B) survey C) designed experiment D) observational study Objective: (1.6) Identify Data Collection Method

59) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the data collection method used by the administration in this study. A) data collected observationally B) data from a published source C) data from a designed experiment Objective: (1.6) Identify Data Collection Method

60) As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. As part of the project, students were asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques. Identify the data collection method used in this study. A) data collected observationally B) data from a published source C) data from a designed experiment Objective: (1.6) Identify Data Collection Method

61) Does online teaching help or hinder student learning? To help answer this question, a statistics teacher decided to teach his three sections of a particular class using three different teaching models - a traditional face-to-face section, a completely online section, and a hybrid or blended section that incorporated both a face-to-face and online component in the section. Students were randomly assigned to the different sections, taught identical information using the different teaching formats, and given identical examinations to measure student learning. The goal was to identify if the teaching method used affected student learning performance. Identify the data collection method used in this study. A) data from a designed experiment B) data collected observationally C) data from a published source Objective: (1.6) Identify Data Collection Method

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 62) What is meant by a representative sample? Objective: (1.6) Identify Data Collection Method

63) What is the most common way to satisfy the representative sample requirement? Objective: (1.6) Identify Data Collection Method

64) Three female students and two male students are to be chosen from a group of 30 female students and 20 male students. Does this sample of five students satisfy the conditions to be a random sample of the 50 students in the group? Explain. Objective: (1.6) Identify Data Collection Method

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 65) In an observational study, the researcher exerts strict control over the units in the study. A) True B) False Objective: (1.6) Identify Data Collection Method

66) When using data from a published source, it is not important to know how the data were collected and whether randomization was used. A) True B) False Objective: (1.6) Identify Data Collection Method

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 67) In one study of the moral of company's employees, 10 employees were randomly chosen from each of the departments within the company. Identify the sampling design used. Objective: (1.6) Understand Sample Survey Designs

68) In an attempt to determine the ages of its customers, one store asked every tenth customer who entered the store his or her age. Identify the sampling design used. Objective: (1.6) Understand Sample Survey Designs

69) What term is used to describe the situation where sampling units contained in a sample do not produce sample observations? Objective: (1.6) Understand Sample Survey Designs

70) What is meant by selection bias? Objective: (1.6) Identify Bias

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 71) Which type of problem has occurred when inaccuracies exist in the values of the data recorded? A) selection bias B) nonresponse bias C) measurement error Objective: (1.6) Identify Bias

72) A watchdog group is investigating how people are treated during the foreclosure process. Surveys were mailed to a random sample of 300 people who had recently been threatened with foreclosure. 75 of the surveys were returned by the postal service because the intended recipients had moved and left no forwarding address. What type of problem has occurred? A) selection bias B) measurement error C) nonresponse bias Objective: (1.6) Identify Bias

73) A university was interested in student reaction to a proposal to spend more on athletic scholarships and less on academic scholarships. 35 student athletes were surveyed. What type of problem has occurred? A) measurement error B) nonresponse bias C) selection bias Objective: (1.6) Identify Bias

74) The way in which an interviewer asks a question about political party affiliation causes respondents to answer that they have no affiliation when they actually do. What type of problem has occurred? A) nonresponse bias B) measurement error C) selection bias Objective: (1.6) Identify Bias

75) A student completing a research project for a criminal justice class obtained a radar gun for determining automobile speeds and recorded the speeds of automobiles passing a fixed location over a period of several hours. The student was unaware that the device needed to be recharged after two hours of use and that the speeds recorded after two hours were not reliable. What type of problem has occurred? A) nonresponse bias B) measurement error C) selection bias Objective: (1.6) Identify Bias

76) Because of the possible legal consequences, many people in a sample of the U.S. population chose not to participate in a survey regarding illegal drug use. What type of problem has occurred? A) measurement error B) nonresponse bias C) selection bias Objective: (1.6) Identify Bias

77) A middle school was interested in surveying their students to find out opinions about the schools media center. To facilitate data collection, the homeroom period was extended 30 minutes to allow everyone in the school ample time to respond to a short questionnaire. Unfortunately, it was learned after the surveys had been completed that all honors students in the middle school were on an all-day field trip and away from school for the entire day. The exclusion of their input into the survey would be considered which type of sampling problem? A) nonresponse bias B) selection bias C) measurement error Objective: (1.6) Identify Bias

78) A county planning commission is attempted to survey 1500 households from the counties 400,000 households. A random sample was selected and surveys were mailed to the randomly selected households, but only 1075 were returned. The inability to collect data from the 425 households that didn't return the survey would be considered which type of sampling problem? A) measurement error B) selection bias C) nonresponse bias Objective: (1.6) Identify Bias

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 79) Define business analytics. Objective: (1.7) Define Business Analytics and Statistical Thinking

80) Define statistical thinking. Objective: (1.7) Define Business Analytics and Statistical Thinking

81) Give an example of unethical statistical practice. Objective: (1.7) Unethical Statistics

82) A health food company has the following statement on their new product packaging: "Prevents all types of cancer!" (Fact: Past studies have shown that some ingredients in the new product have been know to possibly reduce the risk of many types of cancer). Discuss why it is unethical to make this statement. Objective: (1.7) Unethical Statistics

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 83) A researcher studying malnutrition among children in a developing country collected weights of a random sample of children using a scale that she had set to give weights 2.5 kilograms less than the actual weight. Which statement best describes this situation? A) Measurement error has occurred, but the researcher is not guilty of unethical statistical practice. B) Measurement error has occurred, and the researcher is guilty of unethical statistical practice. C) Measurement error has not occurred, and the researcher is not guilty of unethical statistical practice. D) Measurement error has not occurred, but the researcher is guilty of unethical statistical practice. Objective: (1.7) Unethical Statistics

Answer Key Testname: SBE14ECH1

1) B 2) Statistics is the science of data that involves collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical information. 3) B 4) B 5) B 6) A 7) A 8) B 9) Descriptive: 17% of the students sampled (or 850) read at least one best-seller each month. Inferential: Based on the survey, we estimate that about 17% of all high school students read at least one best-seller each month. 10) D 11) A 12) A 13) A 14) A 15) B 16) C 17) D 18) B 19) B 20) B 21) A 22) A 23) A 24) D 25) A 26) D 27) A 28) D

29) C 30) The population of interest are all students at the university who park. The sample is the parking times of the 140 students that were collected by the university administrator. The variable of interest to the administrators is the parking time variable. 31) The variable of interest to the researcher is the failure rate of the copiers. 32) The population of interest to the guidance counselor is all community colleges in the United States. The variable of interest is the annual tuition cost of the community college. 33) When a census is used, there should be no error. 34) B 35) A 36) A 37) A 38) B 39) A 40) C 41) a black box

42) a. serving of hot drinks at coffee shops in the chain b. temperature of hot drinks served c. 10,571 drinks whose temperatures recorded over the two-week period d. average temperature of all hot drinks served at all stores in the chain 43) a. fulfilling customers' orders from receiving the order to pick up by shipping company b. whether or not an order has been pulled correctly c. the set of all orders that are checked (one every 15 minutes) d. number or proportion of all orders that are pulled correctly (incorrectly) 44) B 45) B 46) A 47) A 48) A 49) B 50) B 51) A 52) A 53) Qualitative; The numbers are arbitrarily selected numerical codes for the categories and have no utility beyond that. 54) C 55) A 56) B 57) B 58) B 13

59) A 60) B 61) A 62) a sample that exhibits characteristics typical of those possessed by the population of interest 63) selecting a random sample 64) No; not every sample of 5 students from the group has an equal chance of selection; for example, a sample consisting of 5 males has no chance of being selected. 65) B 66) B 67) stratified random sampling 68) systematic sampling 69) nonresponse 70) Selection bias is when a subset of the experimental units in the population is excluded so that these units have no possibility of being selected in the sample. 71) C 72) C 73) C 74) B 75) B 76) B 77) B 78) C

Answer Key Testname: SBE14ECH1

79) Business analytics refers to methodologies (e.g., statistical methods) that extract useful information from data in order to make better business decisions. 80) Statistical thinking involves applying rational thought and the science of statistics to critically assess data and make inferences. 81) Researchers select a biased sample, with the intention of misleading the public. 82) Answers may vary. One possible answer is that the past studies show that the ingredients only have possible cancer reducing effects on many, not all, types of cancer. 83) B

McClave Statistics for Business and Economics 14e Chapter 2 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) In an eye color study, 25 out of 50 people in the sample had brown eyes. In this situation, what does the number .50 represent? A) a class relative frequency B) a class percentage C) a class frequency D) a class Objective: (2.1) Identify Classes/Compute Class Frequencies/Relative Frequencies/Percentages

2) What class percentage corresponds to a class relative frequency of .37? A) 37% B) .63% C) 63%

D) .37%

Objective: (2.1) Identify Classes/Compute Class Frequencies/Relative Frequencies/Percentages

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) A sample of 100 e-mail users were asked whether their primary e-mail account was a free account, an institutional (school or work) account, or an account that they pay for personally. Identify the classes for the resulting data. Objective: (2.1) Identify Classes/Compute Class Frequencies/Relative Frequencies/Percentages

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) What number is missing from the table? Grades on Test A B C D F

Frequency 6 7 9 2 1

A) .72

Relative Frequency .24 .36 .08 .04

B) .28

C) .70

D) .07

C) 220

D) 480

Objective: (2.1) Construct Frequency/Relative Frequency Table

5) What number is missing from the table? Year in College Freshman Sophomore Junior Senior

A) 440

Frequency 600 560 400

Relative Frequency .30 .28 .22 .20

B) 520

Objective: (2.1) Construct Frequency/Relative Frequency Table

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) Complete the frequency table for the data shown below. green brown blue blue

blue orange brown brown

brown blue green blue

orange red red blue

blue green brown red

Color Frequency Green Blue Brown Orange Objective: (2.1) Construct Frequency/Relative Frequency Table

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 7) A frequency table displays the proportion of observations falling into each class. A) True B) False Objective: (2.1) Construct Frequency/Relative Frequency Table

Solve the problem. 8) 260 randomly sampled college students were asked, among other things, to state their year in school (freshman, sophomore, junior, or senior). The responses are shown in the bar graph below. How many of the students who responded would be classified as upperclassmen (e.g., juniors or seniors)?

A) Approximately 25

B) Approximately 10

Objective: (2.1) Construct, Interpret Bar Graph

C) Approximately 125

D) Approximately 100

The manager of a store conducted a customer survey to determine why customers shopped at the store. The results are shown in the figure. What proportion of customers responded that merchandise was the reason they shopped at the store? 1 2 3 A) B) C) D) 30 2 7 7 Objective: (2.1) Construct, Interpret Bar Graph

10)

The bar graph shows the political affiliation of 1000 registered U.S. voters. What percentage of the voters belonged to one of the traditional two parties (Democratic or Republican)? A) 75% B) 35% C) 40% D) 25% Objective: (2.1) Construct, Interpret Bar Graph

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 11) The data below show the types of medals won by athletes representing the United States in the Winter Olympics. gold bronze gold gold

gold gold silver gold

silver silver silver bronze

gold silver bronze bronze

bronze bronze bronze

silver silver gold

silver gold silver

a. Construct a frequency table for the data. b. Construct a relative frequency table for the data. c. Construct a frequency bar graph for the data. Objective: (2.1) Construct, Interpret Bar Graph

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 12) The bars in a bar graph can be arranged by height in ascending order from left to right. A) True B) False Objective: (2.1) Construct, Interpret Bar Graph

13) Either vertical or horizontal bars can be used when constructing a bar graph. A) True B) False Objective: (2.1) Construct, Interpret Bar Graph

Solve the problem. 14)

The pie chart shows the classifications of students in a statistics class. What percentage of the class consists of freshman, sophomores, and juniors? A) 14% B) 54% C) 86% Objective: (2.1) Construct, Interpret Pie Chart

D) 44%

15) One of the questions posed to a sample of 286 incoming freshmen at a large public university was, "Do you have any tattoos?" Their responses are shown below in the pie chart. Please note that the values shown represent the number of responses in each category.

Based on the responses shown in the pie chart, what percentage of the freshmen responded with "Yes?" A) 26.6% B) 73.4% C) 76% D) 76 Objective: (2.1) Construct, Interpret Pie Chart

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 16) The table shows the number of each type of book found at an online auction site during a recent search. Type of Book Children's Fiction Nonfiction Educational

Number 51,033 141,114 253,074 67,252

a. Construct a relative frequency table for the book data. b. Construct a pie chart for the book data. Objective: (2.1) Construct, Interpret Pie Chart

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 17) If 25% of your statistics class is sophomores, then in a pie chart representing classifications of the students in your statistics class the slice assigned to sophomores is 90°. A) True B) False Objective: (2.1) Construct, Interpret Pie Chart

18) The slices of a pie chart must be arranged from largest to smallest in a clockwise direction. A) True B) False Objective: (2.1) Construct, Interpret Pie Chart

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 19) What characteristic of a Pareto diagram distinguishes it from other bar graphs? Objective: (2.1) Construct, Interpret Pareto Diagram

20) The table shows the number of each type of car sold in June. Car compact sedan small SUV large SUV minivan truck Total a. b.

Number 7,204 9,089 20,418 13,691 15,837 15,350 81,589

Construct a relative frequency table for the car sales. Construct a Pareto diagram for the car sales using the class percentages as the heights of the bars.

Objective: (2.1) Construct, Interpret Pareto Diagram

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 21) Class relative frequencies must be used, rather than class frequencies or class percentages, when constructing a Pareto diagram. A) True B) False Objective: (2.1) Construct, Interpret Pareto Diagram

22) A Pareto diagram is a pie chart where the slices are arranged from largest to smallest in a counterclockwise direction. A) True B) False Objective: (2.1) Construct, Interpret Pareto Diagram

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 23) An annual survey sent to retail store managers contained the question "Did your store suffer any losses due to employee theft?" The responses are summarized in the table for two years. Compare the responses for the two years using side-by-side bar charts. What inferences can be made from the charts? Employee Percentage Percentage Theft in year 1 in year 2 Yes 34 23 No 51 68 Don't know 15 9 Totals

100

Objective: (2.1) Construct, Interpret Side-by-Side Bar Chart

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 24) The payroll amounts for all teams in an international hockey league are shown below using a graphical technique from chapter 2 of the text. How many of the hockey team payrolls exceeded $20 million (Note: Assume that no payroll was exactly $20 million)?

A) 8 teams

B) 10 teams

C) 18 teams

D) 23 teams

Objective: (2.2) Construct, Interpret Histogram

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 25) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. 1

11 11

11 14 14 19 22 23 24 25 29 a.

Complete the class frequency table for the data. Total Medals 1-5 6-10 11-15 16-20 21-25 26-30

Frequency

b. Using the classes from the frequency table, construct a histogram for the data. Objective: (2.2) Construct, Interpret Histogram

26) The total points scored by a basketball team for each game during its last season have been summarized in the table below. Score 41-60 61-80 81-100 101-120

Frequency 3 8 12 7

a. Explain why you cannot use the information in the table to construct a stem-and-leaf display for the data. b. Construct a histogram for the scores. Objective: (2.2) Construct, Interpret Histogram

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 27) All class intervals in a histogram have the same width. A) True

B) False

Objective: (2.2) Construct, Interpret Histogram

28) A histogram can be constructed using either class frequencies or class relative frequencies as the heights of the bars. A) True B) False Objective: (2.2) Construct, Interpret Histogram

29) The bars in a histogram should be arranged by height in descending order from left to right. A) True B) False Objective: (2.2) Construct, Interpret Histogram

Solve the problem. 30) A survey was conducted to determine how people feel about the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below. Stem Leaf 31 2 40 3 4 7 8 9 9 9 50 1 1 2 3 4 5 61 2 5 6 6 72 6 8 99 What percentage of the respondents rated overall television quality as very good (regarded as ratings of 80 and above)? A) 1% B) 9% C) 36% D) 4% Objective: (2.2) Construct, Interpret Stem-and-Leaf Display

31) 252 randomly sampled college students were asked, among other things, to estimate their college grade point average (GPA). The responses are shown in the stem-and-leaf plot shown below. Notice that a GPA of 3.65 would be indicated with a stem of 36 and a leaf of 5 in the plot. How many of the students who responded had GPA's that exceeded 3.55? Stem and Leaf Plot of GPA Leaf Digit Unit = 0.01 19 9 represents 1.99 Stem 1 19 5 20 6 21 11 22 15 23 20 24 33 25 46 26 61 27 79 28 88 29 116 30 (19) 31 117 32 95 33 80 34 49 35 31 36 25 37 13 38 5 39 4 40

Minimum 1.9900 Median 3.1050 Maximum 4.0000

Leaves 9 0668 0 05567 0113 00005 0000000000067 0000005577789 000000134455578 000000000144667799 002356777 0000000000000000000011344559 0000000000112235666 0000000000000000345568 000000000025557 0000000000000000333444566677889 000003355566677899 000005 022235588899 00002579 7 0000

252 cases included

A) 31

B) 19

C) 39

D) 49

Objective: (2.2) Construct, Interpret Stem-and-Leaf Display

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 32) The scores for a statistics test are as follows: 87 76 92 77 93 96 88 85 66 89 79 96 50 99 83 88 82 59 10 69 Create a stem-and-leaf display for the data. Objective: (2.2) Construct, Interpret Stem-and-Leaf Display

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 33) For large data sets, a stem-and-leaf display is a better choice than a histogram. A) True B) False Objective: (2.2) Construct, Interpret Stem-and-Leaf Display

Solve the problem. 34) A dot plot of the speeds of a sample of 50 cars passing a policeman with a radar gun is shown below.

What proportion of the motorists were driving above the posted speed limit of 55 miles per hour? A) 7 B) 0.64 C) 0.14 D) 0.50 Objective: (2.2) Construct, Interpret Dot-Plot

35) Which of the graphical techniques below can be used to summarize qualitative data? A) box plot B) bar graph C) stem-and-leaf plot

D) dot plot

Objective: (2.2) Construct, Interpret Dot-Plot

36) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 80 students and recorded how long it took each of them to find a parking spot. Which of the following types of graphs should not be used to display information concerning the students parking times? A) box plot B) histogram C) stem-and-leaf display D) pie chart Objective: (2.2) Construct, Interpret Dot-Plot

37) Fill in the blank. One advantage of the __________ is that the actual data values are retained in the graphical summarization of the data. A) pie chart B) stem-and-leaf plot C) histogram Objective: (2.2) Construct, Interpret Dot-Plot

38) The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample mean for the data. A) $465 B) $400 C) $450 D) $600 Objective: (2.3) Find Mean, Median, Mode

39) The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample median for the data. A) $450 B) $465 C) $400 D) $600 Objective: (2.3) Find Mean, Median, Mode

40) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 67 73 68 62 59

72 60 91 67 86

65 88 75 80 74

75 64 61 69 63

85 89 80 72 81

Find the median of the observations. A) 72.5 B) 69

C) 73

D) 72

C) 75.95

D) 79.15

Objective: (2.3) Find Mean, Median, Mode

41) The scores for a statistics test are as follows: 67 76 97 77 61 92 86 85 92 89 79 93 50 66 85 68 85 71 18 82 Compute the mean score. A) 66.90

B) 75

Objective: (2.3) Find Mean, Median, Mode

42) A shoe retailer keeps track of all types of information about sales of newly released shoe styles. One newly released style was marketed to tall people. Listed below are the shoe sizes of 12 randomly selected customers who purchased the new style. Find the mode of the shoe sizes. 9

1 2

A) 9

1 2

B) 10

1 2

C) 11

D) 10

1 4

Objective: (2.3) Find Mean, Median, Mode

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 43) Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed: Company A $72.3 Company B 60.3 Company C 55.1 Company D 54.4 Company E 31.1

Company F Company G Company H Company I Company J

$27 24.3 21.3 22.9 20.7

Calculate the mean and median for the data. Objective: (2.3) Find Mean, Median, Mode

44) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the mean, median, and mode of the numbers of medals won by these countries. 1

Objective: (2.3) Find Mean, Median, Mode

45) Calculate the mean of a sample for which

x = 196 and n = 8.

Objective: (2.3) Find Mean, Median, Mode

46) The calculator screens summarize a data set.

a. How many data items are in the set? b. What is the sum of the data? c. Identify the mean, median, and mode, if possible. Objective: (2.3) Find Mean, Median, Mode

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 47) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 99 miles per hour. Suppose that the statistician indicated that the serve speed distribution was skewed to the left. Which of the following values is most likely the value of the median serve speed? A) 105 mph B) 87 mph C) 99 mph D) 93 mph Objective: (2.3) Interpret Measures of Central Tendency

48) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the mean is correct? A) 50% of the students sampled had textbook costs equal to $500 B) 50% of the students sampled had textbook costs that were less than $500 C) The average of the textbook costs sampled was $500 D) The most frequently occurring textbook cost in the sample was $500 Objective: (2.3) Interpret Measures of Central Tendency

49) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the median is correct? A) 50% of the students sampled had textbook costs that were less than $425 B) The most frequently occurring textbook cost in the sample was $425 C) The average of the textbook costs sampled was $425 D) 50% of the students sampled had textbook costs equal to $425 Objective: (2.3) Interpret Measures of Central Tendency

50) During one recent year, U.S. consumers redeemed 6.51 billion manufacturers' coupons and saved themselves $2.42 billion. Calculate and interpret the mean savings per coupon. A) Half of all coupons were worth more than $0.37 in savings. B) Half of all coupons were worth more than 269.0 cents in savings. C) The average savings was 269.0 cents per coupon. D) The average savings was $0.37 per coupon. Objective: (2.3) Interpret Measures of Central Tendency

51) The output below displays the mean and median for the state high school dropout rates in year 1 and in year 5.

N MEAN MEDIAN

Year 1 51 28.99 27.84

Year 5 51 26.28 25.53

Interpret the year 5 median dropout rate of 25.53. A) The most frequently observed dropout rate of the 51 states was 25.53%. B) Most of the 51 states had a dropout rate close to 25.53%. C) Half of the 51 states had a dropout rate of 25.53%. D) Half of the 51 states had a dropout rate below 25.53%. Objective: (2.3) Interpret Measures of Central Tendency

52)

For the distribution drawn here, identify the mean, median, and mode. A) A = mode, B = mean, C = median B) A = mode, B = median, C = mean C) A = median, B = mode, C = mean D) A = mean, B = mode, C = median Objective: (2.3) Interpret Measures of Central Tendency

53) In a distribution that is skewed to the right, what is the relationship of the mean, median, and mode? A) mode > median > mode B) mean > median > mode C) median > mean > mode D) mode > mean > median Objective: (2.3) Interpret Measures of Central Tendency

54) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean of the test scores is 76. Additional information indicated that the median of the test scores was 85. What type of distribution most likely describes the shape of the test scores? A) skewed to the left B) symmetric C) unable to determine with the information given D) skewed to the right Objective: (2.3) Interpret Measures of Central Tendency

55) A shoe company reports the mode for the shoe sizes of men's shoes is 12. Interpret this result. A) Most men have shoe sizes between 11 and 13. B) The most frequently occurring shoe size for men is size 12 C) Half of the shoes sold to men are larger than a size 12 D) Half of all men's shoe sizes are size 12 Objective: (2.3) Interpret Measures of Central Tendency

56) Which of the following is not a measure of central tendency? A) median B) mean C) range

D) mode

Objective: (2.3) Interpret Measures of Central Tendency

57) The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution? A) range B) median C) mean D) mode Objective: (2.3) Interpret Measures of Central Tendency

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 58) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 140 students and recorded how long it took each of them to find a parking spot. The times had a distribution that was skewed to the left. Based on this information, discuss the relationship between the mean and the median for the 140 times collected. Objective: (2.3) Interpret Measures of Central Tendency

59) The output below displays the mean and median for the state high school dropout rates in year 1 and in year 5.

N MEAN MEDIAN

Year 1 51 28.14 27.82

Year 5 51 26.71 25.24

Use the information to determine the shape of the distributions of the high school dropout rates in year 1 and year 5. Objective: (2.3) Interpret Measures of Central Tendency

60) The total points scored by a basketball team for each game during its last season have been summarized in the table below. Identify the modal class of the distribution of scores. Score 41-60 61-80 81-100 101-120

Frequency 3 8 12 7

Objective: (2.3) Interpret Measures of Central Tendency

61) The calculator screens summarize a data set.

a. Identify the mean and the median. b. Based only on the mean and the median, do you expect that the data set is skewed to the right, symmetric, or skewed to the left? Explain. Objective: (2.3) Interpret Measures of Central Tendency

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 62) The mean and the median are useful measures of central tendency for both qualitative and quantitative data. A) True B) False Objective: (2.3) Interpret Measures of Central Tendency

63) In a symmetric and mound shaped distribution, we expect the values of the mean, median, and mode to differ greatly from one another. A) True B) False Objective: (2.3) Interpret Measures of Central Tendency

64) In symmetric distributions, the mean and the median will be approximately equal. A) True B) False Objective: (2.3) Interpret Measures of Central Tendency

65) In skewed distributions, the mean is the best measure of the center of the distribution since it is least affected by extreme observations. A) True B) False Objective: (2.3) Interpret Measures of Central Tendency

66) In practice, the population mean µ is used to estimate the sample mean x. A) True B) False Objective: (2.3) Interpret Measures of Central Tendency

67) In general, the sample mean is a better estimator of the population mean for larger sample sizes. A) True B) False Objective: (2.3) Interpret Measures of Central Tendency

Solve the problem. 68) Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed: Company A $72.7 Company B 61.1 Company C 57 Company D 56.2 Company E 30.9

Company F $27.2 Company G 26.4 Company H 21.4 Company I 23.8 Company J 20.1

Calculate the sample variance. A) 2,142.849 B) 3,887.887

C) 1,920.187

D) 388.993

C) 2

D) 10

Objective: (2.4) Calculate Range, Variance, Standard Deviation

69) Calculate the range of the following data set: 7, 8, 5, 2, 9, 10, 6, 7, 7 A) 8

B) 12

Objective: (2.4) Calculate Range, Variance, Standard Deviation

70) The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. Round to four decimal places. 190, 115, 145, 185, 140 A) 176.0824

B) 137.64

C) 31.8198

D) 247.1336

Objective: (2.4) Calculate Range, Variance, Standard Deviation

71) The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample range for the data. A) $450 B) $98.75 C) $99.37 D) $250 Objective: (2.4) Calculate Range, Variance, Standard Deviation

72) The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample standard deviation for the data. A) $250 B) $98.75 C) $450 D) $99.37 Objective: (2.4) Calculate Range, Variance, Standard Deviation

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 73) The ages of five randomly chosen professors are 51, 47, 43, 67, and 52. Calculate the sample variance of these ages. Objective: (2.4) Calculate Range, Variance, Standard Deviation

74) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the range, sample variance, and sample standard deviation of the numbers of medals won by these countries. 1

Objective: (2.4) Calculate Range, Variance, Standard Deviation

75) The calculator screens summarize a data set.

a. Identify the smallest measurement in the data set. b. Identify the largest measurement in the data set. c. Calculate the range of the data set. Objective: (2.4) Calculate Range, Variance, Standard Deviation

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. x 2 = 1320,

76) Calculate the variance of a sample for which n = 5, A) 3.16

B) 8.00

x = 80.

C) 10.00

D) 326.00

Objective: (2.4) Calculate Range, Variance, Standard Deviation

77) Calculate the standard deviation of a sample for which n = 6, A) 164.00

B) 6.78

2 x = 830,

x = 60.

C) 46.00

D) 6.19

C) 2; 1.41

D) 2.67; 1.63

C) 0.011; 0.106

D) 5.867; 2.422

Objective: (2.4) Calculate Range, Variance, Standard Deviation

78) Compute s2 and s for the data set: -2, 1, -2, -2, -1, -4 A) 1.67; 1.29 B) 19; 4.36 Objective: (2.4) Calculate Range, Variance, Standard Deviation

7 3 7 3 1 1 , , , , , . 79) Compute s2 and s for the data set: 10 10 10 10 2 10

A) 1.305; 1.142

B) 0.059; 0.242

Objective: (2.4) Calculate Range, Variance, Standard Deviation

80) The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score? A) 78 B) cannot be determined C) 99 D) 70.5 Objective: (2.4) Interpret Measures of Variability

81) The temperature fluctuated between a low of 73°F and a high of 89°F. Which of the following could be calculated using just this information? A) median B) standard deviation C) variance D) range Objective: (2.4) Interpret Measures of Variability

82) Which of the following is a measure of the variability of a distribution? A) median B) sample size C) range

D) skewness

Objective: (2.4) Interpret Measures of Variability

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 83) Various state and national automobile associations regularly survey gasoline stations to determine the current retail price of gasoline. Suppose one such national association contacts 200 stations in the United States to determine the price of regular unleaded gasoline at each station. In the context of this problem, define the following descriptive measures: µ, , x, s. Objective: (2.4) Interpret Measures of Variability

84) Given the sample variance of a distribution, explain how to find the standard deviation. Objective: (2.4) Interpret Measures of Variability

85) Which is expressed in the same units as the original data, the variance or the standard deviation? Objective: (2.4) Interpret Measures of Variability

86) Which measures variability about the mean, the range or the standard deviation? Objective: (2.4) Interpret Measures of Variability

87) For a given data set, which is typically greater, the range or the standard deviation? Objective: (2.4) Interpret Measures of Variability

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 88) The total points scored by a basketball team for each game during its last season have been summarized in the table below. Which statement following the table must be true? Score 41-60 61-80 81-100 101-120

Frequency 3 8 12 7

A) The range is 79. C) The range is at least 81 but at most 100.

B) The range is at least 41 but at most 120. D) The range is at least 41 but at most 79.

Objective: (2.4) Interpret Measures of Variability

89) Which number on the screen below is the sample standard deviation of the data?

A) 2.67

B) 408

C) 5.8

D) 2.82

Objective: (2.4) Interpret Measures of Variability

Answer the question True or False. 90) The range is an insensitive measure of data variation for large data sets because two data sets can have the same range but be vastly different with respect to data variation. A) True B) False Objective: (2.4) Interpret Measures of Variability

91) For any quantitative data set, A) True

(x - x ) = 0.

B) False

Objective: (2.4) Interpret Measures of Variability

92) The sample variance and standard deviation can be calculated using only the sum of the data, size, n. A) True

x , and the sample

B) False

Objective: (2.4) Interpret Measures of Variability

93) The sample variance is always greater than the sample standard deviation. A) True B) False Objective: (2.4) Interpret Measures of Variability

94) A larger standard deviation means greater variability in the data. A) True B) False Objective: (2.4) Interpret Measures of Variability

Solve the problem. 95) The mean x of a data set is 36.71, and the sample standard deviation s is 3.22. Find the interval representing measurements within one standard deviation of the mean. A) (27.05, 46.37) B) (30.27, 43.15) C) (35.71, 37.71) D) (33.49, 39.93) Objective: (2.5) Construct, Interpret Intervals About the Mean

96) The following is a list of 25 measurements: 12 13 12

18 14 16

14 11 17

17 16

19 18

16 15

14 13

18 17

15 15

17 14

11 19

How many of the measurements fall within one standard deviation of the mean? A) 18 B) 13 C) 25

D) 16

Objective: (2.5) Construct, Interpret Intervals About the Mean

97) A standardized test has a mean score of 500 points with a standard deviation of 100 points. Five students' scores are shown below. Adam: 575

Beth: 690

Carlos: 750

Doug: 280

Ella: 440

Which of the students have scores within two standard deviations of the mean? A) Adam, Beth, Ella B) Adam, Beth C) Carlos, Doug D) Adam, Beth, Carlos, Ella Objective: (2.5) Construct, Interpret Intervals About the Mean

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 98) The mean x of a data set is 18, and the sample standard deviation s is 2. Explain what the interval (12, 24) represents. Objective: (2.5) Construct, Interpret Intervals About the Mean

99) The calculator screens summarize a data set.

a. b.

Identify the mean and the sample standard deviation. Round to one place after the decimal, where necessary. Find the interval that corresponds to measurements within two standard deviations of the mean.

Objective: (2.5) Construct, Interpret Intervals About the Mean

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 100) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph? A) approximately 16% B) at most 2.5% C) at most 13.5% D) at most 34% Objective: (2.5) Use Empirical Rule

101) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 101 miles per hour (mph) and the standard deviation of the serve speeds was 13 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was mound-shaped and symmetric. What proportion of the player's serves was between 114 mph and 127 mph? A) 0.95 B) 0.270 C) 0.1350 D) 127 Objective: (2.5) Use Empirical Rule

102) The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming the distribution of commuting times is known to be moundshaped and symmetric, what percentage of these commuting times are between 50 and 110 minutes? A) approximately 81.5% B) approximately 68% C) approximately 97.5% D) approximately 95% Objective: (2.5) Use Empirical Rule

103) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. The mean and the standard deviation for their responses were 13 and 3, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a symmetric, mound-shaped distribution. Give an interval where you believe approximately 95% of the television viewing times fell in the distribution. A) between 7 and 19 hours per week B) less than 10 and more than 16 hours per week C) less than 19 D) between 4 and 22 hours per week Objective: (2.5) Use Empirical Rule

104) A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 68 73 66 76 86 74 61 89 65 90 69 92 76 62 81 63 68 81 70 73 60 87 75 64 82 Suppose the mean and standard deviation are 74.04 and 9.75, respectively. If we assume that the distribution of ages is mound-shaped and symmetric, what percentage of the respondents will be between 64.29 and 93.54 years old? A) approximately 84% B) approximately 95% C) approximately 68% D) approximately 81.5% Objective: (2.5) Use Empirical Rule

105) A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 92 jobs and a standard deviation of 8. Where do we expect approximately 95% of the distribution to fall? A) between 68 and 116 jobs per day B) between 76 and 108 jobs per day C) between 84 and 100 jobs per day D) between 108 and 116 jobs per day Objective: (2.5) Use Empirical Rule

106) A study was designed to investigate the effects of two variables (1) a student's level of mathematical anxiety and (2) teaching method on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 420 with a standard deviation of 30 on a standardized test. Assuming a mound-shaped and symmetric distribution, what percentage of scores exceeded 360? A) approximately 97.5% B) approximately 95% C) approximately 84% D) approximately 100% Objective: (2.5) Use Empirical Rule

107) A study was designed to investigate the effects of two variables (1) a student's level of mathematical anxiety and (2) teaching method on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 310 with a standard deviation of 40 on a standardized test. Assuming a mound-shaped and symmetric distribution, in what range would approximately 95% of the students score? A) above 390 B) between 230 and 390 C) below 390 D) below 230 and above 390 Objective: (2.5) Use Empirical Rule

108) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $140 and a standard deviation of $10. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $130? A) approximately 16% B) approximately 84% C) approximately 95% D) approximately 34% Objective: (2.5) Use Empirical Rule

109) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 83 and 2, respectively, and the distribution of scores is mound-shaped and symmetric. What percentage of test-takers scored better than a trainee who scored 77? A) approximately 100% B) approximately 97.5% C) approximately 95% D) approximately 84% Objective: (2.5) Use Empirical Rule

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 110) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. Find the percentage of serves that were hit faster than 55 mph. Objective: (2.5) Use Empirical Rule

111) A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 77 jobs and a standard deviation of 11. On what percentage of days do the number of jobs submitted exceed 88? Objective: (2.5) Use Empirical Rule

112) By law, a box of cereal labeled as containing 16 ounces must contain at least 16 ounces of cereal. The machine filling the boxes produces a distribution of fill weights that is mound-shaped and symmetric, with a mean equal to the setting on the machine and with a standard deviation equal to 0.03 ounce. To ensure that most of the boxes contain at least 16 ounces, the machine is set so that the mean fill per box is 16.09 ounces. What percentage of the boxes do, in fact, contain at least 16 ounces? Objective: (2.5) Use Empirical Rule

113) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 70 and 4, respectively, and the distribution of scores is mound-shaped and symmetric. If a firm wanted to give the best 2.5% of the trainees a big promotion, what test score would be used to identify the trainees in question? Objective: (2.5) Use Empirical Rule

114) The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9. 39 71 79 85 90

51 71 79 86 90

59 73 79 86 91

63 74 80 88 91

66 76 80 88 92

68 76 82 88 95

68 76 83 88 96

69 77 83 89 97

70 78 83 89 97

71 79 85 89 98

What percentage of the scores lies within one standard deviation of the mean? two standard deviations of the mean? three standard deviations of the mean? Based on these percentages, do you believe that the distribution of scores is mound-shaped and symmetric? Explain. Objective: (2.5) Use Empirical Rule

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 115) The distribution of scores on a test is mound-shaped and symmetric with a mean score of 78. If 68% of the scores fall between 72 and 84, which of the following is most likely to be the standard deviation of the distribution? A) 2 B) 6 C) 12 D) 3 Objective: (2.5) Use Empirical Rule

116) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, what percentage of the player's serve speeds are less than 70 mph? A) approximately 2.5% B) at most 11% C) at most 12.5% D) approximately 5% E) at most 25% Objective: (2.5) Use Chebyshev's Rule

117) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 99 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least three-fourths of the player's serves. A) 129 mph to 159 mph B) 69 mph to 129 mph C) 84 mph to 114 mph D) 54 mph to 144 mph Objective: (2.5) Use Chebyshev's Rule

118) The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes? A) at least 0% B) at least 95% C) at least 89% D) at least 75% Objective: (2.5) Use Chebyshev's Rule

119) By law, a box of cereal labeled as containing 18 ounces must contain at least 18 ounces of cereal. The machine filling the boxes produces a distribution of fill weights with a mean equal to the setting on the machine and with a standard deviation equal to 0.04 ounce. To ensure that most of the boxes contain at least 18 ounces, the machine is set so that the mean fill per box is 18.12 ounces. Assuming nothing is known about the shape of the distribution, what can be said about the proportion of cereal boxes that contain less than 18 ounces. A) The proportion is less than 2.5%. B) The proportion is at most 5.5%. C) The proportion is at most 11%. D) The proportion is at least 89%. Objective: (2.5) Use Chebyshev's Rule

120) A study was designed to investigate the effects of two variables (1) a student's level of mathematical anxiety and (2) teaching method on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 270 with a standard deviation of 40 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 190 and 350? A) at least 75% B) approximately 68% C) at least 89% D) approximately 95% Objective: (2.5) Use Chebyshev's Rule

121) A study was designed to investigate the effects of two variables (1) a student's level of mathematical anxiety and (2) teaching method on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 470 with a standard deviation of 20 on a standardized test. Assuming a non-mound-shaped distribution, what percentage of the students scored over 530? A) at most 11% B) at least 89% C) at most 5.5% D) approximately 2.5% Objective: (2.5) Use Chebyshev's Rule

122) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $137 and a standard deviation of $14. If nothing is known about the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $109? A) at least 75% B) at most 25% C) at most 11.1% D) at least 88.9% Objective: (2.5) Use Chebyshev's Rule

123) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 80 and 4, respectively. Assuming nothing is known about the distribution, what percentage of test-takers scored above 92? A) at least 89% B) approximately 0.15% C) approximately 99.85% D) at most 11% Objective: (2.5) Use Chebyshev's Rule

124) If nothing is known about the shape of a distribution, what percentage of the observations fall within 3 standard deviations of the mean? A) at most 11% B) approximately 0.3% C) approximately 99.7% D) at least 89% Objective: (2.5) Use Chebyshev's Rule

125) Fill in the blank. __________ gives us a method of interpreting the standard deviation of any data set, regardless of the shape of the distribution. A) Chebyshev's Rule B) The Empirical Rule C) both A and B D) neither A nor B Objective: (2.5) Use Chebyshev's Rule

126) Fill in the blank. __________ is a method of interpreting the standard deviation of data that have a mound-shaped, symmetric distribution. A) Chebyshev's Rule B) The Empirical Rule C) both A and B D) neither A nor B Objective: (2.5) Use Chebyshev's Rule

127) Given a data set, which of the following is most likely to be the percentage of data within three standard deviations of the mean? A) 65% B) 95% C) 70% D) 85% Objective: (2.5) Use Chebyshev's Rule

Answer the question True or False. 128) Both Chebyshev's rule and the empirical rule guarantee that no data item will be more than four standard deviations from the mean. A) True B) False Objective: (2.5) Use Chebyshev's Rule

129) Chebyshev's rule applies to qualitative data sets, while the empirical rule applies to quantitative data sets. A) True B) False Objective: (2.5) Use Chebyshev's Rule

130) Chebyshev's rule applies to large data sets, while the empirical rule applies to small data sets. A) True B) False Objective: (2.5) Use Chebyshev's Rule

131) Your teacher announces that the scores on a test have a mean of 83 points with a standard deviation of 4 points, so it is reasonable to expect that you scored at least 70 on the test. A) True B) False Objective: (2.5) Use Chebyshev's Rule

Solve the problem. 132) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 74 and 4, respectively, and the distribution of scores is mound-shaped and symmetric. Suppose the trainee in question received a score of 63. Compute the trainee's z-score. A) z = -11 B) z = -44 C) z = 0.80 D) z = -2.75 Objective: (2.6) Compute, Interpret z-Score

133) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the standard deviation of the expenditures was calculated to be $100. Suppose a randomly selected student reported that their textbook expenditure was $700. Calculate the z-score for this student's textbook expenditure. A) -3 B) -2 C) +3 D) +2 Objective: (2.6) Compute, Interpret z-Score

134) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $136 and a standard deviation of $15. Three solar homes reported monthly utility bills of $86, $81, and $84. Which of the following statements is true? A) Homes using solar power always have lower utility bills than homes using only gas and electricity. B) The utility bills for homes using solar power are about the same as those for homes using only gas and electricity. C) Homes using solar power may actually have higher utility bills than homes using only gas and electricity. D) Homes using solar power may have lower utility bills than homes using only gas and electricity. Objective: (2.6) Compute, Interpret z-Score

135) A radio station claims that the amount of advertising each hour has a mean of 12 minutes and a standard deviation of 1.3 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 17 minutes. Calculate the z-score for this amount of advertising time. A) z = 6.5 B) z = 1.31 C) z = 3.85 D) z = -3.85 Objective: (2.6) Compute, Interpret z-Score

136) On a given day, the price of a gallon of milk had a mean price of $2.02 with a standard deviation of $0.06. A particular food store sold milk for $1.96/gallon. Interpret the z-score for this gas station. A) The milk price of this food store falls 6 standard deviations above the mean milk price of all food stores. B) The milk price of this food store falls 1 standard deviation above the mean milk price of all food stores. C) The milk price of this food store falls 6 standard deviations below the mean milk price of all food stores. D) The milk price of this food store falls 1 standard deviation below the milk gas price of all food stores. Objective: (2.6) Compute, Interpret z-Score

137) Which of the following is a measure of relative standing? A) pie chart B) variance Objective: (2.6) Compute, Interpret z-Score

C) mean

D) z-score

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 138) A study was designed to investigate the effects of two variables (1) a student's level of mathematical anxiety and (2) teaching method on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 320 and a standard deviation of 40 on a standardized test. Find and interpret the z-score of a student who scored 560 on the standardized test. Objective: (2.6) Compute, Interpret z-Score

139) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $91.00 and a standard deviation of $8.00. Assuming the distribution is mound-shaped and symmetric, would you expect to see a 3-bedroom house using gas or electric energy with a monthly utility bill of $143.00? Explain. Objective: (2.6) Compute, Interpret z-Score

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 140) Find the z-score for the value 69, when the mean is 62 and the standard deviation is 5. A) z = 1.20 B) z = -1.03 C) z = 1.40

D) z = 1.03

Objective: (2.6) Compute, Interpret z-Score

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 141) Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores for a physics class had a mean of 69 with a standard deviation of 3.7. One student earned a 83 on the history test and a 78 on the physics test. Calculate the z-score for each test. On which test did the student perform better? Objective: (2.6) Compute, Interpret z-Score

142) The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9. 39 71 79 85 90

51 71 79 86 90

59 73 79 86 91

63 74 80 88 91

66 76 80 88 92

68 76 82 88 95

68 76 83 88 96

69 77 83 89 97

70 78 83 89 97

71 79 85 89 98

Find the z-scores for the highest and lowest exam scores. Objective: (2.6) Compute, Interpret z-Score

143) The z-score for a value x is -2.5. State whether the value of x lies above or below the mean and by how many standard deviations. Objective: (2.6) Compute, Interpret z-Score

144) Suppose that 50 and 75 are two elements of a population data set and their z-scores are -3 and 2, respectively. Find the mean and standard deviation. Objective: (2.6) Compute, Interpret z-Score

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 145) According to the empirical rule, z-scores of less than -3 or greater than 3 occur very infrequently for data from a mounded and symmetric distribution A) True B) False Objective: (2.6) Compute, Interpret z-Score

146) If a z-score is 0 or near 0, the measurement is located at or near the mean. A) True B) False Objective: (2.6) Compute, Interpret z-Score

147) If a sample has mean 0 and standard deviation 1, then for every measurement x in the sample the z-score of x is x itself. A) True B) False Objective: (2.6) Compute, Interpret z-Score

Solve the problem. 148) When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated with scores are also given. Suppose a test-taker scored at the 64th percentile on the verbal part of the test and at the 36th percentile on the quantitative part. Interpret these results. A) This student performed better than 36% of the other test-takers on the verbal part and better than 36% on the quantitative part. B) This student performed better than 36% of the other test-takers on the verbal part and better than 64% on the quantitative part. C) This student performed better than 64% of the other test-takers on the verbal part and better than 64% on the quantitative part. D) This student performed better than 64% of the other test-takers on the verbal part and better than 36% on the quantitative part. Objective: (2.6) Find, Interpret Percentile

149) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct? A) 75% of the students sampled had textbook costs that exceeded $500. B) 75% of the students sampled had textbook costs equal to $500. C) 25% of the students sampled had textbook costs that exceeded $500. D) The average of the 500 textbook costs was $500. Objective: (2.6) Find, Interpret Percentile

150) Summary information is given for the weights (in pounds) of 1000 randomly sampled tractor trailers. MIN: MAX: AVE:

3,996 10,596 6,996

25%: 75%: Std. Dev.:

5,596 8,596 1400

Find the percentage of tractor trailers with weights between 5,596 and 8,596 pounds. A) 100% B) 75% C) 50% Objective: (2.6) Find, Interpret Percentile

D) 25%

151) The test scores of 30 students are listed below. Which number could be the 30th percentile? 31 41 45 48 52 55 56 56 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 85 87 90 92 95 99 A) 64 B) 90

C) 56

D) 67

Objective: (2.6) Find, Interpret Percentile

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 152) A retail store's customer satisfaction rating is at the 88th percentile. What percentage of retail stores has higher customer satisfaction ratings than this store? Objective: (2.6) Find, Interpret Percentile

153) In a summary of recent real estate sales, the median home price is given as $325,000. What percentile corresponds to a home price of $325,000? Objective: (2.6) Find, Interpret Percentile

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False.

154) The mean of a data set is at the 50th percentile. A) True

B) False

Objective: (2.6) Find, Interpret Percentile

155) Percentile rankings are of practical value only with large data sets. A) True B) False Objective: (2.6) Find, Interpret Percentile

156) The process for finding a percentile is similar to the process for finding the median. A) True B) False Objective: (2.6) Find, Interpret Percentile

Solve the problem. 157) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 104 miles per hour (mph) and the standard deviation of the serve speeds was 14 mph. Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player's serve speeds? Speeds: 55 mph, 118 mph, and 132 mph

A) 55 is the only outlier. C) None of the three speeds is an outlier.

B) 55 and 118 are both outliers, but 132 is not. D) 55, 118, and 132 are all outliers.

Objective: (2.7) Determine if Datum is an Outlier

158) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player's serve speeds? Speeds: 50 mph, 80 mph, and 105 mph A) 50 and 80 are both outliers, 105 is not. C) 50, 80, and 105 are all outliers.

B) 50 is the only outlier. D) None of the three speeds are outliers.

Objective: (2.7) Determine if Datum is an Outlier

159) The speeds of the fastballs thrown by major league baseball pitchers were measured by radar gun. The mean speed was 84 miles per hour. The standard deviation of the speeds was 5 mph. Which of the following speeds would be classified as an outlier? A) 92 mph B) 79 mph C) 74 mph D) 100 mph Objective: (2.7) Determine if Datum is an Outlier

160) Which of the following statements concerning the box plot and z-score methods for detecting outliers is false? A) The box plot method uses the quartiles as a basis for detecting outliers. B) The z-score method is less affected by an extreme observation in the data set. C) The z-score method uses the mean and standard deviation as a basis for detecting outliers. D) The box plot method is less affected by an extreme observation in the data set. Objective: (2.7) Determine if Datum is an Outlier

161) Which of the following statements could be an explanation for the presence of an outlier in the data? A) The measurement belongs to a population different from that from which the rest of the sample was drawn. B) The measurement may be correct and from the same population as the rest but represents a rare event. Generally, we accept this explanation only after carefully ruling out all others. C) The measurement is incorrect. It may have been observed, recorded, or entered into the computer incorrectly. D) All of the above are explanations for outliers. Objective: (2.7) Determine if Datum is an Outlier

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 162) A radio station claims that the amount of advertising each hour has an a mean of 12 minutes and a standard deviation of 2.9 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 4.75 minutes. Based on your observation, what would you infer about the radio station's claim? Objective: (2.7) Determine if Datum is an Outlier

163) The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9. 39 71 79 85 90

51 71 79 86 90

59 73 79 86 91

63 74 80 88 91

66 76 80 88 92

68 76 82 88 95

68 76 83 88 96

69 77 83 89 97

70 78 83 89 97

71 79 85 89 98

Use the z-score method to identify potential outliers among the scores. Objective: (2.7) Determine if Datum is an Outlier

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 164) The z-score uses the quartiles to identify outliers in a data set. A) True B) False Objective: (2.7) Determine if Datum is an Outlier

165) An outlier is defined as any observation that falls within the outer fences of a box plot. A) True B) False Objective: (2.7) Determine if Datum is an Outlier

166) Box plots are used to detect outliers in qualitative data sets, while z-scores are used to detect outliers in quantitative data sets. A) True B) False Objective: (2.7) Determine if Datum is an Outlier

167) An outlier in a data set may have a simple explanation such as a scale was not working properly or the researcher inverted the digits of a number when recording a measurement. A) True B) False Objective: (2.7) Determine if Datum is an Outlier

168) An outlier may be caused by accidentally including the height of a six-year-old boy in a set of data representing the heights of 12-year-old boys. A) True B) False Objective: (2.7) Determine if Datum is an Outlier

169) The outer fences of a box plot are three standard deviations from the mean. A) True B) False Objective: (2.7) Determine if Datum is an Outlier

Solve the problem. 170) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The lower quartile of a particular player's serve speeds was reported to be 87 mph. Which of the following interpretations of this information is correct? A) 87 serves traveled faster than the lower quartile. B) 75% of the player's serves were hit at speeds greater than 87 mph. C) 25% of the player's serves were hit at 87 mph. D) 75% of the player's serves were hit at speeds less than 87 mph. Objective: (2.7) Calculate Quartiles and IQR

171) A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 68 73 66 76 86 74 61 89 65 90 69 92 76 62 81 63 68 81 70 73 60 87 75 64 82 Find the upper quartile of the data. A) 92 B) 65.5

C) 81.5

Objective: (2.7) Calculate Quartiles and IQR

D) 73

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 172) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). Three hundred parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. The upper quartile for the distribution was given as 19 hours. Interpret this value. Objective: (2.7) Calculate Quartiles and IQR

173) For a given data set, the lower quartile is 45, the median is 50, and the upper quartile is 57. The minimum value in the data set is 32, and the maximum is 81. a. b. c. d.

Find the interquartile range. Find the inner fences. Find the outer fences. Is either of the minimum or maximum values considered an outlier? Explain.

Objective: (2.7) Calculate Quartiles and IQR

174) The calculator screens summarize a data set.

a. Identify the lower and upper quartiles of the data set. b. Find the interquartile range. c. Is there reason to suspect that the data may contain an outlier? Explain. Objective: (2.7) Calculate Quartiles and IQR

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 175) The box plot shown below displays the amount of soda that was poured by a filling machine into 12-ounce soda cans at a local bottling company.

Based on the box plot, what shape do you believe the distribution of the data to have? A) skewed to the center B) skewed to the left C) skewed to the right D) approximately symmetric Objective: (2.7) Construct, Interpret Boxplot

176) The box plot shown below was constructed for the amount of soda that was poured by a filling machine into 12-ounce soda cans at a local soda bottling company.

We see that one soda can received 12.15 ounces of soda on the plot above. Based on the box plot presented, how would you classify this observation? A) it has a lot of soda B) suspect outlier C) expected observation D) highly suspect outlier Objective: (2.7) Construct, Interpret Boxplot

177) The box plot shown below was constructed for the amount of soda that was poured by a filling machine into 12-ounce soda cans at a local soda bottling company.

We see that one soda can received 12.30 ounces of soda on the plot above. Based on the box plot presented, how would you classify this observation? A) expected observation B) highly suspect outlier C) suspect outlier D) it has a lot of soda Objective: (2.7) Construct, Interpret Boxplot

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 178) The following data represent the scores of 50 students on a statistics exam. 39 71 79 85 90

51 71 79 86 90

59 73 79 86 91

63 74 80 88 91

66 76 80 88 92

68 76 82 88 95

68 76 83 88 96

69 77 83 89 97

70 78 83 89 97

71 79 85 89 98

a. Find the lower quartile, the upper quartile, and the median of the scores. b. Find the interquartile range of the data and use it to identify potential outliers. c. In a box plot for the data, which scores, if any, would be outside the outer fences? Which scores, if any, would be outside the inner fences but inside the outer fences? Objective: (2.7) Construct, Interpret Boxplot

179) Use a graphing calculator or software to construct a box plot for the following data set. 12 13 12

18 14 16

14 11 17

17 16

19 18

16 15

14 13

18 17

15 15

17 14

11 19

Objective: (2.7) Construct, Interpret Boxplot

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 180) A sample of professional golfers was taken and their driving distance (measured as the average distance as their drive off the tee) and driving accuracy (measured as the percentage of fairways that their drives landed in) were recorded. A scatterplot of the variables is shown below.

What relationship do these two variables exhibit? A) They exhibit a curvillinear relationship C) They exhibit a positive linear relationship

B) They exhibit no relationship D) They exhibit a negative linear relationship

Objective: (2.8) Construct, Interpret Scatterplot

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 181) The data below represent the numbers of absences and the final grades of 15 randomly selected students from a statistics class. Construct a scattergram for the data. Do you detect a trend? Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Number of Absences 5 6 2 12 9 5 8 15 0 1 9 3 10 3 11

Final Grade as a Percent 79 78 86 56 75 90 78 48 92 78 81 86 75 89 65

Objective: (2.8) Construct, Interpret Scatterplot

182) The scores of nine members of a women's golf team in two rounds of tournament play are listed below. Player 1 2 3 4 5 6 7 8 9 Round 1 85 90 87 78 92 85 79 93 86 Round 2 90 87 85 84 86 78 77 91 82 Construct a scattergram for the data. Objective: (2.8) Construct, Interpret Scatterplot

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 183) Scatterplots are useful for both qualitative and quantitative data. A) True B) False Objective: (2.8) Construct, Interpret Scatterplot

184) The scatterplot below shows a negative relationship between two variables.

A) True

B) False

Objective: (2.8) Construct, Interpret Scatterplot

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 185) What is a time series plot? Objective: (2.9) Define Time Series Plot

186) What is the primary advantage of a time series plot? Objective: (2.9) Define Time Series Plot

187) Explain how stretching the vertical axis of a histogram can be misleading. Objective: (2.10) Understand Misleading Statistics

188) Explain how using a scale break on the vertical axis of a histogram can be misleading. Objective: (2.10) Understand Misleading Statistics

189) Explain how it can be misleading to draw the bars in a histogram so that the width of each bar is proportional to its height rather than have all bars the same width. Objective: (2.10) Understand Misleading Statistics

190) Explain how it can be misleading to report only the mean of a distribution without any measure of the variability. Objective: (2.10) Understand Misleading Statistics

Answer Key Testname: SB14ECH2TEST

1) A 16) a. 20) a. 2) A Type of Book Relative Car 3) free account, Frequency institutional account, compact Children's .10 account paid for sedan Fiction .28 personally small SUV Nonfiction .49 4) B large SUV Educational .13 5) A minivan 6) b. truck Color Frequency Green 3 b. Blue 7 Brown 5 Orange 2 Red 3 7) B 8) C 9) C 10) A 11) a. Medal Frequency 17) A Gold 9 18) B Silver 9 19) In a Pareto diagram, Bronze 7 the bars are arranged by height in a b. descending order Medal Relative from left to right. Frequency Gold .36 Silver .36 Bronze .28

25) a. Total Medals Relative Frequency 1-5 0.09 6-10 0.11 11-15 0.25 16-20 0.17 21-25 0.19 26-30 0.19 b.

26) a. The exact scores would be needed to construct a stem-and-leaf display but the exact scores are not available in the table given. b.

21) B 22) B 23)

12) A 13) A 14) C 15) A

Losses due to employee theft have decreased from year 1 to year 2. 24) D

Frequency 5 2 5 1 4 1

27) A 28) A 29) B 30) D 31) C

Answer Key Testname: SB14ECH2TEST

32)

59) In both year 1 and 74) The range is 29 - 1 = year 5, the mean 28 medals. dropout rates exceed the median dropout The variance is s2 = + 11 +This 1 + 2 + 3 + 3 + 4 + 9 + 9 + 11 + 11 rates. 14 + indicates 14 + 19 + 22 + 23 + 24 + 25 + 29 2 x that18 both the year 1 x2 n and year 5 high 234 = = = 13 medals. school dropout rates n- 1 18 have distributions The median is the (234)2 that are skewed to 4372 mean of the two 18 the right. = middle numbers: 17 60) The modal class is 11 + 11 = 11 medals. the class with the 1330 2 78.24 greatest frequency: 17 The mode is the most 81-100 points. The standard frequent number of 61) a. mean: x 73.65; deviation is s = s2 medals: 11 medals. median: Med=81 1330 45) The mean is divided 8.85 = b. We expect the 17 by n: data to be skewed to 75) a. minX=30 x 196 the left because the = = 24.5. b. maxX=97 n 8 mean is less than the c. 97 - 30 = 67 median. 46) a. n = 21 76) C 62) B x b. x = 1679 77) B is x = 63) B n 78) D c. mean: x 79.95; 64) A 72.3 + 60.3 + 55.1 + 54.4 + 31.1 + 27 24.3 21.3 22.9 20.7 + + + + 79) B median: Med=82; 65) B 10 mode: not possible 80) C 66) B 81) D 389.4 47) A 67) A = 82) C 10 48) C 68) D 49) A = 38.94 $38.94 69) A 50) D million 70) C 51) D 71) D 52) B The median is the 72) D 53) B average of the (x - x)2 54) A 73) s2 = middle two n -1 55) B observations. 56) C x = = x 57) B 31.1 + 27 n M= = 29.05 58) Since the distribution 2 51 + 47 + 43 + 67 + 52 is skewed to the left, $29.05 million 5 we know that the = 52.0 median time will exceed the mean time. s2 = (51 - 52.0)2 + (47 - 52.0)2 + (43 - 52.0)2 + (67 - 52.0)2 + (52 - 52

Stem Leaf 10 2 3 4 50 9 66 9 76 7 9 8 2357889 92 3 6 6 9 33) B 34) D 35) B 36) D 37) B 38) A 39) A 40) D 41) C 42) C 43) The mean of the data

44) The mean is the sum of the numbers divided by 18:

5-1

= 83.00

Answer Key Testname: SB14ECH2TEST

83) µ is the mean price of the regular unleaded gasoline prices of all retail gas stations in the United States. is the standard deviation of the regular unleaded gasoline prices of all retail gas stations in the United States. x is the mean price of the regular unleaded gasoline prices collected from the 200 stations sampled. s is the standard deviation of the regular unleaded gasoline prices collected from the 200 stations sampled. 84) Take the square root of the sample variance to find the sample standard deviation. 85) standard deviation 86) standard deviation 87) range 88) D 89) D 90) A 91) A 92) B 93) B 94) A 95) D 96) D 97) A 98) measurements within three standard deviations of the mean

111) The value 88 falls one standard deviation above the mean in the distribution. Using the Empirical Rule, 68% of the days will have between 66 and 88 jobs submitted. Of the remaining 32% of the days, half, or 32%/2 = 16%, of the days will have more than 88 jobs submitted. 112) The value of 16 ounces falls three standard deviations below the mean. The Empirical Rule states that approximately all of the boxes will contain cereal amounts between 16.00 ounces and 16.18 ounces. Therefore, approximately 100% of the boxes contain at least 16 ounces. 113) The Empirical Rule states that 95% of the data will fall between 62 and 78. Because the distribution is symmetric, half of the remaining 5%, or 2.5%, will have test scores above 78. Thus, 78 is the cutoff point that will identify the trainees who will receive the promotion.

99) a. mean: x = 5.5; sample standard deviation: Sx 3.0 b. (5.5 - 2 × 3.0, 5.5 + 2 × 3.0) = (-.5, 11.5) 100) A 101) C 102) A 103) A 104) D 105) B 106) A 107) B 108) B 109) A 110) We use the Empirical Rule to determine the percentage of serves with speeds faster than 55 mph. We do this by first finding the percentage of serves with speeds between 55 and 100 mph. The Empirical Rule states that approximately 47.5% (95%/2) fall between 55 and 100 mph. Because the distribution is symmetric about the mean speed of 100 mph, we know 50% of the serve speeds were faster than 100 mph. We add these findings together to determine that 47.5% + 50% = 97.5% of the serves were hit faster than 55 mph.

114) 74% of the scores lie within one standard deviation of the mean, 96% within two standard deviations, and 98% within three standard deviations. These percentages are close to those given in the Empirical Rule, so the distribution is roughly mound-shaped and symmetric, though obviously skewed slightly to the left. 115) B 116) E 117) B 118) D 119) C 120) A 121) A 122) B 123) D 124) D 125) A 126) B 127) B 128) B 129) B 130) B 131) A 132) D 133) D 134) D 135) C 136) D 137) D

Answer Key Testname: SB14ECH2TEST

138) The z-score is z = x-µ . For a score of 56, z = 560 - 320 = 6.00. 40 This student's score falls 6.00 standard deviations above the mean score of 320. 139) The z-score for the value $143.00 is: z=

x - x 143 - 91 = s 8

= 6.5 An observation that falls 6.5 standard deviations above the mean is very unlikely. We would not expect to see a monthly utility bill of $143.00 for this home. 140) C 141) history z-score = 0.89; physics z-score = 2.43; The student performed better on the physics test. 142) highest: z = 1.51; lowest: z = -3.45 143) The value of x lies 2.5 standard deviations below the mean. 144) mean: 65; standard deviation: 5 145) A 146) A 147) A 148) D 149) C 150) C 151) A 152) 12% 153) 50th percentile

155) A 156) A 157) A 158) B 159) D 160) B 161) D 162) The z-score for the value 4.75 is -2.5 Since the z-score would not indicate that 4.75 minutes represents an outlier, there is no evidence that the station's claim is incorrect. 163) The z-score of 39 is -3.46. Since this z-score is less than -3, the score of 39 is an outlier. All other scores have z-scores between -3 and 3, so there are no other outliers. 164) B 165) B 166) B 167) A 168) A 169) B 170) B 171) C 172) 75% of the TV viewing times are less than 19 hours per week. 25% of the times exceed 19 hours per week.

173) a. The interquartile range is 57 - 45 = 12. b. The inner fences are 45 - 1.5(12) = 27 and 57 + 1.5(12) = 75. c. The outer fences are 45 - 3(12) = 9 and 57 + 3(12) = 93. d. The maximum of 81 is a potential outlier since it lies outside the inner fences. The minimum is within the inner fence and is not considered to be an outlier. 174) a. lower quartile: Q1=75; upper quartile: Q3=90 b. interquartile range: 90 - 75 = 15 c. Yes; the smallest measurement, 30, is three times the interquartile range less than the lower quartile, so it is a suspected outlier. 175) B 176) B 177) B 178) a. The lower quartile is 73, the upper quartile is 89, and the median is 81. b. The interquartile range is 89 - 73 = 16. The score of 39 is a potential outlier since it is less than 73 - 1.5(16) = 49. c. No scores fall outside the outer fences, 25 and 137. Only the score of 39 lies between the inner and outer fences.

154) B

179) The horizontal axis extends from 10 to 20, with each tick mark representing one unit.

180) D 181)

There appears to be a trend in the data. As the number of absences increases, the final grade decreases.

Answer Key Testname: SB14ECH2TEST

182)

183) B 184) A 185) A scatterplot with the measurements on the vertical axis and time (or the order in which the measurements were made) on the horizontal axis. 186) A time series plot describes behavior over time and reveals movement (trend) and changes (variation) in the variable being monitored. 187) Stretching the vertical axis may overemphasize the differences in the heights of the bars making the taller bars look much taller than the shorter bars.

188) Using a scale break on the vertical axis may make the shorter bars look disproportionately shorter than the taller bars. 189) The reader may think that the area of the bar represents the quantity rather than the height of the bar, giving a disproportionate emphasis on the taller bars. 190) When comparing means from two different distributions, the difference between them may be insignificant if the variability in one or both of the distributions is large.

McClave Statistics for Business and Economics 14e Chapter 3 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Which of the following assignments of probabilities to the sample points A, B, and C is valid if A, B, and C are the only sample points in the experiment? 1 1 3 1 14 , P(C) = A) P(A) = - , P(B) = , P(C) = B) P(A) = 0, P(B) = 4 2 4 15 15 C) P(A) =

1 1 1 , P(B) = , P(C) = 10 10 10

D) P(A) =

1 1 1 , P(B) = , P(C) = 8 3 4

Objective: (3.1) List Sample Space and Assign Probabilities

2) If sample points A, B, C, and D are the only possible outcomes of an experiment, find the probability of D using the table below. Sample Point Probability 3 A) 11

A 1/11

B 1/11

8 11

C 1/11

1 11

1 4

Objective: (3.1) List Sample Space and Assign Probabilities

3) A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: Color Number Red 25 Brown 20 Green 20 Blue 15 Yellow 10 Orange 10 List the sample space for this problem. A) {Red} C) {Red, Brown, Green, Blue, Yellow, Orange}

B) {0.25, 0.20, 0.20, 0.15, 0.10, 0.10} D) {25, 20, 20, 15, 10, 10}

Objective: (3.1) List Sample Space and Assign Probabilities

4) A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: Color Number Red 25 Brown 20 Green 20 Blue 15 Yellow 10 Orange 10 Find the probability that a randomly chosen piece of candy is not blue or red. A) 0.60 B) 0.15 C) 0.40 Objective: (3.1) List Sample Space and Assign Probabilities

D) 0.85

5) Fill in the blank. A(n) ______ is a process that leads to a single outcome that cannot be predicted with certainty. A) event B) sample space C) experiment D) sample point Objective: (3.1) List Sample Space and Assign Probabilities

6) Fill in the blank. A(n) __________ is the most basic outcome of an experiment. A) experiment B) sample space C) event

D) sample point

Objective: (3.1) List Sample Space and Assign Probabilities

7) Fill in the blank. The __________ is the collection of all the sample points in an experiment. A) event B) sample space C) union D) Venn diagram Objective: (3.1) List Sample Space and Assign Probabilities

8) Fill in the blank. A(n) __________ is a collection of sample points. A) event B) experiment C) sample space

D) Venn diagram

Objective: (3.1) List Sample Space and Assign Probabilities

9) The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. What is the sample space for this experiment? A) {HH, HT, TT} B) {nickel, dime} C) {0, 1, 2} D) {HH, HT, TH, TT} Objective: (3.1) List Sample Space and Assign Probabilities

10) A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for this experiment? A) {80} B) {1/4, 5/16, 7/16} C) {20, 25, 35} D) {red, yellow, orange} Objective: (3.1) List Sample Space and Assign Probabilities

11) An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment? A) 7 B) 2 C) 1 D) 6 Objective: (3.1) List Sample Space and Assign Probabilities

12) Which number could be the probability of an event that occurs about as often as it does not occur? A) 0 B) 1 C) -.51 D) .51 Objective: (3.1) List Sample Space and Assign Probabilities

13) Which number could be the probability of an event that rarely occurs? A) -.01 B) .99 C) .51

D) .01

Objective: (3.1) List Sample Space and Assign Probabilities

14) Which number could be the probability of an event that is almost certain to occur? A) .99 B) 1.01 C) .01

D) .51

Objective: (3.1) List Sample Space and Assign Probabilities

15) Suppose that an experiment has five equally likely outcomes. What probability is assigned to each of the sample points? A) .5 B) .2 C) 1 D) .05 Objective: (3.1) List Sample Space and Assign Probabilities

16) An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. List the sample points in E. A) {2, 4, 6, 8, 10} B) {5} C) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} D) {1, 3, 5, 7, 9} Objective: (3.1) List Sample Space and Assign Probabilities

Answer the question True or False. 17) A statistical experiment can be almost any act of observation as long as the outcome is uncertain. A) True B) False Objective: (3.1) List Sample Space and Assign Probabilities

18) The probability of a sample point is usually taken to be the relative frequency of the occurrence of the sample point in a very long series of repetitions of the experiment. A) True B) False Objective: (3.1) List Sample Space and Assign Probabilities

19) In some experiments, we assign subjective probabilities, which can be interpreted as our degree of belief in the outcome. A) True B) False Objective: (3.1) List Sample Space and Assign Probabilities

20) In any experiment with exactly four sample points in the sample space, the probability of each sample point is .25. A) True B) False Objective: (3.1) List Sample Space and Assign Probabilities

21) An event may contain sample points that are not in the original sample space of the experiment. For example, the experiment of rolling two dice has the following sample space: {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} However, the event of rolling a sum of at least 11 on the two dice is {11, 12}. A) True B) False Objective: (3.1) List Sample Space and Assign Probabilities

22) The probability of an event can be calculated by finding the sum of the probabilities of the individual sample points in the event and dividing by the number of sample points in the event. A) True B) False Objective: (3.1) List Sample Space and Assign Probabilities

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 23) A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the sample space for the experiment. Objective: (3.1) List Sample Space and Assign Probabilities

24) An experiment consists of randomly choosing a number between 1 and 10. Let A be the event that the number chosen is less than or equal to 7. List the sample points in A. Objective: (3.1) List Sample Space and Assign Probabilities

25) An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters. An experiment consists of randomly selecting one of the highlighters. Find the probability that a blue highlighter is chosen. Objective: (3.1) List Sample Space and Assign Probabilities

26) Suppose that an experiment has eight equally likely outcomes. What probability is assigned to each of the sample points? Objective: (3.1) List Sample Space and Assign Probabilities

27) The accompanying Venn diagram describes the sample space of a particular experiment and events A and B. Suppose the sample points are equally likely. Find P(A) and P(B).

Objective: (3.1) Use Venn Diagram to Find Probability

28) The accompanying Venn diagram describes the sample space of a particular experiment and events A and B. 1 1 Suppose P(1) = P(2) = P(3) = P(4) = and P(5) = P(6) = P(7) = P(8) = P(9) = P(10) = . Find P(A) and P(B). 16 8

Objective: (3.1) Use Venn Diagram to Find Probability

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 29) Probabilities of different types of vehicle-to-vehicle accidents are shown below: Accident Probability Car to Car 0.60 Car to Truck 0.15 Truck to Truck 0.25 Find the probability that an accident involves a car. A) 0.15 B) 0.60

C) 0.75

D) 0.25

Objective: (3.1) Find Probability Given Sample Space

30) A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.). Simple Events SS SD DS DD

Probabilities 0.56 0.19 0.16 0.09

Find the probability that both patients survive. A) 0.56 B) 0.09

C) 0.3136

D) 0.35

Objective: (3.1) Find Probability Given Sample Space

31) A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.). Simple Events SS SD DS DD

Probabilities 0.53 0.15 0.10 0.22

Find the probability that at least one of the patients does not survive. A) 0.15 B) 0.47 C) 0.25 Objective: (3.1) Find Probability Given Sample Space

D) 0.22

32) A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: Color Number Red 25 Brown 20 Green 20 Blue 15 Yellow 10 Orange 10 Find the probability that a randomly selected piece is either yellow or orange in color. A) 20 B) 10 C) 0.10

D) 0.20

Objective: (3.1) Find Probability Given Sample Space

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 33) A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.). Simple Events SS SD DS DD

Probabilities 0.57 0.18 0.16 0.09

Find the probability that neither patient survives. Objective: (3.1) Find Probability Given Sample Space

34) In a sample of 750 of its online customers, a department store found that 420 were men. Use this information to estimate the probability that a randomly selected online customer is a man. Objective: (3.1) Find Probability Given Sample Space

35) At a small private college with 800 students, 240 students receive some form of government-sponsored financial aid. Find the probability that a randomly selected student receives some form of government-sponsored financial aid. Objective: (3.1) Find Probability Given Sample Space

36) The manager of a warehouse club estimates that 7 out of 10 customers will donate a dollar to help a children's hospital during an annual drive to benefit the hospital. Using the manager's estimate, what is the probability that a randomly selected customer will donate a dollar? Objective: (3.1) Find Probability Given Sample Space

37) A college has 85 male and 75 female fulltime faculty members. Suppose one fulltime faculty member is selected at random and the faculty member's gender is observed. a. List the sample points for this experiment. b. Assign probabilities to the sample points. Objective: (3.1) Find Probability Given Sample Space

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 38) At a community college with 500 students, 120 students are age 30 or older. Find the probability that a randomly selected student is age 30 or older. A) .76 B) .12 C) .24 D) .30 Objective: (3.1) Find Probability Given Sample Space

39) A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly selected online customer does not live within 50 miles of a physical store? A) .28 B) .78 C) .22 D) .50 Objective: (3.1) Find Probability Given Sample Space

40) A music store has 8 male and 12 female employees. Suppose one employee is selected at random and the employee's gender is observed. List the sample points for this experiment, and assign probabilities to the sample points. A) {8, 12}; P(8) = .5 and P(12) = .6 B) {male, female}; P(male) = .8 and P(female) = .12 C) {8, 12}; P(8) = .8 and P(12) = .12 D) {male, female}; P(male) = .4 and P(female) = .6 Objective: (3.1) Find Probability Given Sample Space

41) An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. Assuming that each of the numbers between 1 and 10 is equally likely to be chosen, find P(E). A) .8 B) .5 C) .1 D) .2 Objective: (3.1) Find Probability Given Sample Space

42) The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Find the probability that the number rolled on a single roll of this die is less than 4. Outcome Probability

1 .1

2 .1

A) .7

3 .1

4 .2

5 .2

B) .2

6 .3

C) .3

D) .5

Objective: (3.1) Find Probability Given Sample Space

43) The table displays the probabilities for each of the outcomes when three fair coins are tossed and the number of heads is counted. Find the probability that the number of heads on a single toss of the three coins is at most 2. Outcome Probability

A) .750

0 .125

1 .375

2 .375

3 .125

B) .500

C) .875

D) .125

Objective: (3.1) Find Probability Given Sample Space

44) At a certain university, one out of every 20 students is enrolled in a statistics course. If one student at the university is chosen at random, what is the probability that the student is enrolled in a statistics course? 1 1 1 1 A) B) C) D) 21 20 2 19 Objective: (3.1) Find Probability Given Sample Space

45) Two chips are drawn at random and without replacement from a bag containing four blue chips and three red chips. Find the probability of drawing two red chips. 1 9 6 1 A) B) C) D) 12 49 7 7 Objective: (3.1) Find Probability Given Sample Space

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 46) Three fair coins are tossed and either heads (H) or tails (T) is observed for each coin. a. b. c. d. e.

List the sample points for this experiment. Assign probabilities to the sample points. Find the probability of the event A = {Three heads are observed}. Find the probability of the event B = {Exactly two heads are observed}. Find the probability of the event C = {At least two heads are observed}.

Objective: (3.1) Find Probability Given Sample Space

47) Two chips are drawn at random and without replacement from a bag containing three blue chips and one red chip. a. b. c. d. e.

List the sample points for this experiment. Assign probabilities to the sample points. Find the probability of the event A = {Two blue chips are drawn}. Find the probability of the event B = {A blue chip and a red chip are drawn}. Find the probability of the event C = {Two red chips are drawn}.

Objective: (3.1) Find Probability Given Sample Space

48) In an exit poll, 45% of voters said that the main issue affecting their choices of candidates was the economy, 35% said national security, and the remaining 20% were not sure. Suppose we select one of the voters who participated in the exit poll at random and ask for the main issue affecting his or her choices of candidates. a. List the sample points for this experiment. b. Assign reasonable probabilities to the sample points. c. Find the probability that the main issue affecting his or her choices was either the economy or national security. Objective: (3.1) Find Probability Given Sample Space

49) The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal noted. gold bronze gold gold a. b. c.

gold gold silver gold

silver silver silver bronze

gold silver bronze bronze

bronze bronze bronze

List the sample points for this experiment. Find the probability of each sample point. What is the probability that the medal was not bronze?

Objective: (3.1) Find Probability Given Sample Space

silver silver gold

silver gold silver

50) The table shows the number of each type of book found at an online auction site during a recent search. Suppose that Juanita randomly chose one book to bid on and then noted its type. Type of Book Children's Fiction Nonfiction Educational a. b. c.

Number 51,033 141,114 253,074 67,252

List the sample points for this experiment. Find the probability of each sample point. What is the probability that the book was nonfiction or educational?

Objective: (3.1) Find Probability Given Sample Space

51) The table shows the number of each car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified. Type of Car Sedan Convertible Wagon SUV Van Hatchback Total a. b. c.

Number 7,204 9,089 20,418 13,691 15,837 15,350 81,589

List the sample points for this experiment. Find the probability of each sample point. What is the probability that the car was a Van or an SUV?

Objective: (3.1) Find Probability Given Sample Space

52) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Suppose that one of the countries represented is chosen at random and the total numbers of medals won by that country is noted. 1

a. b. c.

List the sample points for this experiment. Find the probability of each sample point. What is the probability that the country won at least 20 total medals?

Objective: (3.1) Find Probability Given Sample Space

53) The following data represent the scores of 50 students on a statistics exam. Suppose that one of the 50 students is chosen at random and that student's score is noted. 39 71 79 85 90

51 71 79 86 90

a. b. c.

59 73 79 86 91

63 74 80 88 91

66 76 80 88 92

68 76 82 88 95

68 76 83 88 96

69 77 83 89 97

70 78 83 89 97

71 79 85 89 98

What is the probability that the student's score is 88? What is the probability that the student's score is less than 60? What is the probability that the student's score is between 70 and 79, inclusive?

Objective: (3.1) Find Probability Given Sample Space

54) Three companies (A, B, and C) are to be ranked first, second, and third in a list of companies with the highest customer satisfaction. a. List all the possible sets of rankings for these top three companies. b. Assuming that all sets of rankings are equally likely, what is the probability that Company A will be ranked first, Company B second, and Company C third? c. Assuming that all sets of rankings are equally likely, what is the probability that Company B will be ranked first? Objective: (3.1) Find Probability Given Sample Space

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Compute. 55)

8 2

A) 28

B) 56

C) 720

D) 4

C) 720

D) 120

C) 1

D) 8

C) 24

D) 4

Objective: (3.1) Use Combination Rule

56)

10 3

A) 27

B) 7

Objective: (3.1) Use Combination Rule

57)

9 9

A) 9

B) 40,320

Objective: (3.1) Use Combination Rule

58)

5 0

A) 1

B) 5

Objective: (3.1) Use Combination Rule

59)

9 8

A) 1

B) 8

C) 362,880

D) 9

Objective: (3.1) Use Combination Rule

Compute the number of ways you can select n elements from N elements. 60) n = 2, N = 5 A) 20 B) 3 C) 6

D) 10

Objective: (3.1) Use Combination Rule

61) n = 4, N = 10 A) 5,040

B) 34

C) 6

D) 210

Objective: (3.1) Use Combination Rule

Solve the problem. 62) Which quantity is represented on the screen below?

A) The number of ways two dice can be rolled B) The number of sample points when a die is rolled and a coin is flipped C) The number of sample points when a coin is flipped six times D) The number of ways two coins can be chosen from six coins Objective: (3.1) Use Combination Rule

63) Which expression is equal to A)

N! n!(N - n)!

N ? n

N! n!

N! N!(N - n)!

N! (N - n)!

Objective: (3.1) Use Combination Rule

64) Evaluate

8 . 2

A) 4

B) 16

C) 56

D) 28

C) 1

D) 6

Objective: (3.1) Use Combination Rule

65) Evaluate

6 . 0

A) undefined

B) 0

Objective: (3.1) Use Combination Rule

66) Evaluate

7 . 7

A) 1

B) 49

C) 7

D) 14

Objective: (3.1) Use Combination Rule

67) Compute the number of ways you can select 3 elements from 7 elements. A) 343 B) 35 C) 21

D) 10

Objective: (3.1) Use Combination Rule

68) There are 10 movies that Greg would like to rent but the store only allows him to have 4 movies at one time. In how many ways can Greg choose 4 of the 10 movies? A) 210 B) 40 C) 5040 D) 10,000 Objective: (3.1) Use Combination Rule

69) Kim submitted a list of 12 movies to an online movie rental company. The company will choose 3 of the movies and ship them to her. If all movies are equally likely to be chosen, what is the probability that Kim will receive the three movies that she most wants to watch? Express the probability as a fraction. 1 1 1 1 A) B) C) D) 1320 4 220 1728 Objective: (3.1) Use Combination Rule

Answer the question True or False. 70) The quantity 0! is defined to be equal to 0. A) True

B) False

Objective: (3.1) Use Combination Rule

71) The combinations rule applies to situations in which the experiment calls for selecting n elements from a total of N elements, without replacing each element before the next is selected. A) True B) False Objective: (3.1) Use Combination Rule

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 72) Compute

10 . 6

Objective: (3.1) Use Combination Rule

73) Compute

5 . 1

Objective: (3.1) Use Combination Rule

74) Compute the number of ways you can select n elements from N elements for n = 6 and N = 15. Objective: (3.1) Use Combination Rule

75) In how many ways can a manager choose 3 of his 8 employees to work overtime helping with inventory? Objective: (3.1) Use Combination Rule

76) The manager of an advertising department has asked her creative team to propose six new ideas for an advertising campaign for a major client. She will choose three of the six proposals to present to the client. (We will refer to the six proposals as A, B, C, D, E, and F.) a. In how many ways can the manager select the three of the six proposals? List the possibilities. b. It is unlikely that the manager will randomly select three of the six proposals, but if she does what is the probability that she selects proposals A, D, and E? Objective: (3.1) Use Combination Rule

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 77) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Identify the sample points in the event A B. A) {1, 2, 3, 4, 5, 6, 8, 10} C) {2, 4, 6}

B) {1, 2, 3, 4, 5, 6, 7, 9} D) {1, 2, 3, 4, 5, 6, 7, 8, 10}

Objective: (3.2) Find Union or Intersection of Events

78) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Identify the sample points in the event A B. A) {1, 2, 3, 4, 5, 6, 8, 10} C) {2, 4, 6}

B) {1, 2, 3, 4, 5, 6, 7, 8, 10} D) {1, 2, 3, 4, 5, 6, 7, 9}

Objective: (3.2) Find Union or Intersection of Events

79) A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 3} B: {At least one of the dice shows a 2} Identify the sample points in the event A B. A) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} B) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)} C) {(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} D) {(1, 2), (2, 1)} Objective: (3.2) Find Union or Intersection of Events

80) A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 3} B: {At least one of the dice shows a 2} Identify the sample points in the event A B. A) {(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} B) {(1, 2), (2, 1)} C) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} D) {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)} Objective: (3.2) Find Union or Intersection of Events

81) A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 4} B: {The sum of the numbers on the dice is 11} Identify the sample points in the event A B. A) {(1, 3), (2, 2), (3, 1), (5, 6), (6, 5)} C) {(1, 4), (2, 2), (4, 1), (5, 6), (6, 5)}

B) {(1, 4), (2, 3), (3, 2), (4, 1), (5, 6), (6, 5)} D) There are no sample points in the event A B.

Objective: (3.2) Find Union or Intersection of Events

82) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Which expression represents the event that the number is even or less than 7 or both? A) Ac B) A B C) Bc

D) A B

Objective: (3.2) Find Union or Intersection of Events

83) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Which expression represents the event that the number is both even and less than 7? A) A B B) Bc C) Ac Objective: (3.2) Find Union or Intersection of Events

D) A B

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 84) A company evaluates its potential new employees using three criteria. A: The applicant has a minimum college GPA of 3.0. B: The applicant has relevant work experience. C: The applicant has a sufficient score on an aptitude test. a. Write the event that an applicant meets all three criteria as a union or intersection of A, B, and C. b. Write the event that an applicant meets at least one of the three criteria as a union or intersection of A, B, and C. Objective: (3.2) Find Union or Intersection of Events

85) A consumer advocacy group rates the quality of a cellular service provider using three criteria. A: Service is available at least 99% of the time. B: Reception is clear at least 95% of the time. C: Fewer than 5% of its customers have complaints about the quality of service. a. b.

Describe the event represented by A B C. Describe the event represented by A B C.

Objective: (3.2) Find Union or Intersection of Events

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 86) Fill in the blank. The __________ of two events A and B is the event that either A or B or both occur. A) intersection B) Venn diagram C) complement D) union Objective: (3.2) Find Union or Intersection of Events

87) Fill in the blank. The __________ of two events A and B is the event that both A and B occur. A) union B) Venn diagram C) complement D) intersection Objective: (3.2) Find Union or Intersection of Events

Answer the question True or False. 88) Unions and intersections of events are examples of compound events. A) True B) False Objective: (3.2) Find Union or Intersection of Events

89) Unions and intersections cannot be defined for more than two sets, so that A B C and A B C are meaningless. A) True B) False Objective: (3.2) Find Union or Intersection of Events

90) A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 3} B: {At least one of the dice shows a 2} True or False: A B = B. A) True

B) False

Objective: (3.2) Find Union or Intersection of Events

91) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows. A: {Both chips are red} B: {At least one of the chips is blue} True or False: A B = B. A) True

B) False

Objective: (3.2) Find Union or Intersection of Events

Solve the problem. 92) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company's success is customer service. A study was conducted to determine the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown in the following table:

Frequency of Use < 2 per month 2 - 5 per month > 5 per month TOTAL

High 250 140 70 460

Satisfaction level Medium 140 55 25 220

Low 10 5 5 20

TOTAL 400 200 100 700

Suppose that one customer who participated in the study is chosen at random. What is the probability that the customer had a low level of satisfaction and used the company less than two times per month? 3 1 41 29 A) B) C) D) 5 70 70 70 Objective: (3.2) Find Probability Using Unions and Intersections

93) Each manager of a Fortune 500 company was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below: Educational Background Manager Rating H. S. Degree Some College College Degree Master's or Ph.D. Total Good 3 8 21 7 39 Fair 5 11 42 29 87 Poor 4 1 9 20 34 Total 12 20 72 56 160 What is the probability that a randomly chosen manager has earned at least one college degree? 4 1 7 9 A) B) C) D) 5 5 20 20 Objective: (3.2) Find Probability Using Unions and Intersections

94) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below: Educational Background

Manager Rating H. S. Degree Some College College Degree Master's or Ph.D. Totals Good 3 5 28 3 39 Fair 9 16 41 21 87 Poor 7 6 2 19 34 Totals 19 27 71 43 160 If we randomly selected one manager from this company, find the probability that he or she has an advanced (Master's or Ph.D.) degree and is a good manager. 41 59 157 3 A) B) C) D) 80 80 160 160 Objective: (3.2) Find Probability Using Unions and Intersections

95) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below: Number of Vehicles Involved Did Alcohol Play a Role? 1 2 3 or more Totals Yes 56 91 23 170 No 25 176 29 230 Totals 81 267 52 400 Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved more than a single vehicle? 81 23 319 13 A) B) C) D) 400 400 400 100 Objective: (3.2) Find Probability Using Unions and Intersections

96) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich. Region NE SE SW NW 5% 6% 3% 0% <10,000 Population of City 10,000 - 100,000 15% 8% 12% 5% >100,000 20% 4% 3% 19% What is the probability that the restaurant is located in the northern portion of the United States? A) 0.64 B) 0.24 C) 0.40 D) 0.36 Objective: (3.2) Find Probability Using Unions and Intersections

97) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich. Region NE SE SW NW 4% 6% 3% 0% <10,000 Population of City 10,000 - 100,000 15% 6% 12% 5% >100,000 20% 4% 5% 20% What is the probability that the restaurant is located in a city with a population over 100,000 and in the southern portion of the United States? A) 0.05 B) 0.09 C) 0.36 D) 0.04 Objective: (3.2) Find Probability Using Unions and Intersections

98) The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Political Affiliation Republican Democrat Independent White collar 18% 9% 6% Type of job Blue Collar 20% 15% 32% Find the probability that the worker is a white collar worker affiliated with the Democratic Party. A) 0.09 B) 0.48 C) 0.33 D) 0.24 Objective: (3.2) Find Probability Using Unions and Intersections

99) The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once. Let A be the event that the number rolled is less than 4, and let B be the event that the number rolled is odd. Find P(A B). Outcome Probability

1 .1

2 .1

A) .3

3 .1

4 .2

5 .2

B) .7

6 .3

C) .5

D) .2

Objective: (3.2) Find Probability Using Unions and Intersections

100) The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once. Let A be the event that the number rolled is less than 4, and let B be the event that the number rolled is odd. Find P(A B). Outcome Probability

A) .5

1 .1

2 .1

3 .1

4 .2

5 .2

B) .2

6 .3

C) .7

Objective: (3.2) Find Probability Using Unions and Intersections

D) .3

101) A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.

Find the probability that a randomly selected student is both a sophomore and drives a foreign automobile. A) 65/205 B) 45/350 C) 65/350 D) 65/110 Objective: (3.2) Find Probability Using Unions and Intersections

102) A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.

What is the probability of randomly selecting a student who is in the freshman class or drives a foreign automobile? A) 15/350 B) 15/205 C) 215/350 D) 230/350 Objective: (3.2) Find Probability Using Unions and Intersections

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 103) Suppose that an experiment has five sample points, E1 , E2 , E3 , E4 , E5 , and that P(E1 ) = .2, P(E2 ) = .3, P(E3 ) = .1, P(E4) = .1, and P(E5 ) = .3. If the events A and B are defined as A = {E1 , E2 , E3 } and B = {E2 , E3 , E4 } find P(A B). Objective: (3.2) Find Probability Using Unions and Intersections

104) Suppose that an experiment has five sample points, E1 , E2 , E3 , E4 , E5 , and that P(E1 ) = .4, P(E2 ) = .1, P(E3 ) = .1, P(E4) = .2, and P(E5 ) = .2. If the events A and B are defined as A = {E1 , E2 , E5 } and B = {E2 , E3 , E5 } find P(A B). Objective: (3.2) Find Probability Using Unions and Intersections

105) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a chicken sandwich. Region NE SE SW NW 2% 6% 3% 0% <10,000 Population of City 10,000 - 100,000 15% 5% 12% 5% >100,000 20% 4% 10% 18% What is the probability that the restaurant is located in the western portion of the United States? Objective: (3.2) Find Probability Using Unions and Intersections

106) The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Political Affiliation Republican Democrat Independent White collar 17% 19% 15% Type of job Blue Collar 9% 6% 34% What is the probability that the worker is a white collar Republican? Objective: (3.2) Find Probability Using Unions and Intersections

107) A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 6} B: {At least one of the numbers 3} a. b. c. d.

Identify the sample points in the event A B. Identify the sample points in the event A B. Find P(A B). Find P(A B).

Objective: (3.2) Find Probability Using Unions and Intersections

108) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows. A: {Both chips are red} B: {At least one of the chips is blue} a. b.

Identify the sample points in the event A B. Find P(A B).

Objective: (3.2) Find Probability Using Unions and Intersections

109) The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified. Type of Car Sedan Convertible Wagon SUV Van Hatchback Total

Number 7,204 9,089 20,418 13,691 15,837 15,350 81,589

Events A and B are defined as follows. A: {Convertible, SUV, Van} B: {Fewer than 10,000 of the type of car were sold in June} a. b. c. d.

Identify the sample points in the event A B. Identify the sample points in the event A B. Find P(A B). Find P(A B).

Objective: (3.2) Find Probability Using Unions and Intersections

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 110) In the game of Parcheesi each player rolls a pair of dice on each turn. In order to begin the game, you must roll a five on at least one die, or a total of five on both dice. Find the probability that a player begins the game on the first roll. 15 1 5 11 A) B) C) D) 36 6 18 36 Objective: (3.2) Find Probability Using Unions and Intersections

111) Fill in the blank. The __________ of an event A is the event that A does not occur. A) union B) complement C) Venn diagram Objective: (3.3) Find Complement of Event

D) intersection

112) The following Venn diagram shows the six possible outcomes when rolling a fair die. Let A be the event of rolling an even number and let B be the event of rolling a number greater than 1.

Which of the following expressions describes the event of rolling a 1? A) A B B) B C) Bc

D) Ac

Objective: (3.3) Find Complement of Event

113) A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events: A: {The home is constructed of brick} B: {The home is more than 30 years old} In terms of A and B, describe a home that is constructed of brick and is less than or equal to 30 years old. A) A B B) (A B)c C) A Bc D) A B Objective: (3.3) Find Complement of Event

114) A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events: A: {The home is constructed of brick} B: {The home is more than 30 years old} D: {The home is heated with oil} Which of the following describes the event B Dc? A) homes more than 30 years old that are heated with oil B) homes more than 30 years old or homes that are not heated with oil C) homes more than 30 years old that are not heated with oil D) homes that are not older than 30 years old and heated with oil Objective: (3.3) Find Complement of Event

115) An insurance company looks at many factors when determining how much insurance will cost for a home. Two of the factors are listed below: A: {The home's roof is less than 10 years old} B: {The home has a security system} In the words of the problem, define the event Bc. A) The home has a security system C) The home is not less than 10 years old

B) The home does not have a security system D) The home is less than 10 years old

Objective: (3.3) Find Complement of Event

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 116) A fair die is rolled one time. Let A be the event that an odd number is rolled. Describe the event Ac. Objective: (3.3) Find Complement of Event

117) A fair die is rolled one time. Let B be the event {1, 2, 5}. List the sample points in the event Bc. Objective: (3.3) Find Complement of Event

118) A company evaluates its potential new employees using three criteria. A: The applicant has a minimum college GPA of 3.0. B: The applicant has relevant work experience. D: The applicant has a sufficient score on an aptitude test. Describe an applicant represented by A Bc D. Objective: (3.3) Find Complement of Event

119) A consumer advocacy group rates the quality of a cellular service provider using three criteria. A: Service is available at least 99% of the time. B: Reception is clear at least 95% of the time. D: Fewer than 5% of its customers have complaints about the quality of service. Describe a cellular service provider represented by Ac Bc Dc. Objective: (3.3) Find Complement of Event

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False.

120) If an event A includes the entire sample space, then P(Ac) = 0. A) True B) False Objective: (3.3) Find Complement of Event

121) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows. A: {Both chips are red} B: {At least one of the chips is blue} True or False: A = Bc. A) True

B) False

Objective: (3.3) Find Complement of Event

Solve the problem. 122) At a community college with 500 students, 120 students are age 30 or older. Find the probability that a randomly selected student is less than 30 years old. A) .30 B) .24 C) .12 D) .76 Objective: (3.3) Find Probability Using Complement

123) A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is that probability that a a randomly selected online customer lives within 50 miles of a physical store? A) .28 B) .50 C) .78 D) .22 Objective: (3.3) Find Probability Using Complement

124) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company's success is customer service. A study was conducted to determine the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown below in the following table:

Frequency of Use < 2 per month 2 - 5 per month > 5 per month TOTAL

High 250 140 70 460

Satisfaction level Medium 140 55 25 220

Low 10 5 5 20

TOTAL 400 200 100 700

Suppose that one customer who participated in the study is chosen at random. What is the probability that the customer did not have a high level of satisfaction with the company? 12 4 23 3 A) B) C) D) 35 7 35 7 Objective: (3.3) Find Probability Using Complement

125) The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Political Affiliation Republican Democrat Independent White collar 19% 14% 15% Type of job Blue Collar 12% 9% 31% Find the probability the worker is not an Independent. A) 0.54 B) 0.21

C) 0.46

D) 0.33

Objective: (3.3) Find Probability Using Complement

126) A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 61% regularly use the golf course, 48% regularly use the tennis courts, and 4% use neither of these facilities regularly. What is the probability that a member regularly uses at least one of the golf or tennis facilities? A) .48 B) .96 C) .4 D) .13 Objective: (3.3) Find Probability Using Complement

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 127) Suppose that for a certain experiment P(A) = .37. Find P(Ac). Objective: (3.3) Find Probability Using Complement

128) Suppose that for a certain experiment the probability of a particular event occurring is .21. Find the probability that this event does not occur. Objective: (3.3) Find Probability Using Complement

129) Suppose that an experiment has five sample points, E1 , E2 , E3 , E4 , E5 , and that P(E1 ) = .2, P(E2 ) = .3, P(E3 ) = .1, P(E4) = .1, and P(E5 ) = .3. If event A is defined as A = {E1 , E2, E3 }, find P(Ac). Objective: (3.3) Find Probability Using Complement

130) In a sample of 750 of its online customers, a department store found that 420 were men. Use this information to estimate the probability that a randomly selected online customer is not a man. Objective: (3.3) Find Probability Using Complement

131) At a small private college with 800 students, 240 students receive some form of government-sponsored financial aid. Find the probability that a randomly selected student does not receive some form of government-sponsored financial aid. Objective: (3.3) Find Probability Using Complement

132) The manager of a warehouse club estimates that 7 out of 10 customers will donate a dollar to help a children's hospital during an annual drive to benefit the hospital. Using the manager's estimate, what is the probability that a randomly selected customer will not donate a dollar? Objective: (3.3) Find Probability Using Complement

133) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Event A is defined as follows. A: {Both chips are red} a. b. c.

Describe the event Ac.

Identify the sample points in the event Ac. Find P(Ac).

Objective: (3.3) Find Probability Using Complement

134) The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified. Type of Car Sedan Convertible Wagon SUV Van Hatchback Total

Number 7,204 9,089 20,418 13,691 15,837 15,350 81,589

Event A is defined as follows. A: {Convertible, SUV, Van} a. b.

Identify the sample points in the event Ac. Find P(Ac).

Objective: (3.3) Find Probability Using Complement

135) A pair of fair dice is tossed. Events A and B are defined as follows. A: {The two numbers rolled are different} B: {At least one of the numbers is greater than 2} a. b. c. d. e. f.

Identify the sample points in the event Ac. Identify the sample points in the event Bc.

Identify the sample points in the event Ac Bc. Identify the sample points in the event Ac Bc. Find P(Ac Bc). Find P(Ac Bc).

Objective: (3.3) Find Probability Using Complement

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 136) A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.

Which of the following events listed would be considered mutually exclusive events? A) The student is a freshman and the student drives a foreign automobile B) The student is a senior and the student drives a domestic automobile. C) The student is a junior and the student drives a domestic automobile D) The student is a junior and the student is a freshman Objective: (3.4) Determine if Events are Mutually Exclusive

137) If P(A B) = 1 and P(A B) = 0, then which statement is true? A) A and B are both empty events. B) A and B are supplementary events. C) A and B are reciprocal events. D) A and B are complementary events. Objective: (3.4) Determine if Events are Mutually Exclusive

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 138) A pair of fair dice is tossed. Events A and B are defined as follows. A: {The two numbers rolled are different} B: {At least one of the numbers is greater than 2} Are the events A and B mutually exclusive? Explain. Objective: (3.4) Determine if Events are Mutually Exclusive

139) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows. A: {Both chips are red} B: {At least one of the chips is blue} Are the events A and B mutually exclusive? Explain. Objective: (3.4) Determine if Events are Mutually Exclusive

140) A number between 1 and 10, inclusive, is randomly chosen. Events A, B, C, and D are defined as follows. A: {The number is even} B: {The number is less than 7} C: {The number is odd} D: {The number is greater than 5} Identify one pair of mutually exclusive events. Objective: (3.4) Determine if Events are Mutually Exclusive

141) Three fair coins are tossed and either heads or tails is observed for each coin. Events A and B are defined as follows. A: {Three heads are observed}. B: {Exactly two heads are observed}. Is P(A B) equal to the sum of P(A) and P(B)? Explain. Objective: (3.4) Determine if Events are Mutually Exclusive

142) The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified. Type of Car Sedan Convertible Wagon SUV Van Hatchback Total

Number 7,204 9,089 20,418 13,691 15,837 15,350 81,589

Events A and B are defined as follows. A: {Convertible, SUV, Van} B: {Fewer than 10,000 of the type of car were sold in June} Is P(A B) equal to the sum of P(A) and P(B)? Explain. Objective: (3.4) Determine if Events are Mutually Exclusive

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 143) If two events, A and B, are mutually exclusive, then P(A and B) = P(A) × P(B). A) True B) False Objective: (3.4) Determine if Events are Mutually Exclusive

144) An event and its complement are mutually exclusive. A) True

B) False

Objective: (3.4) Determine if Events are Mutually Exclusive

145) If A and B are mutually exclusive events, then P(A B) = 0. A) True

B) False

Objective: (3.4) Determine if Events are Mutually Exclusive

146) If events A and B are not mutually exclusive, then it is possible that P(A) + P(B) > 1. A) True B) False Objective: (3.4) Determine if Events are Mutually Exclusive

Solve the problem. 147) Suppose that for a certain experiment P(A) = .33 and P(B) = .29. If A and B are mutually exclusive events, find P(A B). A) .38 B) .62 C) .03 D) .31 Objective: (3.4) Use Additive Rule to Find Probability

148) Suppose that for a certain experiment P(A) = .47 and P(B) = .25 and P(A B) = .14. Find P(A B). A) .72 B) .36 C) .58 D) .86 Objective: (3.4) Use Additive Rule to Find Probability

149) In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is a woman or earning an A. A) .25 B) .8 C) .975 D) .625 Objective: (3.4) Use Additive Rule to Find Probability

150) In a class of 30 students, 18 are men, 6 are earning a B, and no men are earning a B. If a student is randomly selected from the class, find the probability that the student is a man or earning a B. A) .24 B) .4 C) .54 D) .8 Objective: (3.4) Use Additive Rule to Find Probability

151) In a box of 50 markers, 30 markers are either red or black and 20 are missing their caps. If 12 markers are either red or black and are missing their caps, find the probability that a randomly selected marker is red or black or is missing its cap. A) .76 B) .38 C) 1 D) .24 Objective: (3.4) Use Additive Rule to Find Probability

152) In a box of 75 markers, 36 markers are either red or black and 15 are blue. Find the probability that a randomly selected marker is red or black or blue. A) .32 B) .51 C) .24 D) .68 Objective: (3.4) Use Additive Rule to Find Probability

153) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below: Educational Background Manager Rating H. S. Degree Some College College Degree Master's or Ph.D. Totals Good 2 3 21 13 39 Fair 6 19 45 17 87 Poor 4 8 7 15 34 Totals 12 30 73 45 160 What is the probability that a randomly chosen manager is either a good managers or has an advanced degree? 147 13 71 21 A) B) C) D) 160 160 160 40 Objective: (3.4) Use Additive Rule to Find Probability

154) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below: Number of Vehicles Involved Did Alcohol Play a Role? 1 2 3 or more Totals Yes 54 100 16 170 No 29 171 30 230 Totals 83 271 46 400 Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved alcohol or a single car? 199 83 17 27 A) B) C) D) 400 400 40 200 Objective: (3.4) Use Additive Rule to Find Probability

155) A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.

What proportion of the employees are female or have been employed for more than 10 years? A) 25/65 B) 85/130 C) 110/130 D) 25/130 Objective: (3.4) Use Additive Rule to Find Probability

156) A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.

What proportion of the employees are male or have been employed for less than 11 years? A) 45/130 B) 42/65 C) 165/130 D) 120/130 Objective: (3.4) Use Additive Rule to Find Probability

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 157) A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 60% regularly use the golf course, 44% regularly use the tennis courts, and 8% use both of these facilities regularly. Find the probability that a randomly selected member uses the golf or tennis facilities regularly. Objective: (3.4) Use Additive Rule to Find Probability

158) Suppose that for a certain experiment P(A) = .37, P(B) = .69, and P(A B) = .23. Find P(A B). Objective: (3.4) Use Additive Rule to Find Probability

159) Suppose that for a certain experiment P(A) =

1 1 and P(B) = , and events A and B are mutually exclusive. Find P(A 3 4

B). Objective: (3.4) Use Additive Rule to Find Probability

160) Suppose that for a certain experiment P(A) = .8 and P(B) = .9. Use the Additive Rule to explain why the events A and B can not be mutually exclusive. Objective: (3.4) Use Additive Rule to Find Probability

161) Based on past experience, Josh believes that the probability of catching a red snapper is .21 and the probability of catching a grouper is .19. Is enough information available to find the probability of catching a red snapper or a grouper? Explain. If possible, find the probability of catching a red snapper or a grouper. Objective: (3.4) Use Additive Rule to Find Probability

162) Based on past experience, Josh believes that the probability of catching a red snapper is .21 and the probability of catching a fish that weighs less than 5 pounds is .45. Is enough information available to find the probability of catching a red snapper or a fish that weighs less than 5 pounds? Explain. If possible, find the probability of catching a red snapper or a fish that weighs less than 5 pounds. Objective: (3.4) Use Additive Rule to Find Probability

163) Suppose that 62% of the employees at a company are male and that 35% of the employees just received merit raises. If 20% of the employees are male and received a merit raise, what is the probability that a randomly chosen employee is male or received a merit raise? Objective: (3.4) Use Additive Rule to Find Probability

164) Suppose that 80% of the employees of a company received cash or company stock as a bonus at the end of the year. If 60% of the employees received a cash bonus and 30% received stock, what is the probability that a randomly chosen employee received both cash and stock as a bonus? Objective: (3.4) Use Additive Rule to Find Probability

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 165) A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the probability that a green notepad is selected given that it is either blue or green. 1 1 1 1 A) B) C) D) 3 2 12 4 Objective: (3.5) Find Conditional Probability

166) A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the probability that a yellow or pink notepad is selected given that it is either blue or green. 1 1 A) B) C) 0 D) 1 2 4 Objective: (3.5) Find Conditional Probability

167) An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters. An experiment consists of randomly selecting one of the highlighters and recording its color. Find the probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected. 1 1 A) 0 B) C) 1 D) 3 2 Objective: (3.5) Find Conditional Probability

168) In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is a woman given that the student is earning an A. 11 5 7 7 A) B) C) D) 20 11 22 10 Objective: (3.5) Find Conditional Probability

169) In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is earning an A given that the student is a woman. 5 7 1 7 A) B) C) D) 11 22 4 40 Objective: (3.5) Find Conditional Probability

170) In a class of 30 students, 18 are men, 6 are earning a B, and no men are earning a B. If a student is randomly selected from the class, find the probability that the student is a man given that the student earning a B. 1 3 A) 1 B) C) D) 0 3 5 Objective: (3.5) Find Conditional Probability

171) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company's success is customer service. A study was conducted to determine the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown below in the following table:

Frequency of Use < 2 per month 2 - 5 per month > 5 per month TOTAL

High 250 140 70 460

Satisfaction level Medium 140 55 25 220

Low 10 5 5 20

TOTAL 400 200 100 700

A customer is chosen at random. Given that the customer uses the company two to five times per month, what is the probability that the customer expressed medium satisfaction with the company? 11 73 1 11 A) B) C) D) 140 140 4 40 Objective: (3.5) Find Conditional Probability

172) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below: Educational Background Manager Rating H. S. Degree Some College College Degree Master's or Ph.D. Totals Good 5 4 23 7 39 Fair 8 15 49 15 87 Poor 9 3 2 20 34 Totals 22 22 74 42 160 Given that a manager is rated as fair, what is the probability that this manager has no college background? 1 8 4 101 A) B) C) D) 20 87 11 160 Objective: (3.5) Find Conditional Probability

173) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below: Number of Vehicles Involved Did Alcohol Play a Role? 1 2 3 or more Totals Yes 52 92 26 170 No 25 176 29 230 Totals 77 268 55 400 Given that an accident involved multiple vehicles, what is the probability that it involved alcohol? 13 59 26 118 A) B) C) D) 200 200 55 323 Objective: (3.5) Find Conditional Probability

174) A researcher investigated whether a student's seat preference was related in any way to the gender of the student. The researcher divided a lecture room into three sections (1-front, middle of the room, 2-front, sides of the classroom, and 3-back of the classroom, both middle and sides) and noted where each student sat on a particular day of the class. The researcher's summary table is provided below.

Male Female Total

Area 1 16 11 27

Area 2 8 13 21

Area 3 9 15 24

Total 33 39 72

Suppose a person sitting in the front, middle portion of the class is randomly selected to answer a question. Find the probability that the person selected is female. 9 11 11 11 A) B) C) D) 13 39 72 27 Objective: (3.5) Find Conditional Probability

175) The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of each car and its make (foreign or domestic):

Make Foreign Domestic Total

0-2 43 41 84

Age of Car (in years) 3-5 6 - 10 25 13 27 12 52 25

over 10 19 20 39

Total 100 100 200

A car was randomly selected from the lot. Given that the car selected was a foreign car, what is the probability that it was older than 2 years old? 43 57 43 57 A) B) C) D) 116 100 100 116 Objective: (3.5) Find Conditional Probability

176) A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.

Given that you know the selected student is in the senior class, find the probability they drive a domestic automobile. A) 15/350 B) 25/35 C) 10/35 D) 15/205 Objective: (3.5) Find Conditional Probability

177) A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.

Suppose an employee has been randomly selected from this company. Given that the employee is male, find the probability that they have worked for the company for more than 10 years? A) 20/30 B) 20/65 C) 75/130 D) 20/130 Objective: (3.5) Find Conditional Probability

178) The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Political Affiliation Republican Democrat Independent White collar 10% 19% 12% Type of job Blue Collar 9% 15% 35% Given that the worker is a Democrat, what is the probability that the worker has a white collar job. A) 0.463 B) 0.339 C) 0.559 D) 0.607 Objective: (3.5) Find Conditional Probability

179) A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 57% regularly use the golf course, 48% regularly use the tennis courts, and 9% use both of these facilities regularly. Given that a randomly selected member uses the tennis courts regularly, find the probability that they also use the golf course regularly. A) .1343 B) .4737 C) .1875 D) .7164 Objective: (3.5) Find Conditional Probability

180) For two events, A and B, P(A) = .4, P(B) = .7, and P(A B) = .2. Find P(A | B). A) .5 B) .08 C) .29

D) .14

Objective: (3.5) Find Conditional Probability

181) For two events, A and B, P(A) = A)

1 8

1 1 1 , P(B) = , and P(A B) = . Find P(B | A). 2 3 4

1 2

1 12

3 4

Objective: (3.5) Find Conditional Probability

182) For two events, A and B, P(A) = .6, P(B) = .8, and P(A | B) = .5. Find P(A B). A) .625 B) .4 C) .3

D) .833

Objective: (3.5) Find Conditional Probability

183) For two events, A and B, P(A) = A)

1 2

3 2 5 , P(B) = , and P(B | A) = . Find P(A B). 4 3 6

9 10

5 8

5 9

Objective: (3.5) Find Conditional Probability

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 184) A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. It further estimates that 39 out of every 100 of its online customers is a man who does not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly selected online customer is a man given that the customer does not live within 50 miles of a physical store? Objective: (3.5) Find Conditional Probability

185) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich. Region NE SE SW NW 5% 6% 3% 0% <10,000 Population of City 10,000 - 100,000 15% 6% 12% 5% >100,000 20% 4% 7% 17% What is the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States? Objective: (3.5) Find Conditional Probability

186) The table shows the political affiliations and types of job for workers in a particular state. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Political Affiliation Republican Democrat Independent White collar 19% 10% 12% Type of job Blue Collar 14% 20% 25% Given that a worker is a blue collar worker, what is the probability that the worker is a Democrat? Objective: (3.5) Find Conditional Probability

187) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Find P(A | B) and P(B | A). Objective: (3.5) Find Conditional Probability

188) A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the dice is 7} B: {At least one of the numbers is 3} Find P(A | B) and P(B | A). Objective: (3.5) Find Conditional Probability

189) The table shows the number of each Ford car sold in the United States in June 2006. Suppose the sales record for one of these cars is randomly selected and the type of car is identified. Type of Car Sedan Convertible Wagon SUV Van Hatchback Total

Number 7,204 9,089 20,418 13,691 15,837 15,350 81,589

Events A and B are defined as follows. A: {Convertible, SUV, Van} B: {Fewer than 10,000 of the type of car were sold in June 2006} Find P(A | B) and P(B | A). Objective: (3.5) Find Conditional Probability

190) Suppose that 62% of the employees at a company are male and that 35% of the employees just received merit raises. If 20% of the employees are male and received a merit raise, what is the probability that a randomly chosen employee is male given that the employee received a merit raise? Objective: (3.5) Find Conditional Probability

191) The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once. Let A be the event that the number rolled is less than 4, and let B be the event that the number rolled is odd. Outcome Probability

1 .1

2 .1

3 .1

4 .2

5 .2

6 .3

Find P(A | B). Objective: (3.5) Find Conditional Probability

192) The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal noted. gold bronze gold gold

gold gold silver gold

silver silver silver bronze

gold silver bronze bronze

bronze bronze bronze

silver silver gold

silver gold silver

Given that the medal is not bronze, what is the probability that the medal is gold? Objective: (3.5) Find Conditional Probability

193) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. 1

Suppose that one of the countries represented is selected at random and the total number of medals won by that country is noted. What is the probability that the country won at least 25 medals given that the country did not win fewer than 10 medals? Objective: (3.5) Find Conditional Probability

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 194) The conditional probability of event A given that event B has occurred is written as P(B | A). A) True B) False Objective: (3.5) Find Conditional Probability

195) If A and B are mutually exclusive events, then P(A | B) = 0. A) True

B) False

Objective: (3.5) Find Conditional Probability

196) For all events A and B, the conditional probabilities P(A | B) and P(B | A) are equal. A) True B) False Objective: (3.5) Find Conditional Probability

197) If every sample point in event B is also a sample point in event A, then P(A | B) = 1. A) True B) False Objective: (3.5) Find Conditional Probability

198) For any events A and B, P(A | B) + P(Ac | B) = 1, meaning given that B occurs either A occurs or A does not occur. A) True B) False Objective: (3.5) Find Conditional Probability

199) For any events A and B, P(A | B) + P(A | Bc) = 1, meaning given that A occurs either B occurs or B does not occur. A) True B) False Objective: (3.5) Find Conditional Probability

Solve the problem. 200) Suppose that for a certain experiment P(B) = 0.5 and P(A B) = 0.2. Find P(A B). A) 0.7 B) 0.1 C) 0.3

D) 0.4

Objective: (3.6) Use Multiplication Rule to Find Probability

201) Suppose that for a certain experiment P(A) = 0.6 and P(B) = 0.3. If A and B are independent events, find P(A B). A) 0.30 B) 0.50 C) 0.18 D) 0.90 Objective: (3.6) Use Multiplication Rule to Find Probability

202) A human gene carries a certain disease from a mother to her child with a probability rate of 0.33. That is, there is a 33% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has three children. Assume that the infections, or lack thereof, are independent of one another. Find the probability that all three of the children get the disease from their mother. A) 0.301 B) 0.036 C) 0.148 D) 0.964 Objective: (3.6) Use Multiplication Rule to Find Probability

203) A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.91, P(C) = 0.94, and P(D) = 0.93. Find the probability that the machine works properly. A) 0.7239 B) 0.2761 C) 0.7784 D) 0.7955 Objective: (3.6) Use Multiplication Rule to Find Probability

204) Suppose a basketball player is an excellent free throw shooter and makes 96% of his free throws (i.e., he has a 96% chance of making a single free throw). Assume that free throw shots are independent of one another. Find the probability that the player will make three consecutive free throws. A) 0.9999 B) 0.8847 C) 0.1153 D) 0.0001 Objective: (3.6) Use Multiplication Rule to Find Probability

205) Suppose a basketball player is an excellent free throw shooter and makes 91% of his free throws (i.e., he has a 91% chance of making a single free throw). Assume that free throw shots are independent of one another. Find the probability that the player misses four consecutive free throws. A) 0.9999 B) 0.6857 C) 0.3143 D) 0.0001 Objective: (3.6) Use Multiplication Rule to Find Probability

206) A one-week study revealed that 60% of a warehouse store's customers are women and that 30% of women customers spend at least $250 on a single visit to the store. Find the probability that a randomly chosen customer will be a woman who spends at least $250. A) 0.36 B) 0.90 C) 0.18 D) 0.50 Objective: (3.6) Use Multiplication Rule to Find Probability

207) A study revealed that 45% of college freshmen are male and that 18% of male freshmen earned college credits while still in high school. Find the probability that a randomly chosen college freshman will be male and have earned college credits while still in high school. A) 0.027 B) 0.530 C) 0.081 D) 0.400 Objective: (3.6) Use Multiplication Rule to Find Probability

208) In a particular town, 20% of the homes have monitored security systems. If an alarm is triggered, the security system company will contact the local police to alert them of the alarm. Of all the alarm calls that the local police receive, they only have the manpower to answer 30% of the calls. Suppose we randomly sample one home that was broken into over the last month from this town. What is the probability that this home has a monitored security system and that the police answered the alarm call? A) 0.3000 B) 0.0600 C) 0.9400 D) 0.2000 Objective: (3.6) Use Multiplication Rule to Find Probability

209) A basketball player has an 80% chance of making the first free-throw he shoots. If he makes the first free-throw shot, then he has a 90% chance of making the second free-throw he shoots. If he misses the first free-throw shot, then he only has a 70% chance of making the second free-throw he shoots. Suppose this player has been awarded two free-throw shots. Find the probability that he makes at least one of the two shots. A) 0.80 B) 0.94 C) 0.86 D) 0.72 Objective: (3.6) Use Multiplication Rule to Find Probability

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 210) Suppose that for a certain experiment P(A) = .15 and P(B A) = .8. Find P(A B). Objective: (3.6) Use Multiplication Rule to Find Probability

211) Suppose that for a certain experiment P(A) = .32 and P(B) = .55. If A and B are independent events, find P(A B). Objective: (3.6) Use Multiplication Rule to Find Probability

212) A human gene carries a certain disease from a mother to her child with a probability rate of 0.40. That is, there is a 40% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections, or lack thereof, are independent of one another. Find the probability that none of the children get the disease from their mother. Objective: (3.6) Use Multiplication Rule to Find Probability

213) Suppose there is a 37% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so high, you decide to invest in three independent risky stocks. What is the probability that all three stocks end up in total losses? Objective: (3.6) Use Multiplication Rule to Find Probability

214) An exit poll during a recent election revealed that 55% of those voting were women and that 65% of the women voting favored Democratic candidates. What is the probability that a randomly chosen participant of the exit poll would be a woman who favored Democratic candidates? Objective: (3.6) Use Multiplication Rule to Find Probability

215) In the game of Parcheesi each player rolls a pair of dice on each turn. In order to begin the game, you must roll a five on at least one die, or a total of five on both dice. Find the probability that the player does not get to begin the game on either the first or the second rolls. Objective: (3.6) Use Multiplication Rule to Find Probability

216) If 80% of a website's visitors are teenagers and 60% of those teenaged visitors are male, find the percentage of the website's visitors that are teenaged males. Objective: (3.6) Use Multiplication Rule to Find Probability

217) A certain game has a deck of numbered cards of various colors. The probability of drawing a green card from a well-shuffled deck is .25 and the probability of drawing a card numbered 3 is .1. Assuming that "green" and "3" are independent events, find the probability of drawing a green card numbered 3. Objective: (3.6) Use Multiplication Rule to Find Probability

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 218) If P(A B) = 0 and P(A) 0, then which statement is false? A) Events A and B have no sample points in common. B) Events A and B are dependent. C) Events A and B are mutually exclusive. D) Events A and B are independent. Objective: (3.6) Determine if Events are Independent

219) A number between 1 and 10, inclusive, is randomly chosen. Events A, B, C, and D are defined as follows. A: {The number is even} B: {The number is less than 7} C: {The number is less than or equal to 7} D: {The number is 5} Identify one pair of independent events. A) A and D B) A and B

C) A and C

D) B and D

Objective: (3.6) Determine if Events are Independent

220) The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once. Outcome Probability

1 .1

2 .1

3 .1

4 .2

5 .2

6 .3

Events A, B, C, and D are defined as follows. A: {The number is even} B: {The number is less than 4} C: {The number is less than or equal to 5} D: {The number is greater than or equal to 5} Identify one pair of independent events. A) A and D B) B and C

C) A and B

D) B and D

Objective: (3.6) Determine if Events are Independent

221) If P(A) = .55, P(B A) = .4, P(A B) = .22, and A and B are independent events, find P(B). A) .22 B) .4 C) .55

D) .88

Objective: (3.6) Determine if Events are Independent

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 222) In a box of 50 markers, 30 markers are either red or black, 20 are missing their caps, and 12 markers are either red or black and are missing their caps. Are the events "red or black" and "missing cap" dependent or independent? Explain. Objective: (3.6) Determine if Events are Independent

223) A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers showing is odd} B: {The sum of the numbers showing is 2, 11, or 12} Are A and B independent events? Explain. Objective: (3.6) Determine if Events are Independent

224) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows. A: {Both chips are the same color} B: {At least one of the chips is blue} Are A and B independent events? Explain. Objective: (3.6) Determine if Events are Independent

225) At a certain university, 70% of the students own cars. However, only 45% of the residence hall students own cars. Are the events owning a car and living in a residence hall independent? Explain. Objective: (3.6) Determine if Events are Independent

226) On a certain statistics test, 20% of the students earned a score of 90 or above. It was also true that 20% of the male students earned a score of 90 or above. Are the events earning a score of 90 or above and being male independent? Explain. Objective: (3.6) Determine if Events are Independent

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 227) Classify the events as dependent or independent: Events A and B where P(A) = 0.5, P(B) = 0.3, and P(A and B) = 0.15. A) dependent B) independent Objective: (3.6) Determine if Events are Independent

228) Classify the events as dependent or independent: Events A and B where P(A) = 0.4, P(B) = 0.6, and P(A and B) = 0.23. A) independent B) dependent Objective: (3.6) Determine if Events are Independent

229) Suppose two dice, one blue and one red, are rolled and the outcomes of each are recorded. We define the following two events: A: sum of the roll is 7 B. the result of the blue die is a number greater than 4 Are the two events, A and B, independent events? A) Yes

B) No

Objective: (3.6) Determine if Events are Independent

230) A basketball player has an 80% chance of making the first free-throw he shoots. If he makes the first free-throw shot, then he has a 90% chance of making the second free-throw he shoots. If he misses the first free-throw shot, then he only has a 70% chance of making the second free-throw he shoots. Suppose this player has been awarded two free-throw shots. Are the events, A - the player makes the first shot, and B - the player makes the second shot, independent events? A) Yes B) No Objective: (3.6) Determine if Events are Independent

Answer the question True or False. 231) If A and B are independent events, then A and B are also mutually exclusive. A) True B) False Objective: (3.6) Determine if Events are Independent

232) Two events, A and B, are independent if P(A and B) = P(A) × P(B). A) True B) False Objective: (3.6) Determine if Events are Independent

233) If A and B,are independent events, then P(A) = P(B A). A) True

B) False

Objective: (3.6) Determine if Events are Independent

Solve the problem. 234) Suppose that B1 and B2 are mutually exclusive and complementary events, such that P(B1 ) = .6 and P(B2 ) = .4. Consider another event A such that P(A | B1 ) = .2 and P(A | B2 ) = .5. Find P(A).

A) .32

B) .88

C) .70

D) .38

Objective: (3.7) Use Bayes's Rule

235) Suppose that B1 and B2 are mutually exclusive and complementary events, such that P(B1 ) = .6 and P(B2 ) = .4. Consider another event A such that P(A | B1 ) =.2 and P(A | B2 ) = .5. Find P(B1 | A).

A) .800

B) .625

C) .240

D) .375

Objective: (3.7) Use Bayes's Rule

236) Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given that the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid? A) 0.0995 B) 0.9552 C) 0.9325 D) 0.9928 Objective: (3.7) Use Bayes's Rule

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 237) An exit poll during a recent election revealed that 52% of those voting were women and 48% were men. The results also showed that 70% of the women voting favored Democratic candidates while only 40% of the men favored Democratic candidates. These poll results may be summarized as follows: P(woman) = .52 P(favored Democrats | woman) =.70 a. b. c. d. e.

P(man) = .48 P(favored Democrats | man) = .40

Find P(woman and favored Democrats). Find P(man and favored Democrats). Find P(favored Democrats). Find P(woman | favored Democrats). Find P(man | favored Democrats).

Objective: (3.7) Use Bayes's Rule

Answer Key Testname: SB14ECH3TEST

1) B 2) B 3) C 4) A 5) C 6) D 7) B 8) A 9) C 10) D 11) C 12) D 13) D 14) A 15) B 16) A 17) A 18) A 19) A 20) B 21) B 22) B 23) {yellow, blue, green, pink} 24) {1, 2, 3, 4, 5, 6, 7} 25) P(blue) = 6 6 = = 12 + 6 + 4 + 3 25 .24 1 26) = .125 8

27) P(A) = .3; P(B) = .4 28) P(A) = .3125; P(B) = .5 29) C 30) A 31) B 32) D 33) P(Neither patient survives) = P(DD) = 0.09 420 = .56 34) P(man) = 750

36) P(donates a dollar) = 7 = .7 10

47) a.

b3 , represent the blue chips and r the red chip. The sample space is { b1 b2 ,

37) a. {male, female} 85 b. P(male) = = 160

b1 b3 , b1 r, b2 b3 , b2 r, b3 r}.

.53125; P(female) = 75 = .46875 160

b. Each sample point is assigned the 1 probability . 6

38) C 39) B 40) D 41) B 42) C 43) C 44) B 45) D 46) a. {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} b. Each sample point is assigned the 1 probability . 8 c.

1 = 8

P(A) = P({b1 b2 ,

1 1 b1 b3 , b2 b3}) = + 6 6 + d.

1 1 = 6 2 P(B) = P({b1 r,

1 1 + b2 r, b3 r}) = + 6 6 1 1 = 6 2 e. P(C) = P( ) = 0 48) a. {economy, national security, not sure} b. P(economy) = .45, P(national security) = .35, P(not sure) = .20 c. P(economy) + P(national security) =.45 + .35 =.80 49) a. {gold, silver, bronze} 9 = b. P(gold) = 25

P(A) = P({HHH})

P(B) = P({HHT, 1 1 HTH, THH}) = + 8 8 +

Let b1 , b2 , and

1 3 = 8 8

e. P(C) = P({HHH, HHT, HTH, THH}) = 1 1 1 1 1 + + + = 8 8 8 8 2

.36, P(silver) =

9 = 25

.36, P(bronze) =

4 = 25

.28 c. P(gold) + 9 9 + = P(silver) = 25 25

35) P(receives government aid) = 240 = .3 800

18 = .72 25

50) a. {children’s, fiction, nonfiction, educational} b. Type of Book Children's Fiction Nonfiction Educational

Probabilit .10 .28 .49 .13

c. P(nonfiction) + P(educational) = .49 + .13 = .62 51) a. {Sedan, Convertible, Wagon, SUV, Van, Hatchback} b. Type of Car Sedan Convertible Wagon SUV Van Hatchback c. P(Van) + P(SUV) = .17 +.19 =.36

Prob . . . . . .

Answer Key Testname: SB14ECH3TEST

52) a. {1, 2, 3, 4, 9, 11, 14, 19, 22, 23, 24, 25, 29} 1 b. P(1) = , P(2) = 18 1 1 , P(3) = , P(4) = 18 18 1 1 , P(9) = , P(11) = 18 18 1 , 18 P(14) = =

1 , P(19) 18

1 1 , P(22) = , 18 18

P(23) =

1 , P(24) = 18

56) D 57) C 58) A 59) D 60) D 61) D 62) D 63) A 64) D 65) C 66) A 67) B 68) A 69) C 70) B 71) A 10 10! = = 72) 6 6!(10 - 6)! 10! = 210 6! 4!

1 , 18 P(25) = =

1 , P(29) 18

1 , 18

c. P(22) + P(23) + P(24) + P(25) + P(29) 1 1 1 = + + + 18 18 18 1 1 5 + = 18 18 18

53) a.

P(88) =

4 2 = 50 25

b. P(less than 60) = 3 50 c. P(between 70 and 79, inclusive) = 15 3 = 50 10

54) a. ABC, ACB, BAC, BCA, CAB, CBA 1 b. P({ABC}) = 6 c. P({BAC, BCA}) = 1 1 1 + = 6 6 3

55) A

80) B 81) A 82) B 83) D 84) a. A B C b. A B C 85) a. All three of the criteria are met. b. At least one of the three criteria is met. 86) D 87) D 88) A 89) B 90) A 91) B 92) B 93) A 94) D 95) C 96) A 97) B 98) A 99) C 100) B 101) C 102) C 103) A B = {E2, E3 }; P(A

73)

5 5! = = 1 1!(5 - 1)! 5! =5 1! 4!

15 15! = = 74) 6 6!(15 - 6)! 15! = 5005 6! 9!

75)

B) = P(E2 ) + P(E3 ) =

8 8! = = 3 3!(8 - 3)!

.3 + .1 = .4 104) A B = {E1, E2 , E3 ,

8! = 56 3! 5!

76) a.

E5 }; P(A B) = P(E1 )

6 6! = = 3 3!(6 - 3)!

+ P(E2 ) + P(E3 ) + P( E5 ) = .4 + .1 + .1 + .2 =

6! = 20; {ABC, 3! 3!

.8 105) P(Western US) = P(SW NW) = P(SW) + P(NW) = (3% + 12% + 10%) + (0% + 5% + 18%) = 25% + 23% = 48% = .48

ABD, ABE, ABF, ACD, ACE, ACF, ADE, ADF, AEF, BCD, BCE, BCF, BDE, BDF, BEF, CDE, CDF, CEF, DEF} 1 b. P(ADE) = = .05 20

77) A 78) C 79) A 46

106) P(white collar Republican) = P(white collar Republican) = 17% = . 17 107) a. {(1, 3), (1, 5), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5) (3, 6) (4, 2), (4, 3), (5, 1), (5, 3), (6, 3)} b. {(3, 3)} 15 c. P(A B) = = 36 5 12 d.

P(A B) =

1 36

108) a.

Let b1 and b2 represent the blue chips and r1 and r2 the red chips. A B = { b1 b2 , b1 r1 , b1 r2 , b2 r1 , b2 r2 , r1 r2 } b.

P(A B) =

6 =1 6

109) a. {Sedan, Convertible, SUV, Van} b. {Convertible} c. P(A B) = 7,204 + 9,089 + 13,691 + 15,387 81,589 =

45,821 81,589

.56

d. P(A B) = 9.089 .11 81,589

110) A 111) B 112) C 113) C 114) B 115) B

Answer Key Testname: SB14ECH3TEST

116) Ac is the event that an even number is rolled. 117) Bc = {3, 4, 6}

118) The applicant has a minimum college GPA of 3.0 and a sufficient score on the aptitude test but does not have relevant work experience. 119) The service is available less than 99% of the time or the reception is clear less than 95% of the time or at least 5% of the company’s customers have complaints about the quality of service. 120) A 121) A 122) D 123) D 124) A 125) A 126) B 127) P(Ac) = 1 - 0.37 = .63 128) The probability that the event does occur is 1 - .21 = .79. 129) Ac = {E4 , E5 }; P(Ac) = P(E4 ) + P(E5 ) = .1 + .3 = .4. 130) P(not a man) = 1 420 P(man) = 1 =1 750 - .56 = .44 131) P(does not receive government aid) = 1 - P(receives government aid) = 1 240 = 1 - .3 = .7 800

132) P(will not donate) = 1 - P(will donate) = 1 7 = 1 - .7 = .3 10

140) Events A and C are mutually exclusive since a number can not be both even and odd. 141) Yes, P(A B) is equal to the sum of P(A) and P(B) because events A and B are mutually exclusive. 142) No, P(A B) is not equal to the sum of P(A) and P(B) because events A and B are not mutually exclusive. 143) B 144) A 145) B 146) A 147) B 148) C 149) D 150) D 151) A 152) D 153) C 154) A 155) B 156) D 157) P(uses golf or tennis regularly) = P(golf) + P(tennis) - P(both tennis and golf) = .60 + .44 - .8 = .96 158) P(A B) = .37 + .69 .23 = .83 1 1 159) P(A B) = + = 3 4

133) a. At least one chip is not red. b. {b1 b2 , b1 r1 , b1 r2 , b2 r1 , b2 r2 } 5 c. P(Ac) = 6

134) a. {Sedan, Wagon, Hatchback} 42,972 b. P(Ac) = 81,589 .53 135) a. {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} b. {(1, 1), (1, 2), (2, 1), (2, 2)} c. {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} d. {(1, 1), (2, 2)} 8 e. P(Ac Bc) = = 36 2 9 f.

2 P(Ac Bc) = = 36

1 18

136) D 137) D 138) No, the events are not mutually exclusive. They have at least one sample point in common, (3, 4), for example. 139) Yes, the events are mutually exclusive. If the chips are both red, then neither of the chips is blue, so the events have no sample points in common.

7 12

160) If the events were mutually exclusive, then by the Additive Rule we would have P(A B) = .8 + .9 = 1.7, which is not a valid probability since it is greater than 1. So the events can not be mutually exclusive. 161) Yes, there is enough information, since catching a red snapper and catching a grouper are mutually exclusive events. The probability is .19 + .21 = .40. 162) No, there is not enough information, since catching a red snapper and catching a fish that weighs less than 5 pounds are probably not mutually exclusive events (It may be possible to catch a red snapper that weighs less than 5 pounds). 163) Using the Additive Rule, the probability is .62 + .35 - .20 = .77. 164) The Additive Rule states that P(A B) = P(A) + P(B) - P(A B), so P(A B) = P(A) + P(B) - P(A B) = .60 + .30 - .80 =.10. 165) B 166) C 167) C 168) D 169) B 170) D 171) D 172) B

Answer Key Testname: SB14ECH3TEST

173) D 174) D 175) B 176) C 177) B 178) C 179) C 180) C 181) B 182) B 183) C 184) P(man | does not live within 50 miles) = .39 = .5 .78 185) Let >100,000 = event that the city has a population over 100,000 and SW = event that the location is in the southwestern United States. P(>100,000 | SW) = P(>100,000 and SW) P(SW) =

7% = 0.318 22%

186) Let blue = event that the worker is a blue collar worker and Democrat = event the worker is a Democrat P(Democrat | blue) = P(Democrat and blue) P(blue) =

20% = 0.339 59%

P(A B) = 187) P(A | B) = P(B) .3 = .5; P(B | A) = .6 P(A B) .3 = = .6 P(B) .5

188) P(A | B) =

212) Let D be the event of a single child getting the disease.

P(A B) = P(B)

2/36 2 ; P(B | A) = 11/36 11 =

P(none get the disease) = P(Dc Dc Dc Dc) = P(Dc)P(

P(A B) 2/36 = = P(B) 6/36

1 3

189) P(A | B) = 9,089 7,204 + 9,089

Dc)P(Dc)P(Dc) = (0.6)(0.6)(0.6)(0.6) = = 0.1296 213) Let Li be the event

.558;

that stock i ends up in a total loss.

P(B | A) = 9.089 9,089 + 13,691 + 15,837

P(all three stocks end in total loss) = P(L1

.235 190) P(male | merit raise) .20 4 = = = .571 .35 7

191) P(A | B) =

L2 L3 ) = P(L1 ) × P(L2 ) × P( L3 ) = 0.37 × 0.37 × 0.37 = 0.051 214) P(woman and favored Democrats) = P(woman) P(favored Democrats | woman) = .55 × .65 = .3575

.1 + .1 .1 + .1 + .2

= .5 192) P(gold | not bronze) 9 = = .5 18

193) P(at least 25 | no fewer than 10) =

2 11

194) B 195) A 196) B 197) A 198) A 199) B 200) B 201) C 202) B 203) A 204) B 205) D 206) C 207) C 208) B 209) B 210) P(A B) = P(A) P(B A) = (.15)(.8) = .12 211) P(A B) = P(A) P(B) = (.32)(.55) = .176

215) Let Bi = event that the player can begin on roll i: P(cannot begin on first or second roll) = c P( B 1

c B 2 ) = P(

c c B 1) × (B 2) c c 15 P( B 1 ) = P( B 2 ) = 36 Dice combinations: (1, 4), (4, 1), (2, 3), (3, 2), (1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6) c P( B 2

c 21 × B 2) = 36

21 = .3403 36

216) P(teenager and male) = P(teenager) P(male teenager) = (.8)(.6) = .48 or 48% 217) P(green and 3) = P(green) P(3) = (.25)(.1) = .025 218) D 219) B 220) A 221) B 222) independent; P(red 30 or black) = - .6; 50 P(red or black missing cap) = .6

12 = 20

Answer Key Testname: SB14ECH3TEST

223) P(A) =

18 1 = and 36 2

P(A | B) =

2 1 = ; 4 2

Since these probabilities are equal, A and B are independent events. 2 1 224) P(A) = = and P(A 6 3 | B) =

1 ; Since these 5

probabilities are not equal, A and B are not independent events. 225) No; P(owning car) = .7 and P(owning car | residence hall) = .45; Since these probabilities are not equal, the events are not independent. 226) Yes; P(earning a 90 or above) = .2 and P(earning a 90 or above | male) =.2; Since these probabilities are equal, the events are independent. 227) B 228) B 229) A 230) B 231) B 232) A 233) B 234) A 235) D 236) C

237) a. P(woman and favored Democrats) = P(woman) × P(favored Democrats | woman) = .52 × .7 = .364 b. P(man and favored Democrats) = P(man) × P(favored Democrats | man) = .48 × .4 = .192 c. P(favored Democrats) = P(woman and favored Democrats) + P(man and favored Democrats) = .364 + .192 = .556 d. P(woman | favored Democrats) = P(woman and favored Democrats)/ P(favored Democrats) .364 .655 = .556 e. P(man | favored Democrats) = P(man and favored Democrats)/ P(favored Democrats) .192 .345 = .556

McClave Statistics for Business and Economics 14e Chapter 4 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Classify the following random variable according to whether it is discrete or continuous. The number of cups of coffee sold in a cafeteria during lunch A) discrete B) continuous Objective: (4.1) Classify Variables as Continuous or Discrete

2) Classify the following random variable according to whether it is discrete or continuous. The height of a player on a basketball team A) discrete B) continuous Objective: (4.1) Classify Variables as Continuous or Discrete

3) Classify the following random variable according to whether it is discrete or continuous. The blood pressures of a group of students the day before the final exam A) discrete B) continuous Objective: (4.1) Classify Variables as Continuous or Discrete

4) Classify the following random variable according to whether it is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska A) discrete B) continuous Objective: (4.1) Classify Variables as Continuous or Discrete

5) Classify the following random variable according to whether it is discrete or continuous. The number of goals scored in a soccer game A) continuous B) discrete Objective: (4.1) Classify Variables as Continuous or Discrete

6) Classify the following random variable according to whether it is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic A) continuous B) discrete Objective: (4.1) Classify Variables as Continuous or Discrete

7) Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day A) discrete B) continuous Objective: (4.1) Classify Variables as Continuous or Discrete

8) Classify the following random variable according to whether it is discrete or continuous. The number of pills in a container of vitamins A) discrete B) continuous Objective: (4.1) Classify Variables as Continuous or Discrete

9) 50 students were randomly sampled and asked questions about their exercise habits. One of the questions they were asked concerned the frequency of exercise, defined to be the number of times they exercised in a week. This variable would be characterized as which type of random variable? A) continuous B) discrete Objective: (4.1) Classify Variables as Continuous or Discrete

10) The school newspaper surveyed 100 commuter students and asked two questions. First, students were asked how many courses they were currently enrolled in. Second, the commuter students were asked to estimate how long it took them to drive to campus. Considering these two variables, number of courses would best be considered a _________ variable and drive time would be considered a _________ variable. A) continuous; discrete B) discrete; discrete C) continuous; continuous D) discrete; continuous Objective: (4.1) Classify Variables as Continuous or Discrete

11) Management at a home improvement store randomly selected 195 customers and observed their shopping habits. They recorded the number of items each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the managers of the home improvement store. A) number of items - continuous; total time - continuous B) number of items - continuous; total time - discrete C) number of items - discrete; total time - continuous D) number of items - discrete; total time - discrete Objective: (4.1) Classify Variables as Continuous or Discrete

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 12) A coin is flipped 6 times. The variable x represents the number of tails obtained. List the possible values of x. Is x discrete or continuous? Explain. Objective: (4.1) Classify Variables as Continuous or Discrete

13) A bottle contains 16 ounces of water. The variable x represents the volume, in ounces, of water remaining in the bottle after the first drink is taken. What are the natural bounds for the values of x? Is x discrete or continuous? Explain. Objective: (4.1) Classify Variables as Continuous or Discrete

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 14) A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability for the value of x = 5. x 2 3 5 8 10 p(x) 0.10 0.20 ??? 0.30 0.10

A) 0.2

B) 0.1

C) 0.3

Objective: (4.2) Construct Probability Distribution

D) 0.7

15) The Fresh Oven Bakery knows that the number of pies it can sell varies from day to day. The owner believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies, and she sells 200 pies on the remaining 25% of the days. To make sure she has enough product, the owner bakes 200 pies each day at a cost of $2.50 each. Assume any pies that go unsold are thrown out at the end of the day. If she sells the pies for $5 each, find the probability distribution for her daily profit. A) B) C) D) Profit P(profit) Profit P(profit) Profit P(profit) Profit P(profit) $500 .5 $250 .5 $300 .5 $0 .5 $750 .25 $375 .25 $550 .25 $250 .25 $1,000 .25 $500 .25 $800 .25 $500 .25 Objective: (4.2) Construct Probability Distribution

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 16) Explain why the following is or is not a valid probability distribution for the discrete random variable x. x p(x)

1 .1

3 .1

5 .2

7 .1

9 .2

Objective: (4.2) Construct Probability Distribution

17) Explain why the following is or is not a valid probability distribution for the discrete random variable x. x p(x)

1 .1

0 .2

1 .3

2 .3

3 .1

Objective: (4.2) Construct Probability Distribution

18) Explain why the following is or is not a valid probability distribution for the discrete random variable x. x p(x)

0 -.1

2 .1

4 .2

6 .3

8 .5

Objective: (4.2) Construct Probability Distribution

19) Explain why the following is or is not a valid probability distribution for the discrete random variable x. x p(x)

10 .3

20 .2

30 .2

40 .2

50 .2

Objective: (4.2) Construct Probability Distribution

20) Consider the given discrete probability distribution. Construct a graph for p(x). x p(x)

1 .1

2 .2

3 .2

4 .3

5 .2

Objective: (4.2) Construct Probability Distribution

21) Consider the given discrete probability distribution. Construct a graph for p(x). x p(x)

1 .30

2 .25

3 .20

4 .15

5 .05

6 .05

Objective: (4.2) Construct Probability Distribution

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 22) Consider the given discrete probability distribution. Find the probability that x equals 5. x 2 P(x) 0.28 A) 2.3

5 ?

6 0.01

9 0.17

B) 2.7

C) 0.54

D) 0.46

Objective: (4.2) Find Probability Given Distribution

23) Consider the given discrete probability distribution. Find the probability that x exceeds 4. x 2 P(x) 0.24 A) 0.76

4 ?

6 0.06

9 0.23

B) 0.47

C) 0.29

D) 0.71

Objective: (4.2) Find Probability Given Distribution

24) Consider the given discrete probability distribution. Find P(x > 3). x p(x)

1 .1

2 .2

A) .5

3 .2

4 .3

5 .2

B) .3

C) .7

D) .2

Objective: (4.2) Find Probability Given Distribution

25) Consider the given discrete probability distribution. Find P(x 4). x p(x)

A) .90

0 .30

1 .25

2 .20

3 .15

4 .05

B) .95

5 .05

C) .05

D) .10

Objective: (4.2) Find Probability Given Distribution

26) A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability that the random variable x is a value greater than 5. x 2 3 5 8 10 p(x) 0.10 0.20 0.30 0.30 0.10

A) 0.60

B) 0.40

C) 0.30

Objective: (4.2) Find Probability Given Distribution

D) 0.70

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 27) Consider the given discrete probability distribution. Find P(x < 2 or x > 3). x p(x)

1 .1

2 .2

3 .2

4 .3

5 .2

Objective: (4.2) Find Probability Given Distribution

28) Consider the given discrete probability distribution. Find P(x = 1 or x = 2). x p(x)

0 .30

1 .25

2 .20

3 .15

4 .05

5 .05

Objective: (4.2) Find Probability Given Distribution

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 29) A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below: Price Probability

$10.00 0.4

$12.50 0.15

$15.00 0.45

How much should the lab budget for next year's frog orders assuming this distribution does not change? (Hint: Find the expected price and assume 52 weeks per year.) A) $656.50 B) $12.63 C) $3,413,800.00 D) $1,263.00 Objective: (4.2) Find Expected Value

30) Mamma Temte bakes six pies each day at a cost of $2 each. On 33% of the days she sells only two pies. On 23% of the days, she sells 4 pies, and on the remaining 44% of the days, she sells all six pies. If Mama Temte sells her pies for $4 each, what is her expected profit for a day's worth of pies? [Assume that any leftover pies are given away.] A) $4.88 B) -$7.78 C) -$8.00 D) $16.88 Objective: (4.2) Find Expected Value

31) A local bakery has determined a probability distribution for the number of cheesecakes it sells in a given day. The distribution is as follows: Number sold in a day Prob (Number sold)

0 0.11

5 0.08

10 0.25

15 0.05

20 0.51

Find the number of cheesecakes that this local bakery expects to sell in a day. A) 13.85 B) 10 C) 13.96 Objective: (4.2) Find Expected Value

D) 20

32) A dice game involves rolling three dice and betting on one of the six numbers that are on the dice. The game costs $6 to play, and you win if the number you bet appears on any of the dice. The distribution for the outcomes of the game (including the profit) is shown below: Number of dice with your number 0 1 2 3

Profit -$6 $6 $8 $18

Probability 125/216 75/216 15/216 1/216

Find your expected profit from playing this game. A) $3.39 B) $0.50

C) -$0.77

D) $6.18

Objective: (4.2) Find Expected Value

Answer the question True or False. 33) The expected value of a discrete random variable must be one of the values in which the random variable can result. A) True B) False Objective: (4.2) Find Expected Value

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 34) An airline has requests for standby flights at half of the usual one-way air fare. Past experience has shown that these passengers have about a 1 in 5 chance of getting on the standby flight. When they fail to get on a flight as a standby, the only other choice is to fly first class on the next flight out. Suppose that the usual one-way air fare to a certain city is $160 and the cost of flying first class is $460. Should a passenger who wishes to fly to this city opt to fly as a standby? [Hint: Find the expected cost of the trip for a person flying standby.] Objective: (4.2) Find Expected Value

35) An automobile insurance company estimates the following loss probabilities for the next year on a $25,000 sports car: Total loss: 50% loss: 25% loss: 10% loss: No loss:

0.001 0.01 0.05 0.10 0.839

Assuming the company will sell only a $500 deductible policy for this model (i.e., the owner covers the first $500 damage), how much annual premium should the company charge in order to average $700 profit per policy sold? Objective: (4.2) Find Expected Value

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 36) Calculate the mean for the discrete probability distribution shown here. X 2 4 9 11 P(X) 0.26 0.18 0.29 0.27 A) 6.82

B) 1.705

C) 6.5

Objective: (4.2) Find Mean, Variance, Standard Deviation

D) 26

37) A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the mean of the distribution. x 2 3 5 8 10 p(x) 0.10 0.20 0.30 0.30 0.10

A) 5.7

B) 5.5

C) 5.0

D) 5.6

Objective: (4.2) Find Mean, Variance, Standard Deviation

38) A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the standard deviation of the distribution. x 2 3 5 8 10 p(x) 0.10 0.20 0.30 0.30 0.10

A) 1.845

B) 2.532

C) 5.7

D) 6.41

Objective: (4.2) Find Mean, Variance, Standard Deviation

39) A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below: Price Probability

$10.00 0.25

$12.50 0.15

$15.00 0.6

Suppose the mean cost of the frogs is $13.38 per week. Interpret this value. A) The average cost for all weekly frog purchases is $13.38. B) The median cost for the distribution of frog costs is $13.38. C) Most of the weeks resulted in frog costs of $13.38. D) The frog cost that occurs more often than any other is $13.38. Objective: (4.2) Find Mean, Variance, Standard Deviation

40) The random variable x represents the number of boys in a family with three children. Assuming that births of boys and girls are equally likely, find the mean and standard deviation for the random variable x. A) mean: 2.25; standard deviation: .87 B) mean: 1.50; standard deviation: .76 C) mean: 2.25; standard deviation: .76 D) mean: 1.50; standard deviation: .87 Objective: (4.2) Find Mean, Variance, Standard Deviation

41) In a pizza takeout restaurant, the following probability distribution was obtained for the number of toppings ordered on a large pizza. Find the mean and standard deviation for the random variable. x P(x) 0 .30 1 .40 2 .20 3 .06 4 .04 A) mean: 1.14; standard deviation: 1.04 C) mean: 1.30; standard deviation: 1.54

B) mean: 1.30; standard deviation: 2.38 D) mean: 1.54; standard deviation: 1.30

Objective: (4.2) Find Mean, Variance, Standard Deviation

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 42) Find the mean and standard deviation of the probability distribution for the random variable x, which represents the number of cars per household in a small town. x 0 1 2 3 4

P(x) .125 .428 .256 .108 .083

Objective: (4.2) Find Mean, Variance, Standard Deviation

43) Calculate the mean for the discrete probability distribution shown here. X 2 4 9 10 P(X) .2 .3 .3 .2 Objective: (4.2) Find Mean, Variance, Standard Deviation

44) Consider the given discrete probability distribution. x p(x) a.

1 .1

2 .2

3 .2

4 .3

5 .2

Find µ = E(x).

b. Find = E[(x - µ)2 ]. c. Find the probability that the value of x falls within one standard deviation of the mean. Compare this result to the Empirical Rule. Objective: (4.2) Find Mean, Variance, Standard Deviation

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 45) A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 37% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution? A) No, the employees would not be considered independent in the present sample. B) Yes, the sample is a random and independent sample. C) No, a binomial distribution requires only two possible outcomes for each experimental unit sampled. D) Yes, the sample size is n = 20. Objective: (4.3) Understand the Binomial Random Variable

46) Which binomial probability is represented on the screen below?

A) The probability of 8 failures in 2 trials where the probability of failure is .3. B) The probability of 8 successes in 2 trials where the probability of success is .3. C) The probability of 2 successes in 8 trials where the probability of success is .3. D) The probability of 2 successes in 8 trials where the probability of failure is .3. Objective: (4.3) Understand the Binomial Random Variable

47) Which binomial probability is represented on the screen below?

A) P(x 4)

B) P(x > 4)

C) P(x = 4)

D) P(x < 4)

Objective: (4.3) Understand the Binomial Random Variable

48) For a binomial distribution, which probability is not equal to the probability of 1 success in 5 trials where the probability of success is .4? A) the probability of 1 success in 5 trials where the probability of failure is .6 B) the probability of 4 failures in 5 trials where the probability of success is .6 C) the probability of 4 failures in 5 trials where the probability of success is .4 D) the probability of 4 failures in 5 trials where the probability of failure is .6 Objective: (4.3) Understand the Binomial Random Variable

49) Compute

7! . 3!(7 - 3)!

A) 70

B) 210

C) 35

D) 840

C) 84

D) 3024

Objective: (4.3) Understand the Binomial Random Variable

50) Compute A) 126

9 . 4

B) 15,120

Objective: (4.3) Understand the Binomial Random Variable

51) Compute

5 . 0

A) 5

B) 10

C) 1

D) undefined

C) 6

D) 4

C) 1

D) 5

Objective: (4.3) Understand the Binomial Random Variable

52) Compute

4 . 4

A) 16

B) 1

Objective: (4.3) Understand the Binomial Random Variable

53) Compute

5 . 4

A) 10

B) 20

Objective: (4.3) Understand the Binomial Random Variable

54) A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Which of the following is necessary for this problem to be analyzed using the binomial random variable? I. There are two outcomes possible for each of the 20 voters sampled. II. The outcomes of the 20 voters must be considered independent of one another. III. The probability a voter will actually vote is 0.70, the probability they won't is 0.30. A) II only B) III only C) I, II, and III

D) I only

Objective: (4.3) Understand the Binomial Random Variable

Answer the question True or False. 55) A binomial random variable is defined to be the number of units sampled until x successes is observed. A) True B) False Objective: (4.3) Understand the Binomial Random Variable

56) The binomial distribution can be used to model the number of rare events that occur over a given time period. A) True B) False Objective: (4.3) Understand the Binomial Random Variable

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 57) Compute

6 (.3)2 (.7)6-2 . 2

Objective: (4.3) Understand the Binomial Random Variable

58) For a binomial distribution, if the probability of success is .63 on the first trial, what is the probability of success on the second trial? Objective: (4.3) Understand the Binomial Random Variable

59) For a binomial distribution, if the probability of success is .48 on the first trial, what is the probability of failure on the second trial? Objective: (4.3) Understand the Binomial Random Variable

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round to four decimal places. 60) If x is a binomial random variable, compute p(x) for n = 6, x = 1, p = 0.2. A) 0.3460 B) 0.3657 C) 0.4129

D) 0.3932

Objective: (4.3) Find Probability

61) If x is a binomial random variable, compute p(x) for n = 6, x = 1, q = 0.2. A) 0.3932 B) 0.0014 C) 0.4168

D) 0.0015

Objective: (4.3) Find Probability

Solve the problem. 62) According to a recent study, 1 in every 8 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and asked each whether she has been a victim of domestic abuse at some point in her life. Find the probability that at least 2 of the women sampled have been the victim of domestic abuse. Round to six decimal places. A) 0.217333 B) 0.620391 C) 0.162276 D) 0.837724 Objective: (4.3) Find Probability

63) According to a recent study, 1 in every 10 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and asked each whether she has been a victim of domestic abuse at some point in her life. Find the probability that more than 22 of the women sampled have not been the victim of domestic abuse. A) 0.537094 B) 0.265888 C) -0.005318 D) 0.773503 Objective: (4.3) Find Probability

64) We believe that 91% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 32 students from the population and observed fewer than five in our sample who consider statistics to be an exciting subject. Make an inference about the belief that 91% of the students consider statistics to be an exciting subject. A) The 91% number is exactly right. B) The 91% number is too low. The real percentage is higher than 91%. C) The 91% number is too high. The real percentage is lower than 91%. D) It is impossible to make any inferences about the 91% number based on this information. Objective: (4.3) Find Probability

65) We believe that 91% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 31 students from the population. If the true percentage is really 91%, find the probability of observing 30 or more students who consider statistics to be an exciting subject. Round to six decimal places. A) 0.053738 B) 0.781504 C) 0.164758 D) 0.218496 Objective: (4.3) Find Probability

66) A literature professor decides to give a 10-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than .10. What score should be set as the lowest passing grade? A) 8 B) 7 C) 6 D) 9 Objective: (4.3) Find Probability

67) A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 42% of all employees believe their company president possesses low ethical standards. Assume that responses were randomly and independently collected. A president of a local company that employs 1,000 people does not believe the paper's claim applies to her company. If the claim is true, how many of her company's employees believe that she possesses low ethical standards? A) 420 B) 580 C) 42 D) 958 Objective: (4.3) Find Probability

68) A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 34% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled. Assuming the paper's claim is correct, find the probability that more than eight but fewer than 12 of the 20 sampled believe the company's president possesses low ethical standards. Round to six decimal places. A) 0.357678 B) 0.133574 C) 0.193391 D) 0.261917 Objective: (4.3) Find Probability

69) A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a binomial probability table to find the probability that more than 12 of the eligible voters sampled will vote in the next presidential election. A) 0.608 B) 0.228 C) 0.392 D) 0.772 E) 0.887 Objective: (4.3) Find Probability

70) A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a binomial probability table to find the probability that more than 10 but fewer than 16 of the 20 eligible voters sampled will vote in the next presidential election. A) 0.714 B) 0.649 C) 0.845 D) 0.780 Objective: (4.3) Find Probability

71) It a recent study of college students indicated that 30% of all college students had at least one tattoo. A small private college decided to randomly and independently sample 15 of their students and ask if they have a tattoo. Use a binomial probability table to find the probability that exactly 5 of the students reported that they did have at least one tattoo. A) 0.515 B) 0.207 C) 0.722 D) 0.218 Objective: (4.3) Find Probability

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 72) About 40% of the general population donate time and energy to community projects. Suppose 15 people have been randomly selected from a community and each asked whether he or she donates time and energy to community projects. Let x be the number who donate time and energy to community projects. Use a binomial probability table to find the probability that more than five of the 15 donate time and energy to community projects. Objective: (4.3) Find Probability

73) An automobile manufacturer has determined that 30% of all gas tanks that were installed on its 2002 compact model are defective. If 12 of these cars are independently sampled, what is the probability that more than half need new gas tanks? Objective: (4.3) Find Probability

74) A new drug is designed to reduce a person's blood pressure. Seventeen randomly selected hypertensive patients receive the new drug. Suppose the probability that a hypertensive patient's blood pressure drops if he or she is untreated is 0.5. Then what is the probability of observing 15 or more blood pressure drops in a random sample of 17 treated patients if the new drug is in fact ineffective in reducing blood pressure? Round to six decimal places. Objective: (4.3) Find Probability

75) A local newspaper claims that 70% of the items advertised in its classifieds section are sold within 1 week of the first appearance of the ad. To check the validity of the claim, the newspaper randomly selected n = 25 advertisements from last year's classifieds and contacted the people who placed the ads. They found that 11 of the 25 items sold within a week. Based on the newspaper's claim, is it likely to observe x 11 who sold their item within a week? Use a binomial probability table. Objective: (4.3) Find Probability

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 76) If x is a binomial random variable, calculate µ for n = 75 and p = 0.2. A) 37.5 B) 1.5 C) 12

D) 15

Objective: (4.3) Find Mean/Expected Value, Standard Deviation

77) If x is a binomial random variable, calculate 2 for n = 75 and p = 0.7. A) 36.75 B) 3.969 C) 15.75

D) 52.5

Objective: (4.3) Find Mean/Expected Value, Standard Deviation

78) If x is a binomial random variable, calculate necessary. A) 28 B) 5.292

for n = 40 and p = 0.7. Round to three decimal places when

C) 8.4

D) 2.898

Objective: (4.3) Find Mean/Expected Value, Standard Deviation

79) The probability that an individual is left-handed is 0.19. In a class of 100 students, what is the mean and standard deviation of the number of left-handed students? Round to the nearest hundredth when necessary. A) mean: 100; standard deviation: 3.92 B) mean: 100; standard deviation: 4.36 C) mean: 19; standard deviation: 3.92 D) mean: 19; standard deviation: 4.36 Objective: (4.3) Find Mean/Expected Value, Standard Deviation

80) A recent survey found that 77% of all adults over 50 wear glasses for driving. In a random sample of 70 adults over 50, what is the mean and standard deviation of the number who wear glasses? Round to the nearest hundredth when necessary. A) mean: 16.1; standard deviation: 7.34 B) mean: 16.1; standard deviation: 3.52 C) mean: 53.9; standard deviation: 3.52 D) mean: 53.9; standard deviation: 7.34 Objective: (4.3) Find Mean/Expected Value, Standard Deviation

81) According to a published study, 1 in every 8 men has been involved in a minor traffic accident. Suppose we have randomly and independently sampled twenty-five men and asked each whether he has been involved in a minor traffic accident. How many of the 25 men do we expect to have never been involved in a minor traffic accident? Round to the nearest whole number. A) 8 B) 3 C) 22 D) 25 Objective: (4.3) Find Mean/Expected Value, Standard Deviation

82) We believe that 81% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 39 students from the population. How many of the sampled students do we expect to consider statistics to be an exciting subject? A) 39 B) 32.16 C) 33.82 D) 31.59 Objective: (4.3) Find Mean/Expected Value, Standard Deviation

83) A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. How many of the sampled voters do we expect to vote in the next presidential election? A) 14 B) 6 C) 0.7 D) 0.3 Objective: (4.3) Find Mean/Expected Value, Standard Deviation

84) It a recent study of college students indicated that 30% of all college students had at least one tattoo. A small private college decided to randomly and independently sample 15 of their students and ask if they have a tattoo. Find the standard deviation for this binomial random variable. Round to the nearest hundredth when necessary. A) 4.5 B) 3.15 C) 1.77 D) 10.5 Objective: (4.3) Find Mean/Expected Value, Standard Deviation

85) The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 7. Find the probability that exactly two road construction projects are currently taking place in this city. A) 0.003437 B) 0.058360 C) 0.001316 D) 0.022341 Objective: (4.4) Find Probability (Poisson)

86) The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 5. Find the probability that more than four road construction projects are currently taking place in the city. A) 0.734974 B) 0.440493 C) 0.265026 D) 0.559507 Objective: (4.4) Find Probability (Poisson)

87) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.7. Find the probability that fewer than three accidents will occur next month on this stretch of road. A) 0.007920 B) 0.973797 C) 0.026203 D) 0.992080 Objective: (4.4) Find Probability (Poisson)

88) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7.6. Find the probability of observing exactly five accidents on this stretch of road next month. A) 0.855762 B) 11.521749 C) 0.105742 D) 1.423686 Objective: (4.4) Find Probability (Poisson)

89) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.2. Find the probability that exactly two accidents will occur on this stretch of road each of the next two months. A) 0.000010 B) 0.018468 C) 0.000085 D) 0.009234 Objective: (4.4) Find Probability (Poisson)

90) Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 4. Find the probability that exactly five babies will be born during a particular 1-hour period at this hospital. A) 0.000363 B) 0.019537 C) 0.156293 D) 0.000158 Objective: (4.4) Find Probability (Poisson)

91) Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 4. Some people believe that the presence of a full moon increases the number of births that take place. Suppose during the presence of a full moon, the hospital experienced eight consecutive hours with more than five births each hour. Based on this fact, comment on the belief that the full moon increases the number of births. A) The belief is supported as the probability of observing this many births would be 0.215. B) The belief is supported as the probability of observing this many births would be 0.00000457. C) The belief is not supported as the probability of observing this many births is 0.00000457. D) The belief is not supported as the probability of observing this many births is 0.215. Objective: (4.4) Find Probability (Poisson)

92) The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 5.1. Find the probability that fewer than six tickets are written on a randomly selected day. A) 0.747420 B) 0.401580 C) 0.598420 D) 0.252580 Objective: (4.4) Find Probability (Poisson)

93) The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 8.9. Find the probability that exactly four tickets are written on a randomly selected day. A) .941567 B) .964344 C) .058433 D) .035656 Objective: (4.4) Find Probability (Poisson)

94) The number of goals scored at each game by a certain hockey team follows a Poisson distribution with a mean of 6 goals per game. Find the probability that the team will score more than three goals during a game. A) 0.848796 B) 0.061969 C) 0.151204 D) 0.938031 Objective: (4.4) Find Probability (Poisson)

95) The number of goals scored at each game by a certain hockey team follows a Poisson distribution with a mean of 5 goals per game. Find the probability that the team scored exactly six goals in each of four randomly selected games. A) 0.00002919 B) 0.41510874 C) 0.58489126 D) 0.00045715 Objective: (4.4) Find Probability (Poisson)

96) An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with = 4.6 alarms per year. Find the probability that a randomly selected customer had more than 7 alarms reported. A) 0.087 B) 0.818 C) 0.905 D) 0.095 E) 0.182 Objective: (4.4) Find Probability (Poisson)

97) The number of homeruns hit during a major league baseball game follows a Poisson distribution with a mean of 3.2. Find the probability that a randomly selected game would have exactly 5 homeruns hit. A) 0.105 B) 0.114 C) 0.219 D) 0.895 Objective: (4.4) Find Probability (Poisson)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 98) A small life insurance company has determined that on the average it receives 6 death claims per day. Find the probability that the company receives at least seven death claims on a randomly selected day. Objective: (4.4) Find Probability (Poisson)

99) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.2. Find the probability that fewer than two accidents will occur on this stretch of road during a month. Objective: (4.4) Find Probability (Poisson)

100) Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 5. Find the probability that exactly three babies are born during a randomly selected hour. Objective: (4.4) Find Probability (Poisson)

101) Compute

x ex!

for

= 5 and x = 7.

Objective: (4.4) Find Probability (Poisson)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 102) The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5. Interpret the value of the mean. A) On half of the days less than 6.5 tickets are written and on half of the days have more than 6.5 tickets are written. B) If we sampled all days, the arithmetic average number of tickets written would be 6.5 tickets per day. C) The number of tickets that is written most often is 6.5 tickets per day. D) The mean has no interpretation since 0.5 ticket can never be written. Objective: (4.4) Find Mean/Expected Value, Standard Deviation (Poisson)

103) Suppose a Poisson probability distribution with random variable x.. Find µ for x. A) 10.8 B) 116.64

= 10.8 provides a good approximation of the distribution of a

10.8

D) 5.4

Objective: (4.4) Find Mean/Expected Value, Standard Deviation (Poisson)

104) Suppose a Poisson probability distribution with random variable x. Find for x. A) 139.24 B) 5.9

= 11.8 provides a good approximation of the distribution of a

C) 11.8

11.8

Objective: (4.4) Find Mean/Expected Value, Standard Deviation (Poisson)

105) An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with = 4.7 alarms per year. Identify the mean and standard deviation for this distribution. A) mean = 2.17, standard Deviation = 4.7 B) mean = 4.7, standard Deviation = 2.17 C) mean = 2.17, standard Deviation = 2.17 D) mean = 4.7, standard Deviation = 4.7 Objective: (4.4) Find Mean/Expected Value, Standard Deviation (Poisson)

106) The number of homeruns hit during a major league baseball game follows a Poisson distribution with = 3.2. Find the mean and standard deviation for this distribution. A) mean = 3.2, standard Deviation = 10.24 B) mean = 3.2, standard Deviation = 3.2 C) mean = 3.2, standard Deviation = 1.79 D) mean = 1.79, standard Deviation = 3.2 Objective: (4.4) Find Mean/Expected Value, Standard Deviation (Poisson)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 107) Suppose x is a random variable for which a Poisson probability distribution with = 3 provides a good approximation. a. b. c.

Graph p(x) for x = 0, 1, 2, 3, 4, 5, 6. Find µ and for x. What is the probability that x will fall in the interval µ ± ?

Objective: (4.4) Find Mean/Expected Value, Standard Deviation (Poisson)

108) A bank offers online banking to its customers free of charge. While online, customers can also sign up for additional services that the bank offers. Let x be the number of customers who sign up for additional services online each day. Suppose the distribution of x is approximated well by a Poisson distribution with mean = 42.3. Find E(x) and interpret its value. Objective: (4.4) Find Mean/Expected Value, Standard Deviation (Poisson)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 109) The conditions for both the hypergeometric and the binomial random variables require that each trial results in one of two outcomes. A) True B) False Objective: (4.4) Identify the Characteristics of a Hypergeometric Random Variable

110) The conditions for both the hypergeometric and the binomial random variables require that the trials are independent. A) True B) False Objective: (4.4) Identify the Characteristics of a Hypergeometric Random Variable

111) The hypergeometric random variable x counts the number of successes in the draw of n elements from a set of N elements containing r successes. A) True B) False Objective: (4.4) Identify the Characteristics of a Hypergeometric Random Variable

112) The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 12 elements containing 7 successes. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all possible values of x. A) True B) False Objective: (4.4) Identify the Characteristics of a Hypergeometric Random Variable

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 113) The hypergeometric random variable x counts the number of successes in the draw of 3 elements from a set of 8 elements containing 4 successes. List the possible values of x. Objective: (4.4) Identify the Characteristics of a Hypergeometric Random Variable

114) The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 10 elements containing 2 successes. List the possible values of x. Objective: (4.4) Identify the Characteristics of a Hypergeometric Random Variable

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 115) Given that x is a hypergeometric random variable, compute p(x) for N = 6, n = 3, r = 3, and x = 1. A) .375 B) .125 C) .45 D) .55 Objective: (4.4) Find Probability (Hypergeometric)

116) Given that x is a hypergeometric random variable, compute p(x) for N = 8, n = 5, r = 3, and x = 2. A) .343 B) .140 C) .536 D) .464 Objective: (4.4) Find Probability (Hypergeometric)

117) Given that x is a hypergeometric random variable with N = 10, n = 3, and r = 6, compute P(x = 0). A) 0 B) .216 C) .200 D) .033 Objective: (4.4) Find Probability (Hypergeometric)

118) Given that x is a hypergeometric random variable with N = 15, n = 6, and r = 10, compute P(x = 0). A) 1 B) .002 C) 0 D) .001 Objective: (4.4) Find Probability (Hypergeometric)

119) Suppose that 4 out of 12 liver transplants done at a hospital will fail within a year. Consider a random sample of 3 of these 12 patients. What is the probability that all 3 patients will result in failed transplants? A) .333 B) .037 C) .296 D) .018 Objective: (4.4) Find Probability (Hypergeometric)

120) Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions. A) .343 B) .143 C) .360 D) .160 Objective: (4.4) Find Probability (Hypergeometric)

121) As part of a promotion, both you and your roommate are given free cellular phones from a batch of 13 phones. Unknown to you, four of the phones are faulty and do not work. Find the probability that one of the two phones is faulty. A) .462 B) .231 C) .077 D) .538 Objective: (4.4) Find Probability (Hypergeometric)

122) Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability that none of the four cans selected contains an incorrect mix of paint. A) 0.01818 B) 0.50909 C) 0.21818 D) 0.25455 Objective: (4.4) Find Probability (Hypergeometric)

123) Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability that at least one of the four cans selected contains an incorrect mix of paint. A) 0.74545 B) 0.49091 C) 0.50909 D) 0.78182 Objective: (4.4) Find Probability (Hypergeometric)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 124) Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, find each probability. a. P(x = 0) b. P(x = 1) c. P(x 1) d. P(x 2) Objective: (4.4) Find Probability (Hypergeometric)

125) Given that x is a hypergeometric random variable with N = 8, n = 4, and r = 3: a. Display the probability distribution in tabular form. b. Find P(x 2). Objective: (4.4) Find Probability (Hypergeometric)

126) You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items? Objective: (4.4) Find Probability (Hypergeometric)

127) You test 4 items from a lot of 15. What is the probability that you will test no defective items if the lot contains 3 defective items? Objective: (4.4) Find Probability (Hypergeometric)

128) You randomly select 7 students from a class with 15 male and 20 female students. What is the probability that you will choose exactly 4 females? Objective: (4.4) Find Probability (Hypergeometric)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 129) Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, compute the mean of x. A) 2 B) 4 C) 1 D) 3 Objective: (4.4) Find Mean, Variance, Standard Deviation (Hypergeometric)

130) Given that x is a hypergeometric random variable with N = 8, n = 4, and r = 3, compute the variance of x. A) .469 B) .700 C) .538 D) .732 Objective: (4.4) Find Mean, Variance, Standard Deviation (Hypergeometric)

131) Given that x is a hypergeometric random variable with N = 9, n = 3, and r = 5, compute the standard deviation of x. A) .208 B) .745 C) .456 D) .556 Objective: (4.4) Find Mean, Variance, Standard Deviation (Hypergeometric)

132) Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the mean of this distribution. A) 12 B) 4 C) 3 D) 1 Objective: (4.4) Find Mean, Variance, Standard Deviation (Hypergeometric)

133) Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the standard deviation of this distribution. A) 0.739 B) 0.297 C) 1 D) 0.545 Objective: (4.4) Find Mean, Variance, Standard Deviation (Hypergeometric)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 134) Given that x is a hypergeometric random variable with N = 10, n = 3, and r = 5: a. Display the probability distribution in tabular form. b. Compute µ and for x. c. What is the probability that x will fall within the interval µ ± 2 Objective: (4.4) Find Mean, Variance, Standard Deviation (Hypergeometric)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 135) The number of children in a family can be modelled using a continuous random variable. A) True B) False Objective: (4.5) Understand Probability Distributions for Continuous Random Variable

136) For any continuous probability distribution, P(x = c) = 0 for all values of c. A) True B) False Objective: (4.5) Understand Probability Distributions for Continuous Random Variable

137) The total area under a probability distribution equals 1. A) True

B) False

Objective: (4.5) Understand Probability Distributions for Continuous Random Variable

138) For a continuous probability distribution, the probability that x is between a and b is the same regardless of whether or not you include the endpoints, a and b, of the interval. A) True B) False Objective: (4.5) Understand Probability Distributions for Continuous Random Variable

Solve the problem. 139) Use the standard normal distribution to find P(0 < z < 2.25). A) .5122 B) .4878 Objective: (4.6) Use Standard Normal Distribution

C) .7888

D) .8817

140) Use the standard normal distribution to find P(-2.25 < z < 0). A) .4878 B) .6831 C) .0122

D) .5122

Objective: (4.6) Use Standard Normal Distribution

141) Use the standard normal distribution to find P(-2.25 < z < 1.25). A) .8944 B) .0122 C) .8821

D) .4878

Objective: (4.6) Use Standard Normal Distribution

142) Use the standard normal distribution to find P(-2.50 < z < 1.50). A) .9270 B) .5496 C) .6167

D) .8822

Objective: (4.6) Use Standard Normal Distribution

143) Use the standard normal distribution to find P(z < -2.33 or z > 2.33). A) .9809 B) .7888 C) .0606

D) .0198

Objective: (4.6) Use Standard Normal Distribution

144) Find a value of the standard normal random variable z, called z0 , such that P(-z0 z z0 ) = 0.98. A) 1.645 B) 2.33 C) 1.96 D) .99 Objective: (4.6) Use Standard Normal Distribution

145) Find a value of the standard normal random variable z, called z0 , such that P(z z0 ) = 0.70. A) -.98 B) -.53 C) -.81 D) -.47 Objective: (4.6) Use Standard Normal Distribution

146) Find a value of the standard normal random variable z, called z 0 , such that P(z z 0 ) = 0.70. A) .81

B) .47

C) .53

D) .98

Objective: (4.6) Use Standard Normal Distribution

147) Which shape is used to represent areas for a normal distribution? A) Bell curve B) Rectangle C) Circle

D) Triangle

Objective: (4.6) Use Standard Normal Distribution

148) For a standard normal random variable, find the probability that z exceeds the value -1.65. A) 0.0495 B) 0.5495 C) 0.9505 D) 0.4505 Objective: (4.6) Use Standard Normal Distribution

149) For a standard normal random variable, find the point in the distribution in which 11.9% of the z-values fall below. A) 1.18 B) -1.45 C) -0.30 D) -1.18 Objective: (4.6) Use Standard Normal Distribution

Answer the question True or False. 150) The mean of the standard normal distribution is 1 and the standard deviation is 0. A) True B) False Objective: (4.6) Use Standard Normal Distribution

151) P(-1 < x < 0) = P(0 < x < 1) for any random variable x that is normally distributed. A) True B) False Objective: (4.6) Use Standard Normal Distribution

152) Nearly 100% of the observed occurrences of a random variable x that is normally distributed will fall within three standard deviations of the mean of the distribution of x. A) True B) False Objective: (4.6) Use Standard Normal Distribution

Solve the problem. 153) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 302 seconds. A) .5107 B) .9893 C) .4893 D) .0107 Objective: (4.6) Use Normal Distribution

154) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 60 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association? A) 371.3 seconds B) 393.2 seconds C) 568.7 seconds D) 546.8 seconds Objective: (4.6) Use Normal Distribution

155) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 50 seconds. Between what times do we expect approximately 95% of the boys to run the mile? A) between 362 and 558 seconds B) between 0 and 542.28 seconds C) between 365 and 555 seconds D) between 377.75 and 542.28 seconds Objective: (4.6) Use Normal Distribution

156) The weight of corn chips dispensed into a 48-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 48.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 48-ounce bags contain more than the advertised 48 ounces of chips? A) .0062 B) .4938 C) .5062 D) .9938 Objective: (4.6) Use Normal Distribution

157) The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.48 ounces and a standard deviation of 0.32 ounce. The company receives complaints from consumers who actually measure the amount of soda in the cans and claim that the volume is less than the advertised 12 ounces. What proportion of the soda cans contain less than the advertised 12 ounces of soda? A) .9332 B) .4332 C) .0668 D) .5668 Objective: (4.6) Use Normal Distribution

158) The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. Each can holds a maximum of 12.75 ounces of soda. Every can that has more than 12.75 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this process? A) .8413 B) .6587 C) .1587 D) .3413 Objective: (4.6) Use Normal Distribution

159) The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a standard deviation of 0.22 ounce. Every can that has more than 12.55 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that must be cleaned because of spillage to 3%? A) 12.9636 ounces B) 12.0726 ounces C) 12.1364 ounces D) 13.0274 ounces Objective: (4.6) Use Normal Distribution

160) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $500 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above, what is the probability that during a randomly selected month PCE's were between $375.00 and $590.00? A) .0421 B) .0001 C) .9999 D) .9579 Objective: (4.6) Use Normal Distribution

161) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $500 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the point in the distribution below which 2.5% of the PCE's fell. A) $487.50 B) $598.00 C) $12.50 D) $402.00 Objective: (4.6) Use Normal Distribution

162) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $900 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the probability that a randomly selected month had PCE's below $750. A) 0.9987 B) 0.8333 C) 0.0013 D) 0.1667 Objective: (4.6) Use Normal Distribution

163) The preventable monthly loss at a company has a normal distribution with a mean of $8,300 and a standard deviation of $50. A new policy was put into place, and the preventable loss the next month was $8,000. What inference can you make about the new policy? A) Because the probability that the monthly loss would be as low as $8,000 is small, the new policy is working. B) Because the probability that the monthly loss would be as low as $8,000 is not very small, the new policy is not working. C) The new policy is probably less effective than the one it replaced. D) While the probability that the monthly loss would be as low as $8,000 is small, it is not unexpected. Objective: (4.6) Use Normal Distribution

164) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2,800 miles. What is the probability a particular tire of this brand will last longer than 57,200 miles? A) .1587 B) .8413 C) .7266 D) .2266 Objective: (4.6) Use Normal Distribution

165) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 3,000 miles. What is the probability a certain tire of this brand will last between 53,700 miles and 54,600 miles? A) .9813 B) .4920 C) .4649 D) .0180 Objective: (4.6) Use Normal Distribution

166) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2,900 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty? A) 65,075 miles B) 57,100 miles C) 54,925 miles D) 62,900 miles Objective: (4.6) Use Normal Distribution

167) The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. Find the price for which 12.3% of milk vendors exceeded. A) $3.316 B) $3.238 C) $3.084 D) $3.215 Objective: (4.6) Use Normal Distribution

168) The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. What proportion of the milk vendors had prices that were less than $3.075 per gallon? A) 0.2112 B) 0.8944 C) 0.1056 D) 0.3944 Objective: (4.6) Use Normal Distribution

169) A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml) and a standard deviation of 0.4 ml. Answer the following questions based on this information. What proportion of the paint cans contain less than 5.54 ml of the dye? A) 0.9115 B) 0.0885 C) 0.5885 D) 0.9885 Objective: (4.6) Use Normal Distribution

170) A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml) and a standard deviation of 0.4 ml. Answer the following questions based on this information. Find the dye amount that represents the 9th percentile of the distribution. A) 4.936 ml B) 4.964 ml C) 5.536 ml D) 4.464 ml E) 4.836 ml Objective: (4.6) Use Normal Distribution

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 171) The rate of return for an investment can be described by a normal distribution with mean 28% and standard deviation 3%. What is the probability that the rate of return for the investment will be at least 23.5%? Objective: (4.6) Use Normal Distribution

172) The rate of return for an investment can be described by a normal distribution with mean 33% and standard deviation 3%. What is the probability that the rate of return for the investment exceeds 39%? Objective: (4.6) Use Normal Distribution

173) The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 513 and the standard deviation was 72. If the board wants to set the passing score so that only the best 10% of all applicants pass, what is the passing score? Assume that the scores are normally distributed. Objective: (4.6) Use Normal Distribution

174) The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 577 and the standard deviation was 72. If the board wants to set the passing score so that only the best 80% of all applicants pass, what is the passing score? Assume that the scores are normally distributed. Objective: (4.6) Use Normal Distribution

175) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 6,100 miles. If the manufacturer guarantees the tread life of the tires for the first 52,680 miles, what proportion of the tires will need to be replaced under warranty? Objective: (4.6) Use Normal Distribution

176) Farmers often sell fruits and vegetables at roadside stands during the summer. One such roadside stand has a daily demand for tomatoes that is approximately normally distributed with a mean of 536 tomatoes and a standard deviation of 30 tomatoes. If there are 494 tomatoes available to be sold at the roadside stand at the beginning of a day, what is the probability that they will all be sold? Objective: (4.6) Use Normal Distribution

177) Farmers often sell fruits and vegetables at roadside stands during the summer. One such roadside stand has a daily demand for tomatoes that is approximately normally distributed with a mean of 135 tomatoes and a standard deviation of 30 tomatoes. How many tomatoes must be available on any given day so that there is only a 1.5% chance that all tomatoes will be sold? Objective: (4.6) Use Normal Distribution

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 178) Suppose a random variable x is best described by a normal distribution with µ = 60 and corresponds to the value x = 69. 20 A) 69 B) C) 1 3

= 9. Find the z-score that

D) 9

Objective: (4.6) Use Normal Distribution

179) Suppose a random variable x is best described by a normal distribution with µ = 60 and corresponds to the value x = 80. A) 4 B) 3 C) 20

= 5. Find the z-score that

D) 5

Objective: (4.6) Use Normal Distribution

180) Suppose a random variable x is best described by a normal distribution with µ = 60 and that corresponds to the value x = 60. A) 1

B) 0

C) 11

= 11. Find the z-score

60 11

Objective: (4.6) Use Normal Distribution

181) Suppose a random variable x is best described by a normal distribution with µ = 60 and that corresponds to the value x = 15. A) 12 B) -3.75 C) -12 Objective: (4.6) Use Normal Distribution

= 12. Find the z-score

D) 3.75

182) IQ test scores are normally distributed with a mean of 101 and a standard deviation of 16. An individual's IQ score is found to be 112. Find the z-score corresponding to this value. A) -1.45 B) 1.45 C) -0.69 D) 0.69 Objective: (4.6) Use Normal Distribution

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 183) Determine if it is appropriate to use the normal distribution to approximate a binomial distribution when n = 12 and p = 0.1. Objective: (4.6) Determine if Normal Distribution Can be Used to Approximate Binomial

184) Determine if it is appropriate to use the normal distribution to approximate a binomial distribution when n = 50 and p = 0.4. Objective: (4.6) Determine if Normal Distribution Can be Used to Approximate Binomial

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 185) A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Can the normal approximation be used to estimate the binomial distribution in this problem? A) No B) Yes Objective: (4.6) Determine if Normal Distribution Can be Used to Approximate Binomial

Answer the question True or False. 186) The continuity correction factor is the name given to the .5 adjustment necessary when estimating the binomial with the normal distribution. A) True B) False Objective: (4.6) Determine if Normal Distribution Can be Used to Approximate Binomial

Find the probability. 187) Assume that x is a binomial random variable with n = 400 and p = 0.30. Use a normal approximation to find P(x > 110). A) 0.8621 B) 0.8749 C) 0.5438 D) 0.8508 Objective: (4.6) Find Probability

188) Assume that x is a binomial random variable with n = 400 and p = 0.30. Use a normal approximation to find P(x 140). A) 0.0125 B) 0.4090 C) 0.9834 D) 0.0166 Objective: (4.6) Find Probability

189) Assume that x is a binomial random variable with n = 100 and p = 0.60. Use a normal approximation to find P(x 65). A) 0.5910 B) 0.1314 C) 0.8686 D) 0.8212 Objective: (4.6) Find Probability

190) Assume that x is a binomial random variable with n = 100 and p = 0.60. Use a normal approximation to find P(x < 65). A) 0.8686 B) 0.5753 C) 0.1788 D) 0.8212 Objective: (4.6) Find Probability

191) Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find P(800 < x 830). A) 0.0753 B) 0.4760 C) 0.4920 D) 0.4741 Objective: (4.6) Find Probability

Solve the problem. 192) Transportation officials tell us that 60% of drivers wear seat belts while driving. Find the probability that more than 409 drivers in a sample of 650 drivers wear seat belts. A) 0.9406 B) 0.6 C) 0.4 D) 0.0594 Objective: (4.6) Find Probability

193) Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability of observing 518 or fewer drivers wearing seat belts in a sample of 700 drivers? A) approximately 0 B) 0.8 C) approximately 1 D) 0.2 Objective: (4.6) Find Probability

194) Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability that between 538 and 546 drivers in a sample of 700 drivers wear seat belts? A) 0.1003 B) 0.8997 C) 0.0166 D) 0.0837 Objective: (4.6) Find Probability

195) A certain baseball player hits a home run in 4% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits more than 16 home runs in 650 at-bats? A) 0.04 B) 0.9713 C) 0.96 D) 0.0287 Objective: (4.6) Find Probability

196) A certain baseball player hits a home run in 5% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits at most 23 home runs in 700 at-bats? A) 0.05 B) 0.95 C) 0.0233 D) 0.9767 Objective: (4.6) Find Probability

197) A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Find the approximate probability that more than 30 of the sampled students had at least one tattoo. A) 0.0071 B) 0.9929 C) 0.0034 D) 0.4929 Objective: (4.6) Find Probability

198) A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Find the approximate probability that more than 17 and less than 26 of the sampled students had at least one tattoo. A) 0.1800 B) 0.6644 C) 0.2422 D) 0.4222 Objective: (4.6) Find Probability

199) A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. How many home runs do we expect the baseball player to hit in 800 at-bats? A) 52.08 B) 807 C) 7 D) 56 Objective: (4.6) Find Mean, Standard Deviation, z-Score

200) A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Find the mean and standard deviation for this binomial distribution. A) Mean = 80, Standard Deviation = 15 B) Mean = 20, Standard Deviation = 3.87 C) Mean = 80, Standard Deviation = 3.87 D) Mean = 20, Standard Deviation = 15 Objective: (4.6) Find Mean, Standard Deviation, z-Score

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 201) It is against the law to discriminate against job applicants because of race, religion, sex, or age. Of the individuals who apply for an accountant's position in a large corporation, 38% are over 45 years old. If the company decides to choose 66 of a very large number of applicants for closer credential screening, claiming that the selection will be random and not age-biased, what is the z-value associated with fewer than 31 of those chosen being over 45 years old? (Assume that the applicant pool is large enough so that x, the number in the sample over 45 years old, has a binomial probability distribution.) Objective: (4.6) Find Mean, Standard Deviation, z-Score

202) A loan officer has 56 loan applications to screen during the next week. If past record indicates that she turns down 19% of the applicants, what is the z-value associated with 51 or more of the 56 applications being rejected? Objective: (4.6) Find Mean, Standard Deviation, z-Score

203) Suppose that 88% of the stocks listed on a particular exchange increased in value yesterday. Let x be the number of stocks that increased in value yesterday in a random of 72 stocks listed on the exchange. Find the mean and standard deviation of x. Objective: (4.6) Find Mean, Standard Deviation, z-Score

204) Suppose that 67% of the employees of a company participate in the company's medical savings program. Let x be the number of employees who participate in the program in a random sample of 50 employees. Find the mean and standard deviation of x. Objective: (4.6) Find Mean, Standard Deviation, z-Score

205) You are performing a study about the weight of preschoolers. A previous study found the weights to be normally distributed with a mean of 30 pounds and a standard deviation of 4 pounds. You randomly sample 30 preschool children and find their weights (in pounds) to be as follows. 25 29 33

25 29 33

26 30 34

26.5 30 34.5

27 30.5 35

27 31 35

27.5 31 37

28 32 37

28 32.5 38

28.5 32.5 38

Draw a histogram to display the data. Is it reasonable to assume that the weights are normally distributed? Why? Objective: (4.7) Determine if Data is Normally Distributed

206) The printout below contains summary statistics of the heights of a sample of 200 adult men in the United States. Descriptive Statistics: HT Variable HT

N 200

Mean 70.187

StDev 2.716

Minimum 62.375

Q1 67.875

Median 69.625

Q2 71.500

Maximum 91.125

Use the information in the printout to determine whether the distribution of heights is approximately normal. Explain your reasoning. Objective: (4.7) Determine if Data is Normally Distributed

207) The following data represent the scores of a sample of 50 students on a statistics exam. The mean score is x = 80.3, and the standard deviation is s = 11.37. 49 71 79 85 90

51 71 79 86 91

59 73 79 86 92

63 74 80 88 92

66 76 80 88 93

68 76 82 88 95

68 76 83 88 96

69 77 83 89 97

70 78 83 89 97

71 79 85 89 98

What percentage of the scores fall in each of the intervals x ± s, x ± 2s, and x ± 3s? Based on these percentages, do you believe that the distribution of scores is approximately normal? Explain. Objective: (4.7) Determine if Data is Normally Distributed

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 208) Which of the following statements is not a property of the normal curve? A) symmetric about µ B) P(µ - 3 < x < µ + 3 ) .997 C) mound-shaped (or bell shaped) D) P(µ - < x < µ + ) .95 Objective: (4.7) Determine if Data is Normally Distributed

209) Which of the following is not a method used for determining whether data are from an approximately normal distribution? A) Compute the intervals x ± s, x ± 2s, and x ± 3s. The percentages of measurements falling in each should be approximately 68%, 95%, and 100% respectively. B) Construct a normal probability plot. The points should fall approximately on a straight line. IQR 1.3. C) Find the interquartile range, IQR, and standard deviation, s, for the sample. Then s D) Construct a histogram or stem-and-leaf display. The shape of the graph or display should be uniform (evenly distributed). Objective: (4.7) Determine if Data is Normally Distributed

210) Which one of the following suggests that the data set is approximately normal? A) A data set with Q1 = 14, Q3 = 68, and s = 41. B) A data set with Q1 = 105, Q3 = 270, and s = 33. C) A data set with Q1 = 2.2, Q3 = 7.3, and s = 2.1. D) A data set with Q1 = 1330, Q3 = 2940, and s = 2440. Objective: (4.7) Determine if Data is Normally Distributed

211) Which one of the following suggests that the data set is not approximately normal? A) A data set with 68% of the measurements within x ± 2s. B) A data set with IQR = 752 and s = 574. C)

Stem 3 4 5 6 7 8

Leaves 0 3 9 2 4 7 1 3 4 0 0 5 1 1 5 2 7

7 8 6

8 6

9 7

9 8

Objective: (4.7) Determine if Data is Normally Distributed

212) If a data set is normally distributed, what is the proportion of measurements you would expect to fall within µ ± ? A) 68% B) 95% C) 50% D) 100% Objective: (4.7) Determine if Data is Normally Distributed

213) A statistician received some data to analyze. The sender of the data suggested that the data was normally distributed. Which of the following methods can be used to determine if the data is, in fact, normally distributed? I. Construct a histogram and/or stem-and-leaf display of the data and check the shape. II. Compute the intervals x ± s, x ± 2s, and x ± 3s, and determine the percentage of measurements falling each. Compare these percentages to 68%, 95%, and 100%. IQR III. Calculate a value of . If this value is approximately 1.3, then the data is normal. s IV. Construct a normal probability plot of the data. If the points fall on a straight line, then the data is A) III only B) IV only C) II only D) I only E) I, II, III, and IV Objective: (4.7) Determine if Data is Normally Distributed

normal.

214) Data has been collected and a normal probability plot for one of the variables is shown below. Based on your knowledge of normal probability plots, do you believe the variable in question is normally distributed? The data are represented by the"o" symbols in the plot.

A) Yes. The plot reveals a curve and this indicates the variable is normally distributed. B) No. The plot does not reveal a straight line and this indicates the variable is not normally distributed. C) Yes. The plot reveals a straight line and this indicates the variable is normally distributed. Objective: (4.7) Determine if Data is Normally Distributed

Answer the question True or False. 215) When the points on a normal probability plot lie approximately on a straight line, the data are approximately normally distributed. A) True B) False Objective: (4.7) Determine if Data is Normally Distributed

Find the probability. 216) Suppose x is a random variable best described by a uniform probability distribution with c = 10 and d = 70. Find P(10 x 25). A) 0.35 B) 0.25 C) 0.025 D) 0.15 Objective: (4.8) Find Probability (Uniform)

217) Suppose x is a random variable best described by a uniform probability distribution with c = 10 and d = 50. Find P(30 x 50). A) 0.2 B) 0.05 C) 0.5 D) 0.6 Objective: (4.8) Find Probability (Uniform)

218) Suppose x is a random variable best described by a uniform probability distribution with c = 40 and d = 80. Find P(x < 70). A) 0.075 B) 0.3 C) 0.85 D) 0.75 Objective: (4.8) Find Probability (Uniform)

219) Suppose x is a random variable best described by a uniform probability distribution with c = 10 and d = 50. Find P(x > 18). A) 0.8 B) 0.2 C) 0.08 D) 0.32 Objective: (4.8) Find Probability (Uniform)

220) Suppose x is a random variable best described by a uniform probability distribution with c = 20 and d = 80. Find P(x > 80). A) 0.5 B) 0.6 C) 1 D) 0 Objective: (4.8) Find Probability (Uniform)

221) Suppose x is a random variable best described by a uniform probability distribution with c = 120 and d = 40. Find P(x 120). A) 0 B) 0.5 C) 0.8 D) 1 Objective: (4.8) Find Probability (Uniform)

222) Suppose x is a uniform random variable with c = 30 and d = 60. Find P(x > 39). A) 0.3 B) 0.1 C) 0.9

D) 0.7

Objective: (4.8) Find Probability (Uniform)

223) Suppose x is a uniform random variable with c = 30 and d = 70. Find P(33 < x < 65). Round to the nearest hundredth when necessary. A) 0.2 B) 1 C) 0.5

D) 0.8

Objective: (4.8) Find Probability (Uniform)

Solve the problem. 224) Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 10. Find the value of a that makes the following probability statement true: P(x a) = 0.25. A) 4 B) 2 C) 4.4 D) 8 Objective: (4.8) Find Probability (Uniform)

225) Suppose x is a random variable best described by a uniform probability distribution with c = 5 and d = 7. Find the value of a that makes the following probability statement true: P(x a) = 0.25. A) 0.5 B) 6.1 C) 5.5 D) 6.5 Objective: (4.8) Find Probability (Uniform)

226) Suppose x is a random variable best described by a uniform probability distribution with c = 5 and d = 9. Find the value of a that makes the following probability statement true: P(5.5 x a) = 0.5. A) 7.5 B) 7 C) -0.4 D) 6 Objective: (4.8) Find Probability (Uniform)

227) Suppose x is a random variable best described by a uniform probability distribution with c = 6 and d = 12. Find the value of a that makes the following probability statement true: P(x a) = 1. A) a 12 B) a 6 C) a 6 D) a 12 Objective: (4.8) Find Probability (Uniform)

228) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 64°F to 92°F. What is the probability that the high temperature on a day in August exceeds 69°F? A) 0.1786 B) 0.0357 C) 0.4423 D) 0.8214 Objective: (4.8) Find Probability (Uniform)

229) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 68°F to 98°F. Find the temperature which is exceeded by the high temperatures on 90% of the days in August. A) 71°F B) 78°F C) 95°F D) 98°F Objective: (4.8) Find Probability (Uniform)

230) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 8.5 to 10.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 9.6 millimeters? A) 0.9143 B) 0.45 C) 0.5053 D) 4.5 Objective: (4.8) Find Probability (Uniform)

231) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 7.5 to 9.5 millimeters. Any ball bearing with a diameter of over 9.25 millimeters or under 7.75 millimeters is considered defective. What is the probability that a randomly selected ball bearing is defective? A) .75 B) .25 C) .50 D) 0 Objective: (4.8) Find Probability (Uniform)

232) A machine is set to pump cleanser into a process at the rate of 8 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 7.5 to 10.5 gallons per minute. What is the probability that at the time the machine is checked it is pumping more than 9.0 gallons per minute? A) .25 B) .50 C) .7692 D) .667 Objective: (4.8) Find Probability (Uniform)

233) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 9.0 to 11.0 gallons per minute. Would you expect the machine to pump more than 10.90 gallons per minute? A) Yes, since .95 is a high probability. B) No, since .05 is a low probability. C) No, since .95 is a high probability. D) Yes, since .05 is a high probability. Objective: (4.8) Find Probability (Uniform)

234) A machine is set to pump cleanser into a process at the rate of 7 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 9.5 gallons per minute. Find the probability that between 7.0 gallons and 8.0 gallons are pumped during a randomly selected minute. A) 1 B) 0 C) 0.67 D) 0.33 Objective: (4.8) Find Probability (Uniform)

235) Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 10 to 80. What is the probability that this experiment results in an outcome less than 20? Round to the nearest hundredth when necessary. A) 0.2 B) 0.14 C) 0.11 D) 1 Objective: (4.8) Find Probability (Uniform)

236) The age of customers at a local hardware store follows a uniform distribution over the interval from 18 to 60 years old. Find the probability that the next customer who walks through the door exceeds 50 years old. Round to the nearest ten-thousandth. A) 0.2381 B) 0.3600 C) 0.7619 D) 0.8333 Objective: (4.8) Find Probability (Uniform)

237) After a particular heavy snowstorm, the depth of snow reported in a mountain village followed a uniform distribution over the interval from 15 to 22 inches of snow. Find the probability that a randomly selected location in this village had between 17 and 18 inches of snow. Round to the nearest ten-thousandth. A) 0.2857 B) 0.4286 C) 0.1429 D) 0.5714 Objective: (4.8) Find Probability (Uniform)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 238) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 75°F to 95°F. What is the probability that a random day in August has a high temperature that exceeds 80°F? Objective: (4.8) Find Probability (Uniform)

239) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 4.5 to 7.5 millimeters. What is the probability of a randomly selected ball bearing having a diameter less than 6.5 millimeters? Objective: (4.8) Find Probability (Uniform)

240) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 9.5 gallons per minute. Find the probability that the machine pumps less than 8.75 gallons during a randomly selected minute. Objective: (4.8) Find Probability (Uniform)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 241) Which geometric shape is used to represent areas for a uniform distribution? A) Rectangle B) Triangle C) Bell curve

D) Circle

Objective: (4.8) Find Probability (Uniform)

242) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 5.5 to 7.5 millimeters. What is the mean diameter of ball bearings produced in this manufacturing process? A) 6.0 millimeters B) 6.5 millimeters C) 7.0 millimeters D) 7.5 millimeters Objective: (4.8) Find Mean, Variance, Standard Deviation (Uniform)

243) Suppose x is a uniform random variable with c = 20 and d = 50. Find the standard deviation of x. A) = 8.66 B) = 1.58 C) = 20.21 D) = 2.42 Objective: (4.8) Find Mean, Variance, Standard Deviation (Uniform)

244) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 10.5 gallons per minute. Find the variance of the distribution. A) 0.33 B) 6.75 C) 30.08 D) 0.08 Objective: (4.8) Find Mean, Variance, Standard Deviation (Uniform)

245) Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 30 to 90. What is the mean outcome of this experiment? A) 60 B) 90 C) 30 D) 65 Objective: (4.8) Find Mean, Variance, Standard Deviation (Uniform)

246) The age of customers at a local hardware store follows a uniform distribution over the interval from 18 to 60 years old. Find the average age of customers to this hardware store. A) 50 years old B) 39 years old C) 60 years old D) 45 years old Objective: (4.8) Find Mean, Variance, Standard Deviation (Uniform)

247) After a particular heavy snowstorm, the depth of snow reported in a mountain village followed a uniform distribution over the interval from 15 to 22 inches of snow. Find the standard deviation of the snowfall amounts. A) 2.02 inches B) 1.42 inches C) 18.5 inches D) 4.08 inches Objective: (4.8) Find Mean, Variance, Standard Deviation (Uniform)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 248) Suppose x is a uniform random variable with c = 40 and d = 60. Find the mean of the random variable x. Objective: (4.8) Find Mean, Variance, Standard Deviation (Uniform)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 249) The exponential distribution is sometimes called the waiting-time distribution, because it is used to describe the length of time between occurrences of random events. A) True B) False Objective: (4.8) Identify the Characteristics of an Exponential Distribution

250) The probability density function for an exponential random variable x has a graph called a bell curve. A) True B) False Objective: (4.8) Identify the Characteristics of an Exponential Distribution

251) The exponential distribution has the property that its mean equals its standard deviation. A) True B) False Objective: (4.8) Identify the Characteristics of an Exponential Distribution

252) The exponential distribution is governed by two quantities, µ and , that determine its shape and location A) True B) False Objective: (4.8) Identify the Characteristics of an Exponential Distribution

Solve the problem. 253) Determine the value of e-a A) 0.513417

for

=2 and a = 3. B) 0.223130

C) -4.481689

D) 4.481689

=1.5. Find P(x > 1). C) 0.223130

D) 0.486583

= 2.5. Find P(x 4). C) 0.464739

D) 0.798103

Objective: (4.8) Find Probability (Exponential)

254) Suppose that x has an exponential distribution with A) 0.776870 B) 0.513417 Objective: (4.8) Find Probability (Exponential)

255) Suppose that x has an exponential distribution with A) 0.535261 B) 0.201897 Objective: (4.8) Find Probability (Exponential)

256) Suppose that x has an exponential distribution with A) 0.472367 B) 0.736403

= 2. Find P(x < 1.5). C) 0.263597

D) 0.527633

= 5. Find P(x 10). C) 0.606531

D) 0.393469

Objective: (4.8) Find Probability (Exponential)

257) Suppose that x has an exponential distribution with A) 0.864665 B) 0.135335 Objective: (4.8) Find Probability (Exponential)

258) The time between customer arrivals at a furniture store has an approximate exponential distribution with mean = 8.5 minutes. If a customer just arrived, find the probability that the next customer will arrive in the next 5 minutes. A) 0.817316 B) 0.444694 C) 0.182684 D) 0.555306 Objective: (4.8) Find Probability (Exponential)

259) The time between customer arrivals at a furniture store has an approximate exponential distribution with mean = 8.5 minutes. If a customer just arrived, find the probability that the next customer will not arrive for at least 20 minutes. A) 0.904911 B) 0.346230 C) 0.653770 D) 0.095089 Objective: (4.8) Find Probability (Exponential)

260) The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5 years or more. A) 0.770210 B) 0.229790 C) 0.493383 D) 0.506617 Objective: (4.8) Find Probability (Exponential)

261) The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is less than 1 year. A) 0.254811 B) 0.745189 C) 0.966627 D) 0.033373 Objective: (4.8) Find Probability (Exponential)

262) The waiting time (in minutes) between ordering and receiving your meal at a certain restaurant is exponentially distributed with a mean of 10 minutes. The restaurant has a policy that your meal is free if you have to wait more than 25 minutes after ordering. What is the probability of receiving a free meal? A) 0.082085 B) 0.329680 C) 0.917915 D) 0.670320 Objective: (4.8) Find Probability (Exponential)

263) The time between arrivals at an ATM machine follows an exponential distribution with probability that more than 25 minutes will pass between arrivals. A) 0.082085 B) 0.670320 C) 0.917915

= 10 minutes. Find the

D) 0.329680

Objective: (4.8) Find Probability (Exponential)

264) The time between arrivals at an ATM machine follows an exponential distribution with probability that less than 25 minutes will pass between arrivals. A) 0.329680 B) 0.670320 C) 0.917915 Objective: (4.8) Find Probability (Exponential)

= 10 minutes. Find the

D) 0.082085

265) The time between arrivals at an ATM machine follows an exponential distribution with probability that between 15 and 25 minutes will pass between arrivals. A) 0.141045 B) 0.223130 C) 0.305215

= 10 minutes. Find the

D) 0.082085

Objective: (4.8) Find Probability (Exponential)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 266) Suppose that x has an exponential distribution with

= 1.75. Find each probability.

a. P(x 2) b. P(x < 2) Objective: (4.8) Find Probability (Exponential)

267) The length of time (in months) that a cashier works for a certain fast food restaurant is exponentially distributed with a mean of 7 months. a. Find the probability that a cashier works for the restaurant for at least 2 years. b. Find the probability that a cashier works for the restaurant for less than 1 month. Objective: (4.8) Find Probability (Exponential)

268) The time between equipment failures (in days) at a particular factory is exponentially distributed with a mean of 4.5 days. A machine just failed and was repaired today. a. Find the probability that another machine will fail within the next day. b. Find the probability that there will be no more equipment failures in the next week. Objective: (4.8) Find Probability (Exponential)

269) An online retailer reimburses a customer's shipping charges if the customer does not receive his order within one week. Delivery time (in days) is exponentially distributed with a mean of 3.2 days. What percentage of customers have their shipping charges reimbursed? Objective: (4.8) Find Probability (Exponential)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 270) Suppose that the random variable x has an exponential distribution with = 1.5. Find the mean and standard deviation of x. A) µ = 0; = 1 B) µ = 1.5; = 1 C) µ = 0; = 1.5 D) µ = 1.5; = 1.5 Objective: (4.8) Find Mean, Standard Deviation (Exponential)

271) Suppose that the random variable x has an exponential distribution with assume a value within the interval µ ± 2 . A) .049787 B) .864665 C) .716531

= 1.5. Find the probability that x will

D) .950213

Objective: (4.8) Find Mean, Standard Deviation (Exponential)

272) The time between arrivals at an ATM machine follows an exponential distribution with = 10 minutes. Find the mean and standard deviation of this distribution. A) Mean = 10, Standard Deviation = 10 B) Mean = 3.16, Standard Deviation = 3.16 C) Mean = 10, Standard Deviation = 100 D) Mean = 10, Standard Deviation = 3.16 Objective: (4.8) Find Mean, Standard Deviation (Exponential)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 273) Suppose that the random variable x has an exponential distribution with

= 3.

a. Find the probability that x assumes a value more than three standard deviations from µ. b. Find the probability that x assumes a value less than one standard deviation from µ. c. Find the probability that x assumes a value within a half standard deviation of µ. Objective: (4.8) Find Mean, Standard Deviation (Exponential)

Answer Key Testname: SB14ECH4TEST

1) A 2) B 3) B 4) B 5) B 6) A 7) A 8) A 9) B 10) D 11) C 12) possible values of x: {0, 1, 2, 3, 4, 5, 6}; The variable x is discrete since it has a finite number of distinct possible values. 13) natural bounds for x: 0 ounces and 16 ounces; The variable x is continuous since the values of x correspond to the points in some interval. 14) C 15) D 16) This is not a valid probability distribution because the sum of the probabilities is less than 1. 17) This is a valid probability distribution because the probabilities are all nonnegative and their sum is 1. 18) This is not a valid probability distribution because one of the probabilities given is negative.

19) This is not a valid probability distribution because the sum of the probabilities is greater than 1. 20)

34) Let x = cost of fare paid by passenger. The probability distribution for x is: x p(x)

$80 1/5

$460 4/5

The expected cost is E(x) = µ = $80

21)

x· p(x) =

1 4 + $460 = 5 5

35) To determine the premium, the insurance agency must first determine the average loss paid on the sports car. Let x = amount paid on the sports car loss. The probability distribution for x is:

$384.00

x p(x)

$24,500 .001

$12,000 .01

Since the expected cost is more than the usual one-way air fare, the passenger should not opt to fly as a standby.

Note: These losses paid have already considered the $500 deductible paid by the owner. The expected loss paid is: µ=

xp(x) = $24,500(.001) + $1

= $632 In order to average $700 profit per policy sold, the insurance company must charge an annual premium of $632 + $700 = $1,332.00. 36) A 37) A 38) B 39) A 40) D 41) A 42) µ = 1.596; = 1.098

22) C 23) C 24) A 25) B 26) B 27) P(x < 2 or x > 3) = p(x = 1) + p(x = 4) + p(x = 5) = .1 + 03 + .2 = .6 28) P(x = 1 or x = 2) = p(x = 1) + p(x = 2) = .25 + .20 = .45 29) A 30) A 31) A 32) C 33) B

43) µ =

x·p(x) = 2(.2) +

4(.3) + 9(.3) + 10(.2) = 6.3

Answer Key Testname: SB14ECH4TEST

44) a. µ = E(x) = 1(.1) + 2(.2) + 3(.2) + 4(.3) + 5(.2) = 3.3

58) Since the probability of success remains the same from trial to trial, the probability of success on the = b. second also 2 2 2 2 (.3) +trial 2.3 (.1) + 1.3 (.2) + 0.3 (.2) + 0.7 1.72is(.2) .63. 1.27. 59) Since the probability of success remains c. P(µ - < x < µ + the same from trial to ) = P(2.03 < x < 4.57) trial, the probability = .2 + .3 = .5; The of success on the Empirical Rule states second trial is .48, so that about .68 of the the probability of data lie within one failure on the second standard deviation of trial is 1 -.48 = .52. the mean for a 60) D mound-shaped 61) D symmetric 62) D distribution. For our 63) A distribution, this 64) C value is only .5, but it 65) D is not a surprise that 66) A these numbers aren't 67) A closer since our 68) C distribution is not 69) D symmetric. 70) A 45) C 71) B 46) C 72) X is a binomial 47) A random variable with 48) B n = 15 and p = 0.4. 49) C 50) A 51) C 52) B 53) D 54) C 55) B 56) B 6 (.3)2(.7)6-2 = 57) 2

6! (.3)2 (.7)4 = 2!(6 - 2)! 15(.09)(.2401) .324

74) Let x = the number of the 17 hypertensive patients whose blood pressure drops. Then X is a binomial random variable with n = 17 and p = .5. P(x 15) = P(x = 15) + P(x = 16) + P(x = 17) = 0.001175 75) Let x = the number of the 25 ads that resulted in the item being sold within a week. Then X is a binomial random variable with n = 25 and p = 0.70. P(x 11) = 0.006 (from a binomial probability table) A value of x that is less than or equal to 11 will occur in about 0.6% of all such samples. 76) D 77) C 78) D 79) C 80) C 81) C 82) D 83) A 84) C 85) D 86) D 87) A 88) C 89) C 90) C 91) B 92) C 93) D 94) A 95) D

P(x > 5) = 1 - P(x 5) = 1 - 0.403 (from a binomial probability table) = 0.597 73) Let x = the number of the 12 cars with defective gas tanks. Then X is a binomial random variable with n = 12 and p = .30. P(more than half) = P(x > 6) = P(x 7) = 1 - P(x 6) = 1 - 0.961 = 0.039

96) D 97) B 98) Let x = the number of death claims received per day. Then x is a Poisson random variable with = 6. P(x 7) = 1 - P(x 6) = 0.393697 99) Let x = the number of accidents that occur on the stretch of road during a month. Then x is a Poisson random variable with = 8.2. P(x < 2) = P(x = 0) + P(x = 1) = 0.002527 100) Let x = the number of babies born during a one-hour period at this hospital. Then x is a Poisson random variable with = 5. P(x = 3) = 0.140374 x e5 7 e-5 = = 101) x! 7!

.1044445 102) B 103) A 104) D 105) B 106) C

Answer Key Testname: SB14ECH4TEST

107) a.

124) a. P(x = 0) = 0 b. P(x = 1) =

b. µ = = 3; = µ = 3 1.73 c. P(µ - < x < µ + ) = P(1.27 < x < 4.73) = .22 + .22 + .17 = .61 108) E(x) = = 42.3; If the daily numbers of customers who sign up for additional services online were averaged for all days, the result would be 42.3 customers per day. 109) A 110) B 111) A 112) B 113) 0, 1, 2, 3 114) 0, 1, 2 115) C 116) C 117) D 118) C 119) D 120) A 121) A 122) D 123) A

6(1) 1 = 252 42

134) a.

6 4 1 4

b. µ =

3(5) = 1.5; 10

.024

3 12 0 4 15 4

.363; P(x 1) = 1 - P(x = 0) 1 - .363 = .637 20 15 4 3 128) P(x = 0) = 35 7 .328 129) D 130) C 131) B 132) D 133) A

5(10 - 5) · 3(10 - 3) 102 (9)

7 ; 12

7 12

c. P(-.028 < x < 3.028) = 1 135) B 136) A 137) A 138) A 139) B 140) A 141) C 142) A 143) D 144) B 145) B 146) C 147) A 148) C 149) D 150) B 151) B 152) A 153) D 154) B 155) A 156) D 157) C 158) C 159) C 160) D 161) D 162) C 163) A 164) B 165) D 166) C 167) A 168) C

b. P(x 2) = .071 + .429 + .429 = .929 2 10 0 3 126) P(x = 0) = 12 3

127) P(x = 0) =

p(x) .083 .417 .417 .083

10 5

c. P(x 1) = P(x = 0) + P(x = 1) 0 + .024 = .024 d. P(x 2) = 1 - P(x 1) 1 - .024 = .976 125) a. x p(x) 0 .071 1 .429 2 .429 3 .071

.545

x 0 1 2 3

.764

169) A 170) D 171) Let x be the rate of return. Then x is a normal random variable with µ = 28% and = 3%. To determine the probability that x is at least 23.5%, we need to find the z-value for x = 23.5%. z=

x-µ

23.5 - 28 = -1.5 3 P(x 23.5%) = P(-1.5 z) = .5 + P(-1.5 z 0) = .5 + .4332 = .9332 172) Let x be the rate of return. Then x is a normal random variable with µ = 33% and = 3%. To determine the probability that x exceeds 39%, we need to find the z-value for x = 39%. z=

x-µ

39 - 33 =2 3 P(x > 39%) = P(z 2) = .5 - P(0 z 2) = .5 - .4772 = .0228

Answer Key Testname: SB14ECH4TEST

173) Let x be a score on this exam. Then x is a normally distributed random variable with µ = 513 and = 72. We want to find the value of x 0 , such that

174) Let x be a score on this exam. Then x is a normally distributed random variable with µ = 577 and = 72. We want to find the value of x0 , such that

P(x > x 0 ) = .10. The

P(x > x 0 ) = .80. The

z-score for the value x = x 0 is

x0 - µ

x 0 - 513 72

x 0 - 577

P(x > x 0 ) = P z>

x 0 - 513 72

We find

x0 - µ

175) Let x be the tread life of this brand of tire. Then x is a normal random variable with µ = 60,000 and = 6100. To determine what proportion of tires fail before reaching 52,680 miles, we need to find the z-value for x = 52,680.

= z=

x 0 - 513 72

x 2 - 577 72

We find

52,680 - 60,000 = 6100 -1.20

P(x > x 0 ) = P = .10

x-µ

P(x 52,680) = P(z -1.20) = .5 - P(-1.20 z 0) = .5 - .3849 = .1151 176) Let x be the number of tomatoes sold per day. Then x is a normal random variable with µ = 536 and = 30.

= .80

x 0 - 577 72

1.28.

-.84.

x 0 - 513 = 1.28(72)

x 0 - 577 = -.84(72)

x 0 = 513 + 1.28(72) =

x 0 = 577 - .84(72) =

605.16

516.52

To determine the probability that all 494 tomatoes will be sold, we need to find the z-value for x = 494. z=

x-µ

494 - 536 = -1.4 30 P(x 494) = P(z -1.4) = .5 + P(-1.4 z 0) = .5 + .4192 = .9192

177) Let x be the number of tomatoes sold per day. Then x is a normal random variable with µ = 135 and = 30. We want to find the value x 0 , such that P(x > x 0 ) = .015. The z-value for the point x = x 0 is z=

x-µ

x0 - 135 30

P(x > x 0 ) = P(z > x 0 - 135 30

We find

)= .015 x 0 - 135 30

2.17 x 0 - 135 = 2.17(30) x 0 = 135 + 2.17(30) = 200 178) C 179) A 180) B 181) B 182) D 183) cannot use normal distribution 184) can use normal distribution 185) B 186) A 187) D 188) D 189) C 190) D 191) B 192) D 193) A 194) D 195) B 196) C

Answer Key Testname: SB14ECH4TEST

197) C 198) B 199) D 200) B 201) x is a binomial random variable with n = 66 and p = 0.38. z=

205)

211) A 212) A 213) E 214) B 215) A 216) B 217) C 218) D 219) A 220) D 221) D 222) D 223) D 224) A 225) D 226) A 227) A 228) D 229) A 230) B 231) B 232) B 233) B 234) D 235) B 236) A 237) C 238) Let x = high temperature in August. Then x is a uniform random variable with c = 75°F and d = 95°F.

(x + .5) - np = np(1 - p)

(31 + .5) - 66(0.38) = 66(0.38)(1 - 0.38) 1.63 202) Let x be the number of the 56 applications rejected. Then x is a binomial random variable with n = 56 and p = 0.19. (x - .5) - np z= = np(1 - p) (51 - .5) - 56(0.19) (56)(0.19)(1 - 0.19) = 13.58 203) Mean = µ = .88(72) = 63.36; standard deviation = = 72(.88)(.12) 2.76 204) Mean = µ = .67(72) = 33.5; standard deviation = = 50(.67)(.33) 3.32

It is not reasonable to assume that the heights are normally distributed since the histogram is not mound-shaped and symmetric about the mean of 31 pounds. IQR = 206) s 71.500 - 67.875 2.176 1.33; Since this number is reasonably close to 1.3, the distribution of heights is approximately normal. 207) The percentages are 70%, 96%, and 100%, respectively. Since these percentages are reasonably close to 68%, 95%, and 100%, we conclude that the distribution of scores is approximately normal. 208) D 209) D 210) A

P(x > a) =

d-a d-c

P(x > 80) = 15 = .75 20

95 - 80 = 95 - 75

239) Let x = ball bearing diameter. Then x is a uniform random variable with c = 4.5 and d = 7.5. P(x < a) =

a-c d-c

P(x < 6.5) = =

6.5 - 4.5 7.5 - 4.5

2 = 0.67 3

240) Let x = gallons pumped per minute. Then x is a uniform random variable with c = 8.5 and d = 9.5. P(x < a) =

a-c d-c

P(x < 8.75) = 8.75 - 8.5 .25 = = .25 9.5 - 8.5 1

241) A 242) B 243) A 244) A 245) A 246) B 247) A 248) µ = 50 249) A 250) B 251) A 252) B 253) B 254) B 255) B 256) D 257) A 258) B 259) D 260) B 261) A

c + d 40 + 60 = = 2 2

Answer Key Testname: SB14ECH4TEST

262) A 263) A 264) C 265) A 266) a. P(x 2) = e-2/1.75 .318907 b. P(x < 2) = 1 - P(x 2) = 1 - e-2/1.75 1 .318907 = .681093 267) a. P(x 24) = e-24/7 .032433 b. P(x < 1) = 1 - P(x 1) = 1 - e-1/7 1 -

.866878 = .133122 268) a. P(x < 1) = 1 - P(x 1) = 1 - e-1/4.5 1 .800737 = .199263 b. P(x > 7) = e-7/4.5 .211072

269) a. P(x 7) = e-7/3.2 .112197; about 11.2 percent 270) D 271) D 272) A 273) a. P(x < -6) + P(x > 12) = 0 + P(x > 12) = e-12/3 = e-4 .018316 b. P(0 < x < 6) = P(x < 6) = 1 - P(x 6) = 1 e-6/3 = 1 - e-2

.864665 c. P(1.5 < x < 4.5) = P(x 1.5) - P(x 4.5)= e-1.5/3 - e-4.5/3 = e-.5 - e-1.5 .383400

McClave Statistics for Business and Economics 14e Chapter 5 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 1) In most situations, the true mean and standard deviation are unknown quantities that have to be estimated. A) True B) False Objective: (5.1) Understand Sampling Distributions

2) The probability of success, p, in a binomial experiment is a parameter, while the mean and standard deviation, µ and , are statistics. A) True B) False Objective: (5.1) Understand Sampling Distributions

3) The sample mean, x, is a statistic. A) True

B) False

Objective: (5.1) Understand Sampling Distributions

4) The term statistic refers to a population quantity, and the term parameter refers to a sample quantity. A) True B) False Objective: (5.1) Understand Sampling Distributions

5) When estimating the population mean, the sample mean is always a better estimate than the sample median. A) True B) False Objective: (5.1) Understand Sampling Distributions

6) Sample statistics are random variables, because different samples can lead to different values of the sample statistics. A) True B) False Objective: (5.1) Understand Sampling Distributions

7) If x is a good estimator for µ, then we expect the values of x to cluster around µ. A) True B) False Objective: (5.1) Understand Sampling Distributions

8) The sampling distribution of a sample statistic calculated from a sample of n measurements is the probability distribution of the statistic. A) True B) False Objective: (5.1) Understand Sampling Distributions

Solve the problem. 9) The length of time a traffic signal stays green (nicknamed the "green time") at a particular intersection follows a normal probability distribution with a mean of 200 seconds and the standard deviation of 10 seconds. Use this information to answer the following questions. Which of the following describes the derivation of the sampling distribution of the sample mean? A) The mean and median of a large randomly selected sample of "green times" are calculated. Depending on whether or not the population of "green times" is normally distributed, either the mean or the median is chosen as the best measurement of center. B) The standard deviations of a large number of samples of size n randomly selected from the population of "green times" are calculated and their probabilities are plotted. C) The means of a large number of samples of size n randomly selected from the population of "green times" are calculated and their probabilities are plotted. D) A single sample of sufficiently large size is randomly selected from the population of "green times" and its probability is determined. Objective: (5.1) Understand Sampling Distributions

10) The probability distribution shown below describes a population of measurements. x 0 2 4 p(x) 1/3 1/3 1/3 Suppose that we took repeated random samples of n = 2 observations from the population described above. Which of the following would represent the sampling distribution of the sample mean?

A) C)

p(x) 1/3 1/3 1/3 x

p(x) 1/5 1/5 1/5 1/5 1/5

p(x) 1/9 2/9 3/9 2/9 1/9 x

p(x) 2/9 2/9 1/9 2/9 2/9

Objective: (5.1) Find Sampling Distribution

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 11) Consider the population described by the probability distribution below. x p(x)

2 .2

5 .5

7 .3

The random variable x is observed twice. The observations are independent. The different samples of size 2 and their probabilities are shown below. Sample 2, 2 2, 5 2, 7

Probability .04 .10 .06

Sample 5, 2 5, 5 5, 7

Probability .10 .25 .15

Sample 7, 2 7, 5 7, 7

Find the sampling distribution of the sample mean x. Objective: (5.1) Find Sampling Distribution

Probability .06 .15 .09

12) The probability distribution shown below describes a population of measurements that can assume values of 1, 4, 7, and 10, each of which occurs with the same frequency: x

1 1 4

p(x)

4 1 4

7 1 4

10 1 4

Consider taking samples of n = 2 measurements and calculating x for each sample. Construct the probability histogram for the sampling distribution of x. Objective: (5.1) Construct Histogram

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 13) The probability distribution shown below describes a population of measurements. x 0 2 4 p(x) 1/3 1/3 1/3 Suppose that we took repeated random samples of n = 2 observations from the population described above. Find the expected value of the sampling distribution of the sample mean. A) 0 B) 2 C) 3 D) 1 E) 4 Objective: (5.1) Find Expected Value

14) The sampling distribution of the sample mean is shown below. x

p(x) 1/9 2/9 3/9 2/9 1/9 Find the expected value of the sampling distribution of the sample mean. A) 7 B) 4 C) 6

D) 5

Objective: (5.1) Find Expected Value

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 15) The probability distribution shown below describes a population of measurements that can assume values of 1, 2, 3, and 4, each of which occurs with the same frequency: x p(x)

1 1 4

2 1 4

3 1 4

4 1 4

Find E(x) = µ. Then consider taking samples of n = 2 measurements and calculating x for each sample. Find the expected value, E(x), of x. Objective: (5.1) Find Expected Value

16) Consider the probability distribution shown here. x

6 1 3

p(x)

8 1 3

10 1 3

Let x be the sample mean for random samples of n = 2 measurements from this distribution. Find E(x) and E(x). Objective: (5.1) Find Expected Value

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 17) A point estimator of a population parameter is a rule or formula which tells us how to use sample data to calculate a single number that can be used as an estimate of the population parameter. A) True B) False Objective: (5.2) Understand Unbiasedness

18) A statistic is biased if the mean of the sampling distribution is equal to the parameter it is intended to estimate. A) True B) False Objective: (5.2) Understand Unbiasedness

Solve the problem. 19) Which of the following describes what the property of unbiasedness means? A) The center of the sampling distribution is found at the population parameter that is being estimated. B) The center of the sampling distribution is found at the population standard deviation. C) The shape of the sampling distribution is approximately normally distributed. D) The sampling distribution in question has the smallest variation of all possible sampling distributions. Objective: (5.2) Understand Unbiasedness

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 20) Consider the population described by the probability distribution below. x p(x)

3 .1

5 .7

7 .2

Find µ.

Find the sampling distribution of the sample mean x for a random sample of n = 2 measurements from the distribution.

Show that x is an unbiased estimator of µ.

Objective: (5.2) Understand Unbiasedness

21) Consider the population described by the probability distribution below. x p(x) a. b. c.

3 .1

5 .7

7 .2

Find 2 .

Find the sampling distribution of the sample variance s2 for a random sample of n = 2 measurements from the distribution. Show that s2 is an unbiased estimator of 2 .

Objective: (5.2) Understand Unbiasedness

22) Consider the population described by the probability distribution below. x p(x) a. b. c.

3 .1

5 .7

7 .2

Find µ. Find the sampling distribution of the sample median for a random sample of n = 2 observations from this population. Show that the median is an unbiased estimator of µ.

Objective: (5.2) Understand Unbiasedness

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 23) The ideal estimator has the greatest variance among all unbiased estimators. A) True B) False Objective: (5.2) Understand Minimum Variance

24) The minimum-variance unbiased estimator (MVUE) has the least variance among all unbiased estimators. A) True B) False Objective: (5.2) Understand Minimum Variance

Solve the problem. 25) Which of the following describes what the property of minimum variance means? A) The center of the sampling distribution is found at the population parameter that is being estimated. B) The shape of the sampling distribution is approximately normally distributed. C) The center of the sampling distribution is found at the population standard deviation. D) The sampling distribution in question has the smallest variation of all possible unbiased sampling distributions. Objective: (5.2) Understand Minimum Variance

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 26) Consider the population described by the probability distribution below. x p(x) a. b. c. d. e. f.

0 1 3

2 1 3

4 1 3

Find µ. Find the sampling distribution of the sample mean for a random sample of n = 3 measurements from this distribution. Find the sampling distribution of the sample median for a random sample of n = 3 observations from this population. Show that both the mean and the median are unbiased estimators of µ for this population. Find the variances of the sampling distributions of the sample mean and the sample median. Which estimator would you use to estimate µ? Why?

Objective: (5.2) Understand Minimum Variance

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 27) The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used? A) The sample size must be large (e.g., at least 30). B) The population size must be large (e.g., at least 30). C) The population from which we are sampling must be normally distributed. D) The population from which we are sampling must not be normally distributed. Objective: (5.3) Understand Central Limit Theorem

28) The Central Limit Theorem is important in statistics because _____. A) for a large n, it says the population is approximately normal B) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the population C) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size D) for any size sample, it says the sampling distribution of the sample mean is approximately normal Objective: (5.3) Understand Central Limit Theorem

29) Which of the following statements about the sampling distribution of the sample mean is incorrect? A) The sampling distribution is approximately normal whenever the sample size is sufficiently large (n 30). B) The mean of the sampling distribution is µ. C) The standard deviation of the sampling distribution is . D) The sampling distribution is generated by repeatedly taking samples of size n and computing the sample means. Objective: (5.3) Understand Central Limit Theorem

30) Which of the following does the Central Limit Theorem allow us to disregard when working with the sampling distribution of the sample mean? A) The mean of the population distribution. B) The standard deviation of the population distribution. C) The shape of the population distribution. D) All of the above can be disregarded when the Central Limit Theorem is used. Objective: (5.3) Understand Central Limit Theorem

31) The Central Limit Theorem is considered powerful in statistics because __________. A) it works for any sample provided the population distribution is known B) it works for any population distribution provided the population mean is known C) it works for any sample size provided the population is normal D) it works for any population distribution provided the sample size is sufficiently large Objective: (5.3) Understand Central Limit Theorem

Answer the question True or False. 32) As the sample size gets larger, the standard error of the sampling distribution of the sample mean gets larger as well. A) True B) False Objective: (5.3) Understand Central Limit Theorem

33) The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large. A) True B) False Objective: (5.3) Understand Central Limit Theorem

34) The standard error of the sampling distribution of the sample mean is equal to , the standard deviation of the population. A) True B) False Objective: (5.3) Understand Central Limit Theorem

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 35) A random sample of size n is to be drawn from a population with µ = 500 and = 300. What size sample would be necessary in order to reduce the standard error to 20? Objective: (5.3) Understand Central Limit Theorem

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 36) The daily revenue at a university snack bar has been recorded for the past five years. Records indicate that the mean daily revenue is $3,800 and the standard deviation is $350. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days are randomly selected and the average daily revenue computed. Which of the following describes the sampling distribution of the sample mean? A) skewed to the right with a mean of $3,800 and a standard deviation of $350 B) normally distributed with a mean of $380 and a standard deviation of $35 C) normally distributed with a mean of $3,800 and a standard deviation of $350 D) normally distributed with a mean of $3,800 and a standard deviation of $35 Objective: (5.3) Find Mean, Standard Deviation

37) The number of cars running a red light in a day, at a given intersection, possesses a distribution with a mean of 1.5 cars and a standard deviation of 4. The number of cars running the red light was observed on 100 randomly chosen days and the mean number of cars calculated. Describe the sampling distribution of the sample mean. A) approximately normal with mean = 1.5 and standard deviation = 4 B) approximately normal with mean = 1.5 and standard deviation = 0.4 C) shape unknown with mean = 1.5 and standard deviation = 4 D) shape unknown with mean = 1.5 and standard deviation = 0.4 Objective: (5.3) Find Mean, Standard Deviation

38) Suppose students' ages follow a skewed right distribution with a mean of 21 years old and a standard deviation of 2 years. If we randomly sample 500 students, which of the following statements about the sampling distribution of the sample mean age is incorrect? A) The mean of the sampling distribution is approximately 21 years old. B) The shape of the sampling distribution is approximately normal. C) The standard deviation of the sampling distribution is equal to 2 years. D) All of the above statements are correct. Objective: (5.3) Find Mean, Standard Deviation

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 39) The amount of time it takes a student to walk from her home to class has a skewed right distribution with a mean of 14 minutes and a standard deviation of 1.6 minutes. If times were collected from 40 randomly selected walks, describe the sampling distribution of x, the sample mean time. Objective: (5.3) Find Mean, Standard Deviation

40) Suppose a random sample of n = 36 measurements is selected from a population with mean µ = 256 and variance 2 = 144. Find the mean and standard deviation of the sampling distribution of the sample mean x. Objective: (5.3) Find Mean, Standard Deviation

41) Suppose a random sample of n = 64 measurements is selected from a population with mean µ = 65 and standard deviation = 12. Find the values of µx and x . Objective: (5.3) Find Mean, Standard Deviation

42) Suppose a random sample of n = 64 measurements is selected from a population with mean µ = 65 and standard deviation

= 12. Find the z-score corresponding to a value of x = 68.

Objective: (5.3) Find Mean, Standard Deviation

43) The weight of corn chips dispensed into a 10-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of .2 ounce. Suppose 100 bags of chips are randomly selected. Find the probability that the mean weight of these 100 bags exceeds 10.45 ounces. Objective: (5.3) Find Probability

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 44) The weight of corn chips dispensed into a 10-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of 0.1 ounce. Suppose 100 bags of chips are randomly selected. Find the probability that the mean weight of these 100 bags exceeds 10.6 ounces. A) approximately 0 B) .3085 C) .6915 D) .1915 Objective: (5.3) Find Probability

45) The average score of all golfers for a particular course has a mean of 68 and a standard deviation of 4. Suppose 64 golfers played the course today. Find the probability that the average score of the 64 golfers exceeded 69. A) .1293 B) .3707 C) .4772 D) .0228 Objective: (5.3) Find Probability

46) One year, the distribution of salaries for professional sports players had mean $1.6 million and standard deviation $0.9 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players that year exceeded $1.1 million. A) .7357 B) .2357 C) approximately 1 D) approximately 0 Objective: (5.3) Find Probability

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 47) Suppose a random sample of n = 64 measurements is selected from a population with mean µ = 65 and standard deviation

= 12. Find the probability that x falls between 65.75 an 68.75.

Objective: (5.3) Find Probability

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 48) A random sample of n = 600 measurements is drawn from a binomial population with probability of success .08. ^

Give the mean and the standard deviation of the sampling distribution of the sample proportion, p. A) .08; .011 B) .92; .011 C) .92; .003 D) .08; .003 Objective: (5.4) Find Mean, Standard Deviation

49) A random sample of n = 300 measurements is drawn from a binomial population with probability of success .26. ^

Give the mean and the standard deviation of the sampling distribution of the sample proportion, p. A) .26; .025 B) .74; .011 C) .26; .011 D) .74; .025 Objective: (5.4) Find Mean, Standard Deviation

50) A random sample of n = 300 measurements is drawn from a binomial population with probability of success .43. ^

Give the mean and the standard deviation of the sampling distribution of the sample proportion, p. A) 57; .014 B) .43; .029 C) .57; .029 D) .43; .014 Objective: (5.4) Find Mean, Standard Deviation

51) A random sample of n = 400 measurements is drawn from a binomial population with probability of success .21. ^

Give the mean and the standard deviation of the sampling distribution of the sample proportion, p. A) .21; .02 B) .21; .008 C) .79; .008 D) .79; .02 Objective: (5.4) Find Mean, Standard Deviation

52) Suppose a random sample of n measurements is selected from a binomial population with probability of success p = .35. Given n = 100, describe the shape, and find the mean and the standard deviation of the sampling ^

distribution of the sample proportion, p. A) approximately normal; 0.35, 0.048 C) skewed right; 35, 4.77

B) approximately normal; 0.35, 0.0023 D) skewed right; 0.35, 0.048

Objective: (5.4) Find Mean, Standard Deviation

Answer Key Testname: SB14ECH5TEST

1) A 2) B 3) A 4) B 5) B 6) A 7) A 8) A 9) C 10) B 11) 12)

22) a. µ = E(x) = .1(3) + .7(5) + .2(7) = 5.2 b. M 3 4 5 p(M) .01 .14 .53

1 16) E(x) = µ = (6)( ) + ( 3 1 1 8)( ) + (10)( ) = 8 3 3 1 2 E(x) = (6)( ) + (7)( ) 9 9

c. E(M) = .01(3) + .14(4) + .53(5) + .28(6) + .04(7) = 5.2; Since E(M) = µ, the sample median is an unbiased estimator of µ. 23) B 24) A 25) D 1 26) a. µ = E(x) = (0) + 3 6 7

p(x)

.01

.14

.53

.28

3 2 + (8)( ) + (9)( ) + ( 9 9 x

3.5

4.5

p(x)

.04

.20

.12

1 10)( ) = 8 6 97

A .09 .25 17).30 18) B 19) A 20) a. µ = E(x) = .1(3) + .7(5) + .2(7) = 5.2 b.

2.5 5.5 8.5

1 4 7 10

1 15) E(x) = (1)( ) + (2)( 4 1 1 1 ) + (3)( ) + (4)( ) 4 4 4 E(x) = (1)(

+ .7(5 - 5.2)2 + .2 (7 - 5.2)2 = 1.16

1 3 ) + ( )( 16 2

s2 p(s2 )

.54

.42

.04

p(x)

1 27

1 9

2 9

7 27

0 7 27

2 13 27

E(x) =

1 1 (0) + 27 9

2 2 4 7 (2) + + + 3 9 3 27

c. E(s2 ) = .54(0) + .42(2) + .04(8) = 1.16; Since E(s2 ) = 2 , s2 is an unbiased

estimator of 2.

2 3 2.5 ) + (2)( ) + ( )( 16 16 2 4 3 7 ) + (3)( ) + ( )( 16 16 2 2 1 ) + (4)( ) = 2.5 16 16

13 (0 - 2)2 + (2 - 2)2 + 27 8 10 4 3 7 3(4 - 2)2 = 56 27 27 2 1 1 9 f. 9 sample 27 mean; The variance is smaller. 27) A 28) B 29) C 30) C 31) D 32) B 33) B 34) B 35) The standard error is

2 8 1 10 1 + + (4) 9 3 9 3 27

= 2; Since E(x) = µ, the sample mean is an unbiased estimator of µ. 7 E(M) = (0) + 27

standard error is desired to be 20, we get: 300 20 = / n = n n

13 7 (2) + (4) = 2; 27 27 Since E(M) = µ, the

2 7 M = 27

4 7 27

2 1 10 -2 + 9 3

1 8 (4 - 2)2 = 27 9

4 3

2 2 8 -2 9 3 +

2 3

p(M)

2 2 1 2 -2 + 9 3 9

2 7 4 -2 + (2 - 2)2 3 27

13) B 14) C

= 2.5

E(x) = µ, x is an unbiased estimator of µ. 2 = .1(3 - 5.2)2 21) a.

1 1 .04 (2) + (4) = 2 3 3 b.

c. E(x) = .01(3) + .14(4) + .53(5) + .28(6) + .04(7) = 5.2; Since

6 .28

sample median is an unbiased estimator of µ. 7 2 1 2 e. .04 x = 27 (0 - 2)

. If the

· 20 = 300 = 15 36) D 37) B

n = 225

300 20

Answer Key Testname: SB14ECH5TEST

38) C 39) By the Central Limit Theorem, the sampling distribution of x is approximately normal with µx = µ = 14 minutes and x =

47) P(65.75 x 68.75) = P(.5 z 2.5) .3023 48) A 49) A 50) B 51) A 52) A

1.6 40

= 0.2530 minutes. 40) µx = µ = 256; x = 144 12 = =2 6 36

41) µx = µ = 65; x = 12 12 = = 1.5 8 64 42) z =

68 - 65 =2 1.5

43) P(x > 10.45) = P 10.45 - 10.50 z> .2/ 100 = P (z > -2.5) = .5 + .4938 = .9938

44) A 45) D 46) C 12

McClave Statistics for Business and Economics 14e Chapter 6 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Which statement best describes a parameter? A) A parameter is a numerical measure of a population that is almost always unknown and must be estimated. B) A parameter is a sample size that guarantees the error in estimation is within acceptable limits. C) A parameter is a level of confidence associated with an interval about a sample mean or proportion. D) A parameter is an unbiased estimate of a statistic found by experimentation or polling. Objective: (6.1) Define Target Parameter

2) A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. Which of the following would represent the target parameter of interest? A) p B) µ Objective: (6.1) Define Target Parameter

3) Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus. Which of the following would represent the target parameter of interest? A) p B) µ Objective: (6.1) Define Target Parameter

Answer the question True or False. 4) For data with two outcomes (success or failure), the binomial proportion of successes is likely to be the parameter of interest. A) True B) False Objective: (6.1) Define Target Parameter

5) For quantitative data, the target parameter is most likely to be the mode of the data. A) True B) False Objective: (6.1) Define Target Parameter

Solve the problem. 6) What is z /2 when A) 1.96

= 0.05?

B) 2.33

C) 2.575

D) 1.645

Objective: (6.2) Understand Confidence Level, Confidence Interval,

7) What is the confidence level of the following confidence interval for µ? x ± 1.96

A) 95%

B) 196%

C) 99%

Objective: (6.2) Understand Confidence Level, Confidence Interval,

D) 98%

8) The registrar's office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and surveys the first 200 students who park in the chosen lot on a given day. The confidence interval is A) not meaningful because the sampling distribution of the sample mean is not normal. B) meaningful because the sample size exceeds 30 and the Central Limit Theorem ensures normality of the sampling distribution of the sample mean. C) not meaningful because of the lack of random sampling. D) meaningful because the sample is representative of the population. Objective: (6.2) Understand Confidence Level, Confidence Interval,

9) A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (2.9%, 5.4%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight? A) 2.5% B) 2.70% C) 4.15% D) 1.25% Objective: (6.2) Understand Confidence Level, Confidence Interval,

10) A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($132,358, $150,362). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? A) Decrease the sample size and increase the confidence level. B) Decrease the sample size and decrease the confidence level. C) Increase the sample size and decrease the confidence level. D) Increase the sample size and increase the confidence level. Objective: (6.2) Understand Confidence Level, Confidence Interval,

11) Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 308 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. Which of the following should be used to estimate the parameter of interest for this problem? A) A small sample confidence interval for µ. B) A large sample confidence interval for p. C) A small sample confidence interval for p. D) A large sample confidence interval for µ. Objective: (6.2) Understand Confidence Level, Confidence Interval,

12) Explain what the phrase 95% confident means when we interpret a 95% confidence interval for µ. A) In repeated sampling, 95% of similarly constructed intervals contain the value of the population mean. B) The probability that the sample mean falls in the calculated interval is 0.95. C) 95% of similarly constructed intervals would contain the value of the sampled mean. D) 95% of the observations in the population fall within the bounds of the calculated interval. Objective: (6.2) Understand Confidence Level, Confidence Interval,

13) Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus. A survey of 338 College of Business (COBA) students yields the following descriptive information regarding the length of time (in minutes) it took them to find a parking spot. Note that the "Lo 95%" and "Up 95%" refer to the endpoints of the desired confidence interval. Variable N Lo 95% CI Parking Time 338 9.1944

Mean 10.466

Up 95% CI SD 11.738 11.885

University officials have determined that the confidence interval would be more useful if the interval were narrower. Which of the following changes in the confidence level would result in a narrower interval? A) The university could increase their confidence level. B) The university could decrease their confidence level. Objective: (6.2) Understand Confidence Level, Confidence Interval,

14) A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects (60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00). What value of alpha was used to create this confidence interval? A) 0.05 B) 0.025 C) 0.10 D) 0.01 Objective: (6.2) Understand Confidence Level, Confidence Interval,

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 15) Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of µ. Objective: (6.2) Understand Confidence Level, Confidence Interval,

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 16) One way of reducing the width of a confidence interval is to reduce the confidence level. A) True B) False Objective: (6.2) Understand Confidence Level, Confidence Interval,

17) The Central Limit Theorem guarantees an approximately normal sampling distribution for the sample mean for large sample sizes, so no knowledge about the distribution of the population is necessary for the corresponding interval to be valid. A) True B) False Objective: (6.2) Understand Confidence Level, Confidence Interval,

18) Since the population standard deviation is almost always known, we use it instead of the sample standard deviation s when finding a confidence interval. A) True B) False Objective: (6.2) Understand Confidence Level, Confidence Interval,

19) The confidence coefficient is the relative frequency with which the interval estimator encloses the population parameter when the estimator is used repeatedly a very large number of times. A) True B) False Objective: (6.2) Understand Confidence Level, Confidence Interval,

20) The confidence level is the confidence coefficient expressed as a percentage. A) True B) False Objective: (6.2) Understand Confidence Level, Confidence Interval,

Solve the problem. 21) What is the confidence coefficient in a 95% confidence interval for µ? A) .95 B) .025 C) .05

D) .475

Objective: (6.2) Understand Confidence Level, Confidence Interval,

22) Which information is not shown on the screen below?

A) the sample size C) the sample mean

B) the confidence level D) the sample standard deviation

Objective: (6.2) Understand Confidence Level, Confidence Interval,

23) Find z /2 for the given value of . = 0.01 A) 2.05

B) 0.19

C) 2.575

D) 2.33

Objective: (6.2) Calculate, Interpret Confidence Interval

24) Determine the confidence level for the given confidence interval for µ. x ± 2.05

A) 96%

B) 98%

C) 94%

D) 2%

Objective: (6.2) Calculate, Interpret Confidence Interval

25) A random sample of n measurements was selected from a population with unknown mean µ and known standard deviation . Calculate a 95% confidence interval for µ for the given situation. Round to the nearest hundredth when necessary. n = 150, x = 54, A) 54 ± 0.13

= 10

B) 54 ± 19.6

C) 54 ± 1.34

Objective: (6.2) Calculate, Interpret Confidence Interval

D) 54 ± 1.6

26) A 99% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($95,121, $110,053). Give a practical interpretation of the interval. A) We are 99% confident that the mean salary of all CEOs in the electronics industry falls in the interval $95,121 to $110,053. B) We are 99% confident that the mean salary of the sampled CEOs falls in the interval $95,121 to $110,053. C) 99% of all CEOs in the electronics industry have salaries that fall between $95,121 to $110,053. D) 99% of the sampled CEOs have salaries that fell in the interval $95,121 to $110,053. Objective: (6.2) Calculate, Interpret Confidence Interval

27) A random sample of 250 students at a university finds that these students take a mean of 15 credit hours per quarter with a standard deviation of 2 credit hours. Estimate the mean credit hours taken by a student each quarter using a 99% confidence interval. Round to the nearest thousandth. A) 15 ± .015 B) 15 ± .021 C) 15 ± .326 D) 15 ± .230 Objective: (6.2) Calculate, Interpret Confidence Interval

28) A random sample of 250 students at a university finds that these students take a mean of 14.5 credit hours per quarter with a standard deviation of 2.2 credit hours. The 90% confidence interval for the mean is 14.5 ± 0.229. Interpret the interval. A) We are 90% confident that the average number of credit hours per quarter of students at the university falls in the interval 14.271 to 14.729 hours. B) We are 90% confident that the average number of credit hours per quarter of the sampled students falls in the interval 14.271 to 14.729 hours. C) 90% of the students take between 14.271 to 14.729 credit hours per quarter. D) The probability that a student takes 14.271 to 14.729 credit hours in a quarter is 0.90. Objective: (6.2) Calculate, Interpret Confidence Interval

29) The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 49 different 24-hour periods and determines the number of admissions for each. For this sample, x = 19.3 and s2 = 16. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval. A) 19.3 ± .543 B) 19.3 ± 4.480

C) 19.3 ± 1.120

D) 19.3 ± .160

Objective: (6.2) Calculate, Interpret Confidence Interval

30) Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 309 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. If the mean and standard deviation of the sample are x = 9.1 hours and s = 3.5 hours, find a 99% confidence interval for the true mean number of hours a union member is absent per month. Round to the nearest thousandth. A) 9.1 ± .274 B) 9.1 ± .197 C) 9.1 ± .513 D) 9.1 ± .029 Objective: (6.2) Calculate, Interpret Confidence Interval

31) Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus. A survey of 338 College of Business (COBA) students yields the following descriptive information regarding the length of time (in minutes) it took them to find a parking spot. Note that the "Lo 95%" and "Up 95%" refer to the endpoints of the desired confidence interval. Variable N Lo 95% CI Parking Time 338 9.1944

Mean 10.466

Up 95% CI SD 11.738 11.885

Give a practical interpretation for the 95% confidence interval given above. A) 95% of the COBA students had parking times that fell between 9.19 and 11.74 minutes. B) 95% of the COBA students had parking times of 10.466 minutes. C) We are 95% confident that the average parking time of the 338 COBA students surveyed falls between 9.19 and 11.74 minutes. D) We are 95% confident that the average parking time of all COBA students falls between 9.19 and 11.74 minutes. Objective: (6.2) Calculate, Interpret Confidence Interval

32) Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus. A survey of 338 College of Business (COBA) students yields the following descriptive information regarding the length of time (in minutes) it took them to find a parking spot. Note that the "Lo 95%" and "Up 95%" refer to the endpoints of the desired confidence interval. Variable N Lo 95% CI Parking Time 338 9.1944

Mean 10.466

Up 95% CI SD 11.738 11.885

Explain what the phrase "95% confident" means when working with a 95% confidence interval. A) In repeated sampling, 95% of the intervals created will contain the population mean. B) In repeated sampling, 95% of the population means will fall within the interval created. C) 95% of the observations in the population will fall within the endpoints of the interval. D) In repeated sampling, 95% of the sample means will fall within the interval created. Objective: (6.2) Calculate, Interpret Confidence Interval

33) A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects (60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00). State the appropriate interpretation for this confidence interval. Note that all answers begin with "We are 95 percent confidence that…" A) The average term life insurance cost for sampled 65 subjects falls between $850.00 and $1050.00 B) The average term life insurance costs for all 60-year-old male non-smokers falls between $850.00 and $1050.00 C) The term life insurance cost of the retired statistician's insurance policy falls between $850.00 and $1050.00 D) The term life insurance cost for all 60-year-old male non-smokers' insurance policies falls between $850.00 and $1050.00 Objective: (6.2) Calculate, Interpret Confidence Interval

34) A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects (60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00). Explain what the phrase "95 percent confident" means in this situation. A) 95 percent of all the life insurance costs will fall within the specified interval. B) In repeated sampling, 95 percent of the intervals constructed would contain the value of the true population mean. C) In repeated sampling, the mean of the population will fall within the specified intervals 95 percent of the time. D) 95 percent of all retired statisticians are underinsured. Objective: (6.2) Calculate, Interpret Confidence Interval

35) How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show that the sample mean was $70.00 and prior sampling indicated that the population standard deviation was $17.50. Use this information to create a 95 percent confidence interval for the population mean. 17.50 17.50 17.50 17.50 A) 70 ± 1.833 B) 70 ± 1.645 C) 70 ± 1.671 D) 70 ± 1.960 60 60 60 60 Objective: (6.2) Calculate, Interpret Confidence Interval

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 36) How much money does the average professional football fan spend on food at a single football game? That question was posed to 59 randomly selected football fans. The sample results provided a sample mean and standard deviation of $14.00 and $3.10, respectively. Find and interpret a 99% confidence interval for µ. Objective: (6.2) Calculate, Interpret Confidence Interval

37) To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded a mean nicotine content of 25 milligrams and standard deviation of 2.6 milligrams for a sample of n = 82 cigarettes. Find a 95% confidence interval for µ. Objective: (6.2) Calculate, Interpret Confidence Interval

38) The following data represent the scores of a sample of 50 randomly chosen students on a standardized test. 39 71 79 85 90 a. b.

48 71 79 86 91

55 73 79 86 92

63 74 80 88 92

66 76 80 88 93

68 76 82 88 95

68 76 83 88 96

69 77 83 89 97

70 78 83 89 97

71 79 85 89 99

Write a 95% confidence interval for the mean score of all students who took the test. Identify the target parameter and the point estimator.

Objective: (6.2) Calculate, Interpret Confidence Interval

39) Suppose that 100 samples of size n = 50 are independently chosen from the same population and that each sample is used to construct its own 95% confidence interval for an unknown population mean µ. How many of the 100 confidence intervals would you expect to actually contain µ? Objective: (6.2) Calculate, Interpret Confidence Interval

40) A random sample of n = 100 measurements was selected from a population with unknown mean µ and standard deviation . Calculate a 95% confidence interval if x = 26 and s2 = 16. Objective: (6.2) Calculate, Interpret Confidence Interval

41) A random sample of n = 144 measurements was selected from a population with unknown mean µ and standard deviation . Calculate a 90% confidence interval if x = 3.55 and s = .49. Objective: (6.2) Calculate, Interpret Confidence Interval

42) A random sample of 80 observations produced a mean x = 35.4 and a standard deviation s = 3.1. a. Find a 90% confidence interval for the population mean µ. b. Find a 95% confidence interval for µ. c. Find a 99% confidence interval for µ. d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed? Objective: (6.2) Calculate, Interpret Confidence Interval

43) Suppose you selected a random sample of n = 7 measurements from a normal distribution. Compare the standard normal z value with the corresponding t value for a 90% confidence interval. Objective: (6.3) Compare t-Distribution to Normal Distribution

44) Suppose you selected a random sample of n = 29 measurements from a normal distribution. Compare the standard normal z value with the corresponding t value for a 95% confidence interval. Objective: (6.3) Compare t-Distribution to Normal Distribution

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 45) An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). Which of the following statements is true? A) In construction of the confidence interval, a z-value was used. B) In construction of the confidence interval, a t-value with 19 degrees of freedom was used. C) In construction of the confidence interval, a z-value with 20 degrees of freedom was used. D) In construction of the confidence interval, a t-value with 20 degrees of freedom was used. Objective: (6.3) Compare t-Distribution to Normal Distribution

46) Find the value of t0 such that the following statement is true: P(-t0 t t0 ) = .99 where df = 9. A) 2.262 B) 1.833 C) 2.2821 D) 3.250 Objective: (6.3) Use t-Distribution

47) Find the value of t0 such that the following statement is true: P(-t0 t t0 ) = .95 where df = 15. A) 2.602 B) 2.131 C) 2.947 D) 1.753 Objective: (6.3) Use t-Distribution

48) Find the value of t0 such that the following statement is true: P(-t0 t t0 ) = .90 where df = 14. A) 2.624 B) 1.345 C) 2.145 D) 1.761 Objective: (6.3) Use t-Distribution

49) Let t0 be a specific value of t. Find t0 such that the following statement is true: P(t t0) = .025 where df = 20. A) -2.093

B) 2.093

C) 2.086

D) -2.086

Objective: (6.3) Use t-Distribution

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 50) Let t0 be a particular value of t. Find a value of t0 such that P(t t0 or t t0 ) = .1 where df = 14. Objective: (6.3) Use t-Distribution

51) Let t0 be a particular value of t. Find a value of t0 such that P(t t0 ) = .005 where df = 9. Objective: (6.3) Use t-Distribution

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 52) Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is invested in a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars): 79.5, 49.5, 247.7, 483.5, 118, 195.3, 100, and 208. What value will be used as the point estimate for the mean endowment of all private colleges in the United States? A) 185.188 B) 211.643 C) 1,481.5 D) 8 Objective: (6.3) Use t-Distribution

53) Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon. Which of the following would represent a 90% confidence interval for the average highway mileage of all SmartCars? 5 5 5 5 A) 47 ± 1.345 B) 47 ± 1.753 C) 47 ± 1.761 D) 47 ± 1.645 15 15 15 15 Objective: (6.3) Use t-Distribution

54) How much money does the average professional football fan spend on food at a single football game? That question was posed to ten randomly selected football fans. The sampled results show that the sample mean and sample standard deviation were $70.00 and $17.50, respectively. Use this information to create a 95 percent confidence interval for the population mean. 17.50 17.50 17.50 17.50 A) 70 ± 2.228 B) 70 ± 1.833 C) 70 ± 1.960 D) 70 ± 2.262 60 60 60 60 Objective: (6.3) Use t-Distribution

55) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 99% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $12,140 with a standard deviation of $700. What is the 99% confidence interval for the true mean resale value of a 5- year-old car of this model? A) 12,140 ± 2.921(700/ 16) B) 12,140 ± 2.575(700/ 17) C) 12,140 ± 2.898(700/ 17) D) 12,140 ± 2.921(700/ 17) Objective: (6.3) Calculate, Interpret Confidence Interval

56) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 90% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $12,150 with a standard deviation of $800. Suppose that the interval is calculated to be ($11,811.23, $12,488.77). How could we alter the sample size and the confidence coefficient in order to guarantee a decrease in the width of the interval? A) Keep the sample size the same but increase the confidence coefficient. B) Decrease the sample size but increase the confidence coefficient. C) Increase the sample size and increase the confidence coefficient. D) Increase the sample size but decrease the confidence coefficient. Objective: (6.3) Calculate, Interpret Confidence Interval

57) How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sample results provided a sample mean and standard deviation of $12.00 and $3.45, respectively. Use this information to construct a 90% confidence interval for the mean. A) 12 ± 1.812(3.45/ 10) B) 12 ± 1.796(3.45/ 10) C) 12 ± 1.383(3.45/ 10) D) 12 ± 1.833(3.45/ 10) Objective: (6.3) Calculate, Interpret Confidence Interval

58) A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). Explain what the phrase "90% confident" means. A) 90% of the sample means from similar samples fall within the interval. B) 90% of the population values will fall within the interval. C) In repeated sampling, 90% of the intervals constructed would contain µ. D) 90% of the similarly constructed intervals would contain the value of the sample mean. Objective: (6.3) Calculate, Interpret Confidence Interval

59) A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What additional assumption is necessary for this confidence interval to be valid? A) The population of total compensations of CEOs in the service industry is approximately normally distributed. B) None. The Central Limit Theorem applies. C) The distribution of the sample means is approximately normal. D) The sample standard deviation is less than the degrees of freedom. Objective: (6.3) Calculate, Interpret Confidence Interval

60) A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What would happen to the confidence interval if the confidence level were changed to 95%? A) There would be no change in the width of the interval. B) The interval would get narrower. C) The interval would get wider. D) It is impossible to tell until the 95% interval is constructed. Objective: (6.3) Calculate, Interpret Confidence Interval

61) A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = SAMPLE STANDARD DEV = ` SAMPLE SIZE OF X = CONFIDENCE = UPPER LIMIT = SAMPLE MEAN OF X = LOWER LIMIT =

46,300 13,747 15 90 52,550.6 46,300 40,049.4

At what level of reliability is the confidence interval made? A) 10% B) 55%

C) 45%

D) 90%

Objective: (6.3) Calculate, Interpret Confidence Interval

62) A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = SAMPLE STANDARD DEV = SAMPLE SIZE OF X = CONFIDENCE = UPPER LIMIT = SAMPLE MEAN OF X = LOWER LIMIT =

46,300 13,747 15 95 53,913.6 46,300 38,686.4

Which of the following is a practical interpretation of the interval above? A) We are 95% confident that the mean sale price of all homes in this neighborhood falls between $38,686.40 and $53,913.60. B) 95% of the homes in this neighborhood have sale prices that fall between $38,686.40 and $53,913.60. C) We are 95% confident that the true sale price of all homes in this neighborhood fall between $38,686.40 and $53,913.60. D) All are correct practical interpretations of this interval. Objective: (6.3) Calculate, Interpret Confidence Interval

63) A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = SAMPLE STANDARD DEV = SAMPLE SIZE OF X = CONFIDENCE = UPPER LIMIT = SAMPLE MEAN OF X = LOWER LIMIT =

46,500 13,747 15 90 52,750.60 46,500 40,249.40

A friend suggests that the mean sale price of homes in this neighborhood is $48,000. Comment on your friend's suggestion. A) Your friend is wrong, and you are 90% certain. B) Based on this printout, all you can say is that the mean sale price might be $48,000. C) Your friend is correct, and you are 90% certain. D) Your friend is correct, and you are 100% certain. Objective: (6.3) Calculate, Interpret Confidence Interval

64) To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of 25.3 milligrams and standard deviation of 2.8 milligrams for a sample of n = 9 cigarettes. Construct a 95% confidence interval for the mean nicotine content of this brand of cigarette. A) 25.3 ± 2.283 B) 25.3 ± 2.152 C) 25.3 ± 2.111 D) 25.3 ± 2.239 Objective: (6.3) Calculate, Interpret Confidence Interval

65) Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is invested in a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield x = 180.975 and s = 143.042. Calculate a 99% confidence interval for the mean endowment of all private colleges in the United States. A) 180.975 ± 181.387 B) 180.975 ± 189.173 C) 180.975 ± 169.672 D) 180.975 ± 176.955 Objective: (6.3) Calculate, Interpret Confidence Interval

66) An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). The researcher claimed that the average GPA of all male students exceeded 2.94. Using the confidence interval supplied above, how do you respond to this claim? A) We are 100% confident that the researcher is incorrect. B) We are 95% confident that the researcher is incorrect. C) We cannot make any statement regarding the average GPA of male university students at the 95% confidence level. D) We are 95% confident that the researcher is correct. Objective: (6.3) Calculate, Interpret Confidence Interval

67) An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). What assumption is necessary for the confidence interval analysis to work properly? A) The population that we are sampling from needs to be approximately normally distributed. B) The sampling distribution of the sample mean needs to be approximately normally distributed. C) The Central Limit theorem guarantees that no assumptions about the population are necessary. D) The population that we are sampling from needs to be a t-distribution with n-1 degrees of freedom. Objective: (6.3) Calculate, Interpret Confidence Interval

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 68) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $13,400 with a standard deviation of $700. Create a 95% confidence interval for the true mean resale value of a 5-year-old car of that model. Objective: (6.3) Calculate, Interpret Confidence Interval

69) A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Give a practical interpretation of the confidence interval. Objective: (6.3) Calculate, Interpret Confidence Interval

70) A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the service industry is more than $1,500,000? Objective: (6.3) Calculate, Interpret Confidence Interval

71) A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. X = sale_price SAMPLE MEAN OF X = SAMPLE STANDARD DEV = SAMPLE SIZE OF X = CONFIDENCE = UPPER LIMIT = SAMPLE MEAN OF X = LOWER LIMIT =

46300 13747 25 90 51003.90 46300 41596.10

A friend suggests that the mean sale price of homes in this neighborhood is $43,000. Comment on your friend's suggestion. Objective: (6.3) Calculate, Interpret Confidence Interval

72) The following random sample was selected from a normal population: 9, 11, 8, 10, 14, 8. Construct a 95% confidence interval for the population mean µ. Objective: (6.3) Calculate, Interpret Confidence Interval

73) The following sample of 16 measurements was selected from a population that is approximately normally distributed. 61 85 92 77 83 81 75 78 95 87 69 74 76 84 80 83 Construct a 90% confidence interval for the population mean. Objective: (6.3) Calculate, Interpret Confidence Interval

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 74) A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 176 college students produced the following confidence interval for the proportion of college students who prefer drink A: (.344, .494). Is this a large enough sample for this analysis to work? A) Yes, since n = 176 (which is 30 or more). ^

B) No.

C) Yes, since both np 15 and nq 15.

D) It is impossible to say with the given information.

Objective: (6.4) Determine if Assumptions are Satisfied

75) A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 337 college students produced the following 95% confidence interval for the proportion of college students who prefer one of the colas: (.337, .463). What additional assumptions are necessary for the interval to be valid? A) The sample was randomly selected from an approximately normal population. B) The sample proportion equals the population proportion. C) No additional assumptions are necessary. D) The population proportion has an approximately normal distribution. Objective: (6.4) Determine if Assumptions are Satisfied

76) What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION = .396226 SAMPLE SIZE = 159 UPPER LIMIT = .46262 LOWER LIMIT = .331167 Is the sample large enough for the interval to be valid? A) Yes, since n > 30. B) No, the population of college students is not normally distributed. C) No, the sample size should be at 10% of the population. ^

D) Yes, since np and nq are both greater than 15. Objective: (6.4) Determine if Assumptions are Satisfied

77) A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. A computer program was used to generate the following 95% confidence interval for the population proportion: (0.64814, 0.75186). The sample size that was used in this problem is considered a large sample. What criteria should be used to determine if n is large? A) If n > 30, then n is considered large. ^

B) Both np 15 and nq 15. C) When working with proportions, any n is considered large. D) If n > 25, then n is considered large. Objective: (6.4) Determine if Assumptions are Satisfied

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ^

78) For n = 40 and p = .35, is the sample size large enough to construct a confidence for p? Objective: (6.4) Determine if Assumptions are Satisfied

79) For n = 40 and p = .45, is the sample size large enough to construct a confidence for p? Objective: (6.4) Determine if Assumptions are Satisfied

80) For n = 800 and p = .99, is the sample size large enough to construct a confidence for p? Objective: (6.4) Determine if Assumptions are Satisfied

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. ^

81) The sampling distribution for p is approximately normal for a large sample size n, where n is considered large if ^

both n p 15 and n(1 - p) A) True

15.

B) False

Objective: (6.4) Determine if Assumptions are Satisfied

82) When the sample size is small, confidence intervals for a population proportion are more reliable when the population proportion p is near 0 or 1. A) True B) False Objective: (6.4) Determine if Assumptions are Satisfied

Solve the problem. 83) A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.404, .504). Identify the point estimate for estimating the true proportion of college students who prefer that drink. A) .454 B) .05 C) .504 D) .404 Objective: (6.4) Construct, Interpret Confidence Interval

84) What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION = .398455 SAMPLE SIZE = 159 UPPER LIMIT = .464240 LOWER LIMIT = .331153 What proportion of the sampled students prefer foreign automobiles? A) .331153 B) .601545 C) .398455

D) .464240

Objective: (6.4) Construct, Interpret Confidence Interval

85) What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below of a 95% confidence interval for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION = .396 SAMPLE SIZE = 159 UPPER LIMIT = .472 LOWER LIMIT = .320 Which of the following is a correct practical interpretation of the interval? A) 95% of all college students prefer American cars between .320 and .472 of the time. B) We are 95% confident that the proportion of the 159 sampled students who prefer American cars falls between .320 and .472. C) We are 95% confident that the proportion of all college students who prefer American cars falls between .320 and .472. D) We are 95% confident that the proportion of all college students who prefer foreign cars falls between .320 and .472. Objective: (6.4) Construct, Interpret Confidence Interval

86) What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below of a 90% confidence interval for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION = .396 SAMPLE SIZE = 159 UPPER LIMIT = .460 LOWER LIMIT = .332 Based on the interval above, do you believe that 30% of all college students prefer American automobiles? A) No, and we are 100% sure of it. B) Yes, and we are 90% confident of it. C) No, and we are 90% confident of it. D) Yes, and we are 100 %sure of it. Objective: (6.4) Construct, Interpret Confidence Interval

87) A newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 526 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 90% confidence level. A) .63 ± .035 B) .37 ± .002 C) .37 ± .035 D) .63 ± .002 Objective: (6.4) Construct, Interpret Confidence Interval

88) A newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 549 teenagers. Using 99% reliability, can we say that more than 30% of all teenagers want to discuss school with their parents? A) No, since the value .30 is not contained in the 99% confidence interval. B) No, since the value .30 is not contained in the 99% confidence interval. C) Yes, since the value .30 falls inside the 99% confidence interval. D) Yes, since the values inside the 99% confidence interval are greater than .30. Objective: (6.4) Construct, Interpret Confidence Interval

89) A random sample of 4000 U.S. citizens yielded 2,250 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation. A) 2,250 B) .4,375 C) .5,625 D) 4000 Objective: (6.4) Construct, Interpret Confidence Interval

90) A random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval. A) .5625 ± .0129 B) .4375 ± .4,048 C) .4375 ± .0129 D) .5625 ± .4,048 Objective: (6.4) Construct, Interpret Confidence Interval

91) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 90% confidence interval to estimate the true proportion of students who receive financial aid. A) .59 ± .398 B) .59 ± .002 C) .59 ± .057 D) .59 ± .004 Objective: (6.4) Construct, Interpret Confidence Interval

92) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 99% confidence interval for p is 59 ± .09. Interpret this interval. A) We are 99% confident that 59% of the students are on some sort of financial aid. B) We are 99% confident that the true proportion of all students receiving financial aid is between .50 and .68. C) 99% of the students receive between 50% and 68% of their tuition in financial aid. D) We are 99% confident that between 50% and 68% of the sampled students receive some sort of financial aid. Objective: (6.4) Construct, Interpret Confidence Interval

93) A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following 95% confidence interval: (.438, .642). State the level of reliability used to create the confidence interval. A) 64.2% B) between 43.8% and 64.2% C) 95% D) 72% Objective: (6.4) Construct, Interpret Confidence Interval

94) A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following 90% confidence interval: (.438, .642). Based on the interval, is the population proportion of females equal to 52%? A) Yes, and we are 90% sure of it. B) No, and we are 90% sure of it. C) Maybe. 52% is a believable value of the population proportion based on the information above. D) No, the proportion is 54%. Objective: (6.4) Construct, Interpret Confidence Interval

95) A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. A computer program was used to generate the following 95% confidence interval for the population proportion: (0.64814, 0.75186). Which of the following practical interpretations is correct for this confidence interval? A) We are 95% confident that the percentage of all college students who consider themselves full-time students was 0.700. B) We are 95% confident that the percentage of the 300 students who responded that they considered themselves full-time students falls between 0.648 and 0.752. C) We are 95% confident that the percentage of the 300 students who responded that they considered themselves full-time students was 0.700. D) We are 95% confident that the percentage of all college students who consider themselves full-time students falls between 0.648 and 0.752. Objective: (6.4) Construct, Interpret Confidence Interval

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 96) The U.S. Commission on Crime randomly selects 600 files of recently committed crimes in an area and finds 380 in which a firearm was reportedly used. Find a 99% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used. Objective: (6.4) Construct, Interpret Confidence Interval

97) A newspaper reports on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 505 teenagers. Estimate the proportion of all teenagers who want more family discussions about religion. Use a 99% confidence level. Objective: (6.4) Construct, Interpret Confidence Interval

98) A random sample of 50 employees of a large company was asked the question, "Do you participate in the company's stock purchase plan?" The answers are shown below. yes no no yes no

no yes yes no yes

yes yes no yes no

no no yes yes yes

no yes yes yes yes

yes no no yes yes

yes no yes yes yes

no yes yes no yes

no yes yes yes yes

Use a 90% confidence interval to estimate the proportion of employees who participate in the company's stock purchase plan. Objective: (6.4) Construct, Interpret Confidence Interval

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 99) We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 6 minutes. We want our 95 percent confidence interval to have a margin of error of no more than plus or minus 5 minutes. What is the smallest sample size that we should consider? A) 28 B) 1 C) 3 D) 6 Objective: (6.5) Determine Sample Size

100) A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 90% confident that the margin of error of their estimate is about 5%? A) 165 B) 1,083 C) 542 D) 271 Objective: (6.5) Determine Sample Size

101) A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following confidence interval: (.438, .642). Using the information above, what sample size would be necessary if we wanted to estimate the true proportion to within 2% using 90% reliability? A) 1,681 B) 1,624 C) 1,692 D) 1,759 Objective: (6.5) Determine Sample Size

102) Sales of a new line of athletic footwear are crucial to the success of a company. The company wishes to estimate the average weekly sales of the new footwear to within $500 with 95% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately $1,200. How many weeks of data must be sampled for the company to get the information it desires? A) 12 weeks B) 5 weeks C) 23 weeks D) 11,064 weeks Objective: (6.5) Determine Sample Size

103) The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, x = 19.8 and s2 = 36. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 90% reliability, what is the minimum sample size she should use? A) 98 B) 2,132 C) 60 D) 3,508 Objective: (6.5) Determine Sample Size

104) A previous random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. How many citizens would need to be sampled for a 90% confidence interval to estimate the true proportion within 2%? A) 1,759 B) 1,556 C) 1,692 D) 1,665 Objective: (6.5) Determine Sample Size

105) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 90% reliability, how many students would need to be sampled? A) 22 B) 176 C) 728 D) 443 Objective: (6.5) Determine Sample Size

106) After elections were held, it was desired to estimate the proportion of voters who regretted that they did not vote. How many voters must be sampled in order to estimate the true proportion to within 2% (e.g., + 0.02) at the 90% confidence level? Assume that we believe this proportion lies close to 30%. A) n = 2401 B) n = 1692 C) Cannot determine because no estimate of p or q exists in this problem. D) n = 1421 E) n = 2017 Objective: (6.5) Determine Sample Size

107) Suppose it is desired to estimate the average time a customer spends in a particular store to within 5 minutes (e.g., + 5 minutes) at 99% reliability. It is estimated that the standard deviation of the times is 15 minutes. How large a sample should be taken to get the desired interval? A) n = 60 B) n = 299 C) n = 35 D) n = 25 Objective: (6.5) Determine Sample Size

108) It is desired to estimate the average time it takes Statistics students to finish a computer project to within two hours at 90% reliability. It is estimated that the standard deviation of the times is 14 hours. How large a sample should be taken to get the desired interval? A) n = 231 B) n = 133 C) n = 325 D) n = 189 Objective: (6.5) Determine Sample Size

109) It is desired to estimate the proportion of college students who feel a sudden relief now that their statistics class is over. How many students must be sampled in order to estimate the true proportion to within 2% at the 90% confidence level? A) n = 189 B) n = 2401 C) Cannot determine because no estimate of p or q exists in this problem D) n = 1692 E) n = 133 Objective: (6.5) Determine Sample Size

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 110) A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 95% confident that the margin of error of their estimate is within 2%? Objective: (6.5) Determine Sample Size

111) Suppose you wanted to estimate a binomial proportion, p, correct to within .04 with probability 0.95. What size sample would need to be selected if p is known to be approximately 0.6? Objective: (6.5) Determine Sample Size

112) The standard deviation of a population is estimated to be 250 units. To estimate the population mean to within 50 units with 95% reliability, what size sample should be selected? Objective: (6.5) Determine Sample Size

113) Sales of a new line of athletic footwear are crucial to the success of a newly formed company. The company wishes to estimate the average weekly sales of the new footwear to within $250 with 99% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately $1,550. How many weeks of data must be sampled for the company to get the information it desires? Objective: (6.5) Determine Sample Size

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 114) In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a __________ interval. A) biased B) less significant C) wider D) narrower Objective: (6.5) Determine Sample Size

Answer the question True or False. 115) One way of reducing the width of a confidence interval is to reduce the size of the sample taken. A) True B) False Objective: (6.5) Determine Sample Size

116) If no estimate of p exists when determining the sample size for a confidence interval for a proportion, we can use .5 in the formula to get a value for n. A) True B) False Objective: (6.5) Determine Sample Size

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 117) What is the rule of thumb for the finite population correction factor? Objective: (6.6) Calculate Finite Population Correction Factor

118) When is the finite population correction factor used? Objective: (6.6) Calculate Finite Population Correction Factor

119) Calculate the percentage of the population sampled if n = 250 and N = 1000. Should the standard error in this situation be multiplied by a finite population correction factor? Explain. Objective: (6.6) Calculate Finite Population Correction Factor

120) Calculate the percentage of the population sampled if n = 100 and N = 10,000. Should the standard error in this situation be multiplied by a finite population correction factor? Explain. Objective: (6.6) Calculate Finite Population Correction Factor

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 121) Calculate the finite population correction factor for n = 300 and N = 1500. A) .8000 B) .4472 C) 2.000

D) .8944

Objective: (6.6) Calculate Finite Population Correction Factor

122) Suppose the population standard deviation is known to be and N = 1500. A) 3.87 B) 17.32

= 150. Calculate the standard error of x when n = 300

C) 6.92

D) 7.75

Objective: (6.6) Compute Standard Error

123) Suppose you want to estimate a population mean µ and that x = 145, s = 21, n = 750, and N = 4000. Find an approximate 95% confidence interval for µ. A) 145 ± 1.38 B) 145 ± 0.30 C) 145 ± 0.66 D) 145 ± 2.71 Objective: (6.6) Construct Confidence Interval for Mean

124) A sociologist develops a test to measure attitudes towards public transportation, and 47 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct an approximate 95% confidence interval for the mean score of all such subjects. A) 76.2 ± 0.91 B) 76.2 ± 6.87 C) 76.2 ± 3.12 D) 76.2 ± 6.24 Objective: (6.6) Construct Confidence Interval for Mean

125) Suppose you want to estimate a population proportion p where p = 0.61, n = 1000, and N = 7500. Find an approximate 95% confidence interval for p. A) 0.61 ± .046 B) 0.61 ± .056 C) 0.61 ± .036 D) 0.61 ± .029 Objective: (6.6) Construct Confidence Interval for Proportion

126) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct an approximate 95% confidence interval for the true proportion of all voters in the state who favor approval. A) 0.47 ± 0.049 B) 0.47 ± 0.017 C) 0.47 ± 0.034 D) 0.47 ± 0.025 Objective: (6.6) Construct Confidence Interval for Proportion

127) For the given combination of

and degrees of freedom (df), find the value of

lower endpoint of a confidence interval for 2 . = 0.1, df = 8 A) 15.5073 B) 13.3616

C) 14.0671

Objective: (6.7) Construct, Interpret Confidence Interval

/2 that would be used to find the

D) 2.7326

128) For the given combination of

and degrees of freedom (df), find the value of

find the upper endpoint of a confidence interval for 2 . = 0.1, df = 8 A) 3.48954 B) 15.5073

C) 2.73264

2 (1 - /2) that would be used to

D) 2.16735

Objective: (6.7) Construct, Interpret Confidence Interval

129) Given the values of x, s, and n, form a 99% confidence interval for 2 . x = 18.8, s = 7.1, n = 8 A) (17.4, 356.7)

B) (2.69, 40.11)

C) (19.1, 284.79)

D) (19.89, 407.66)

Objective: (6.7) Construct, Interpret Confidence Interval

130) Given the values of x, s, and n, form a 99% confidence interval for . x = 10.3, s = 2.4, n = 24 A) (3, 14.31)

B) (1.25, 5.96)

C) (1.78, 3.6)

D) (1.73, 3.78)

Objective: (6.7) Construct, Interpret Confidence Interval

131) The daily intakes of milk (in ounces) for ten five-year old children selected at random from one school were: 31.1 14.0 28.0 25.9 22.4 25.4 29.9 14.3 28.6 28.3 Find a 99% confidence interval for the standard deviation, , of the daily milk intakes of all five-year olds at this school. Round to the nearest hundredth when necessary. A) (0.88, 3.38) B) (3.78, 13.93) C) (3.66, 12.52) D) (3.78, 12.52) Objective: (6.7) Construct, Interpret Confidence Interval

132) The mean systolic blood pressure for a random sample of 28 women aged 18-24 is 113.8 mm Hg and the standard deviation is 13.0 mm Hg. Construct a 90% confidence interval for the standard deviation , of the systolic blood pressures of all women aged 18-24. Round to the nearest hundredth when necessary. A) (10.14, 18.2) B) (10.51, 16.42) C) (10.67, 16.81) D) (11.14, 15.87) Objective: (6.7) Construct, Interpret Confidence Interval

133) The mean replacement time for a random sample of 12 CD players is 8.6 years with a standard deviation of 2.5 years. Construct the 99% confidence interval for the population variance, 2 . Assume the data are normally distributed, and round to the nearest hundredth when necessary. A) (1.03, 10.56) B) (2.57, 26.41) C) (1.6, 5.14)

D) (2.78, 22.52)

Objective: (6.7) Construct, Interpret Confidence Interval

134) A random sample of 15 crates have a mean weight of 165.2 pounds and a standard deviation of 15.6 pounds. Construct a 95% confidence interval for the population standard deviation . Assume the population is normally distributed, and round to the nearest hundredth when necessary. A) (11.99, 22.77) B) (11.42, 24.6) C) (2.89, 6.23) D) (130.44, 605.3) Objective: (6.7) Construct, Interpret Confidence Interval

135) The volumes (in ounces) of juice in eight randomly selected juice bottles are as follows: 15.3 15.7 15.0 15.2 15.0 15.0 15.3 15.1 Find a 99% confidence interval for the standard deviation, , of the volumes of juice in all such bottles. Round to the nearest hundredth when necessary. A) (0.13, 0.55) B) (0.14, 0.55) C) (0.18, 0.80) D) (0.14, 0.64) Objective: (6.7) Construct, Interpret Confidence Interval

Answer Key Testname: SB14ECH6TEST

1) A 2) A 3) B 4) A 5) B 6) A 7) A 8) C 9) C 10) C 11) D 12) A 13) B 14) A 15) An increase in the sample size reduces the sampling variation of the point estimate as it is calculated as / n. The larger the sample size, the smaller this variation which leads to narrower intervals. 16) A 17) A 18) B 19) A 20) A 21) A 22) B 23) C 24) A 25) D 26) A 27) C 28) A 29) C 30) C 31) D 32) A 33) B 34) B 35) D

36) For confidence coefficient .99, 1 = 1 - .99 = .01. /2 = .01/2 = .005 z.005 = 2.575. The

38) a. The sample mean is 79.98 and the sample standard deviation is 12.34. The interval is 12.34 79.98 ± 1.96 50

confidence interval is: x ± z /2

s = 14.00 n

± 2.575

3.10 = 14.00 59

79.98 ± 3.42. b. The target parameter is the mean score of all students who took the test, and the point estimator is the sample mean 79.98. 39) 95% of the 100 samples, or 95, are expected to produce a confidence interval that contains µ. s = 26 ± 40) x ± z /2 n

± 1.039 = ($12.96, $15.04) We are 99% confident that the average amount a fan spends on food at a single professional football game is between $12.96 and $15.04. 37) For confidence coefficient .95, 1 - = .95 = 1 - .95 = .05. /2 = .05/2 = .025. z /2 = z.025 = 1.96.

1.96 .784

41) x ± z /2

The 95% confidence interval is: x ± z /2 1.96

2.6 82

16 = 26 ± 100

1.645 .067

s = 25 ± n 25 ± .563

s = 3.55 ± n

.49 = 3.55 ± 144

42) a. x ± z /2 35.4 ± 1.645

s = n 3.1 = 80

35.4 ± .57 b. x ± z /2

s = n

35.4 ± 1.96

3.1 = 80

35.4 ± .68 c. x ± z /2

s = n

35.4 ± 2.575

3.1 = 80

35.4 ± .89 d. increases 43) z: 1.645 and t: 1.943; The t value is considerably bigger than the z value. 44) z: 1.96 and t: 2.048; The t value is a little bigger than the z value. 45) B 46) D 47) B 48) D 49) C 50) t0 = 1.761; Use table

for t.050 with 14

degrees of freedom. 51) t0 = 3.250; Use table

= (24.437, 25.563)

for t.005 with 9

degrees of freedom. 52) A 53) C 54) D 55) D 56) D 57) D 58) C 59) A 60) B 61) D

Answer Key Testname: SB14ECH6TEST

62) A 63) B 64) B 65) D 66) D 67) A 68) For confidence coefficient .95, 1 = 1 - .95 = .05. /2 = 0.05/2 = 0.025. With df = n - 1 = 17 1 = 16, t0.025 = 2.120. The 95% confidence interval is: x ± t /2

s = n

13,400 ± 2.120

700 17

= (13,040.08, 13,759.92) For this interval to be valid, we must assume that the population of resale values for all 5-year-old cars of this model follows an approximately normal distribution. 69) We are 95% confident that the average total compensation of CEOs in the service industry is contained in the interval $2,181,260 to $5,836,180. 70) Since all of the values in the interval are greater than $1,500,000, it seems very likely that the mean is greater than $1,500,000, but we can't be 100% certain.

71) Your friend could be correct. $43,000 is contained in the 90% confidence interval. It cannot be ruled out as a possible value for the mean sales price.

96) Let p = the true fraction of crimes in the area in which some type of firearm was reportedly used. ^

72) x = 10; s = 2.28; x ± s = 10 ± t /2 n 2.571

^ 380 = .6333 and q 600 ^

= 1 - p = 1 - .6333 = .3667.

2.28 = 10 ± 6

The confidence ^

interval for p is p ±

2.393

z /2

73) x = 80; s = 8.367; x ± s = 80 ± t /2 n

pq . n

For confidence coefficient .99, 1 - = .99 = 1 - .99 = .01. /2 = .01/2 = .005. z /2 = z.005 = 2.575.

8.367 1.753 = 80 ± 16 3.667 74) C 75) C 76) D 77) B

The 99% confidence interval is: .6333 ± 2.575 .6333(.3667) = 600

78) No; np = 14 < 15 ^

79) Yes; np = 18 > 15 and

.6333 ± .0507 97) For confidence coefficient .99, 1 - = .99 = 1 - .99 = .01. /2 = .01/2 = .005. z /2 = z.005 = 2.575.

nq = 22 > 15 ^

80) No; nq = 8 < 15 81) A 82) B 83) A 84) B 85) C 86) C 87) C 88) D 89) C 90) A 91) C 92) B 93) C 94) C 95) D

The 99% confidence interval for p is: ^^

p ± z /2 2.575

pq n

.30 ±

.30(.70) 505

.30 ±

.0525 ^ 32 = .64; The 98) p = 50

confidence interval is (.64)(.36) .64 ± 1.645 50 .64 ± .112.

99) D 100) D 101) A 102) C 103) A 104) D 105) C 106) D 107) A 108) B 109) D 110) To determine the sample size necessary to estimate p, we use n = z /2 2 pq SE For confidence coefficient .95, 1 - = = 1 - .95 = .05. .95 /2 = .05/2 = .025. z /2 = z.025 = 1.96. Since no estimate of p exists, we use p = q = .5. 1.96 2 n= (.5)(.5) = .02 2,401. Round up to n = 2,401. 111) To determine the sample size necessary to estimate p, we use n = z /2 2 p(1 - p). SE

For confidence coefficient .95, 1 - = = 1 - .95 = .05. .95 /2 = .05/2 = .025. z /2 = z.025 = 1.96. n=

1.96 2 (.60)(1 - . .04

60) = 576.24. Round up to n = 577.

Answer Key Testname: SB14ECH6TEST

112) To determine the sample size necessary to estimate z /2 2 µ, we use n = SE 2.

For confidence coefficient .95, 1 - = .95 = 1 - .95 = .05. /2 = .05/2 = .025. z /2 = z.025 = 1.96. n=

1.96 2 2502 = 50

96.0400. Round up to n = 97. 113) To determine the sample size necessary to estimate z /2 2 µ, we use n = SE

120) 1%; No, less than 5% of the population was sampled. 121) D 122) D 123) A 124) D 125) D 126) C 127) A 128) C 129) A 130) D 131) B 132) C 133) B 134) B 135) D

For confidence coefficient .99, 1 - = .99 = 1 - .99 = .01. /2 = .01/2 = .005. z /2 = z.005 = 2.575. n=

2.575 2 1,5502 = 250

254.8812. Round up to n = 255. 114) D 115) B 116) A 117) Use the finite population correction factor when: n/N > .05. 118) The finite population correction factor is used when the sample size is large relative to the size of the population. 119) 25%; Yes, more than 5% of the population was sampled.

McClave Statistics for Business and Economics 14e Chapter 7 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 5.6 hours. In order to test whether the time to fill out the form has been reduced, a sample of 92 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 5.3 hours with a standard deviation of 2.2 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses. A) H0 : µ = 5.6 B) H0 : µ = 5.6 C) H0 : µ > 5.6 D) H0 : µ = 5.6 Ha : µ > 5.6

Ha : µ < 5.6

Ha : µ 5.6

Objective: (7.1) Write Null and Alternative Hypotheses

2) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 44 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: x = 32, s = 24. Identify the null and alternative hypothesis for a test to determine if the mean number of tissues used during a cold is less than 44. A) H0 : µ = 44 vs. Ha : µ < 44 B) H0 : µ = 44 vs. Ha : µ 44

C) H0 : µ > 44 vs. Ha : µ 44

D) H0 : µ = 44 vs. Ha : µ > 44

Objective: (7.1) Write Null and Alternative Hypotheses

3) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 36 minutes. The owner has randomly selected 21 customers and delivered pizzas to their homes. What hypotheses should the owner test to demonstrate that the pizza delivery will not be successful? A) H0 : µ < 36 vs. Ha : µ = 36 B) H0 : µ = 36 vs. Ha : µ < 36 C) H0 : µ = 36 vs. Ha : µ > 36

D) H0 : µ = 36 vs. Ha : µ 36

Objective: (7.1) Write Null and Alternative Hypotheses

4) Researchers have claimed that the average number of headaches per student during a semester of Statistics is 11. Statistics students believe the average is higher. In a sample of n = 23 students the mean is 16 headaches with a deviation of 1.8. Which of the following represent the null and alternative hypotheses necessary to test the students' belief? A) H0 : µ < 11 vs. Ha : µ = 11 B) H0 : µ = 11 vs. Ha : µ 11 C) H0 : µ = 11 vs. Ha : µ < 11

D) H0 : µ = 11 vs. Ha : µ > 11

Objective: (7.1) Write Null and Alternative Hypotheses

5) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but are now beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. What null and alternative hypothesis should be tested? A) H0 : µ = 215 vs. HA: µ < 215 B) H0 : µ = 215 vs. HA: µ 215 C) H0 : µ 215 vs. HA: µ < 215

D) H0 : µ = 215 vs. HA: µ > 215

Objective: (7.1) Write Null and Alternative Hypotheses

Answer the question True or False. 6) The null hypothesis represents the status quo to the party performing the sampling experiment. A) True B) False Objective: (7.1) Write Null and Alternative Hypotheses

7) The alternative hypothesis is accepted as true unless there is overwhelming evidence that it is false. A) True B) False Objective: (7.1) Write Null and Alternative Hypotheses

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 8) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 22% of women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 62 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in seven. Specify the null and alternative hypotheses that the researchers wish to test. Objective: (7.1) Write Null and Alternative Hypotheses

9) According to an advertisement, a strain of soybeans planted on soil prepared with a specified fertilizer treatment has a mean yield of 459 bushels per acre. Twenty farmers who belong to a cooperative plant the soybeans in soil prepared as specified. Each uses a 40-acre plot and records the mean yield per acre. The mean and variance for the sample of 20 farms are x = 412 and s2 = 9,690. Specify the null and alternative hypotheses used to determine if the mean yield for the soybeans is different than advertised. Objective: (7.1) Write Null and Alternative Hypotheses

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) The owner of Get-A-Away Travel has recently surveyed a random sample of 310 customers to determine whether the mean age of the agency's customers is over 20. The appropriate hypotheses are H0 : µ = 20, Ha : µ > 20. If he concludes the mean age is over 20 when it is not, he makes a __________ error. If he concludes the mean age is not over 20 when it is, he makes a __________ error. A) Type I; Type II B) Type I; Type I C) Type II; Type II D) Type II; Type I Objective: (7.1) Interpret Type I and Type II Errors

11) An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 6 days, and an alternative hypothesis that the average time for processing a claim is greater than 6 days. After completing the statistical test, it is concluded that the average time exceeds 6 days. However, it is eventually learned that the mean process time is really 6 days. What type of error occurred in the statistical test? A) Type II error B) No error occurred in the statistical sense. C) Type III error D) Type I error Objective: (7.1) Interpret Type I and Type II Errors

12) Suppose we wish to test H0 : µ = 37 vs. Ha : µ > 37. What will result if we conclude that the mean is greater than 37 when its true value is really 41? A) a Type II error B) a Type I error

C) a correct decision

Objective: (7.1) Interpret Type I and Type II Errors

D) none of the above

13) I want to test H0 : p = .6 vs. Ha : p .6 using a test of hypothesis. If I concluded that p is .6 when, in fact, the true value of p is not .6, then I have made a __________. A) correct decision C) Type I and Type II error

B) Type I error D) Type II error

Objective: (7.1) Interpret Type I and Type II Errors

14) A significance level for a hypothesis test is given as = .05. Interpret this value. A) There is a 5% chance that the sample will be biased. B) The probability of making a Type I error is .05. C) The smallest value of that you can use and still reject H0 is .05. D) The probability of making a Type II error is .95. Objective: (7.1) Interpret Type I and Type II Errors

15) A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 13 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of n = 124 wind speed recordings (taken at random intervals), the wind speed at the site averaged x = 12 mph, with a standard deviation of s = 2.6 mph. To determine whether the site meets the organization's requirements, consider the test, H0 : µ = 13 vs. Ha : µ > 13, where µ is the true mean wind speed at the site and = .05. Fill in the blanks. "A Type I error in the context of this problem is to conclude that the true mean wind speed at the site _____ 13 mph when it actually _____ 13 mph." A) equals; equals B) exceeds; equals C) equals; exceeds D) exceeds; exceeds Objective: (7.1) Interpret Type I and Type II Errors

16) If I specify A) True

to be .39, then the value of

must be .61.

B) False

Objective: (7.1) Interpret Type I and Type II Errors

17) What is the probability associated with not making a Type II error? A) B) C) (1 - )

D) (1 - )

Objective: (7.1) Interpret Type I and Type II Errors

18) We never conclude "Accept H0 " in a test of hypothesis. This is because: A)

= p(Type II error) is not known.

B) We want H0 to be false.

C) H0 is never true.

= p(Type I error) is not known.

Objective: (7.1) Interpret Type I and Type II Errors

19) A __________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis. A) critical value B) significance level C) test statistic D) parameter Objective: (7.1) Interpret Type I and Type II Errors

20) The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the association's name. The association's by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if meeting is necessary. Suppose the association decided to conduct a test of hypothesis using the following null and alternative hypotheses: H0 : p = 0.6 HA: p > 0.6 Define a Type I Error in the context of this problem. A) They conclude that exactly 60% of the association wants a name change when that is, in fact, true. B) They conclude that more than 60% of the association wants a name change when, in fact, that is not true. C) They conclude that more than 60% of the association wants a name change when that is, in fact, true. D) They conclude that exactly 60% of the association wants a name change when, in fact, that is not true. Objective: (7.1) Interpret Type I and Type II Errors

21) The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the association's name. The association's by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if meeting is necessary. Suppose the association decided to conduct a test of hypothesis using the following null and alternative hypotheses: H0 : p = 0.6 HA: p > 0.6 Define a Type II Error in the context of this problem. A) They conclude that more than 60% of the association wants a name change when that is, in fact, true. B) They conclude that exactly 60% of the association wants a name change when that is, in fact, true. C) They conclude that exactly 60% of the association wants a name change when, in fact, that is not true. D) They conclude that more than 60% of the association wants a name change when, in fact, that is not true. Objective: (7.1) Interpret Type I and Type II Errors

Answer the question True or False. 22) We do not accept H0 because we are concerned with making a Type II error. A) True

B) False

Objective: (7.1) Interpret Type I and Type II Errors

23) In a test of hypothesis, the sampling distribution of the test statistic is calculated under the assumption that the alternative hypothesis is true. A) True B) False Objective: (7.1) Interpret Type I and Type II Errors

24) A Type I error occurs when we accept a false null hypothesis. A) True B) False Objective: (7.1) Interpret Type I and Type II Errors

25) The rejection region refers to the values of the test statistic for which we will reject the alternative hypothesis. A) True B) False Objective: (7.1) Interpret Type I and Type II Errors

Find the rejection region for the specified hypothesis test. 26) Consider a test of H0 : µ = 8. For the following case, give the rejection region for the test in terms of the z-statistic: Ha : µ > 8,

= 0.01

A) |z| > 2.33

B) z > 2.33

C) |z| > 2.575

D) z > 1.28

Objective: (7.2) Identify Rejection Region

27) Consider a test of H0 : µ = 6. For the following case, give the rejection region for the test in terms of the z-statistic: Ha : µ < 6,

= 0.01

A) z < -2.575

B) z < -2.33

C) z < 2.575

D) z > -2.33

Objective: (7.2) Identify Rejection Region

28) Consider a test of H0 : µ = 9. For the following case, give the rejection region for the test in terms of the z-statistic: Ha : µ 9,

= 0.10

A) z > 1.28

B) |z| > 1.28

C) |z| > 1.645

D) z > 1.645

Objective: (7.2) Identify Rejection Region

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 29) The hypotheses for H0 : µ = 65 and Ha : µ > 65 are tested at

= .05. Sketch the appropriate rejection region.

Objective: (7.2) Identify Rejection Region

30) The hypotheses for H0 : µ = 125.4 and Ha : µ 125.4 are tested at

= .10. Sketch the appropriate rejection region.

Objective: (7.2) Identify Rejection Region

For the given rejection region, sketch the sampling distribution for z and indicate the location of the rejection region. 31) z > 2.575 Objective: (7.2) Identify Rejection Region

32) z < -1.28 Objective: (7.2) Identify Rejection Region

33) z < -1.96 Objective: (7.2) Identify Rejection Region

34) z < -2.33 or z > 2.33 Objective: (7.2) Identify Rejection Region

35) z < -1.96 or z > 1.96 Objective: (7.2) Identify Rejection Region

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 36) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 57 tissues during a cold. Suppose a random sample of 2,500 people yielded the following data on the number of tissues used during a cold: x = 52, s = 19. Using the sample information provided, set up the calculation for the test statistic for the relevant hypothesis test, but do not simplify. 52 - 57 52 - 57 52 - 57 52 - 57 A) z = B) z = C) z = D) z = 19 2 19 19 19 2 2,500 2,500 2,500 Objective: (7.2) Identify Rejection Region

37) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 47 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: x = 42, s = 22. We want to test the alternative hypothesis Ha : µ < 47. State the correct rejection region for = .05. A) Reject H0 if z > 1.96 or z < -1.96.

B) Reject H0 if z < -1.645.

C) Reject H0 if z > 1.645.

D) Reject H0 if z < -1.96.

Objective: (7.2) Identify Rejection Region

38) The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the association's name. The association's by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if meeting is necessary. Identify the null and alternative hypothesis that should be tested to determine if a name change is warranted. A) H0 : p = 0.6 vs. Ha : p < 0.6 B) H0 : p = 0.6 vs. Ha : p > 0.6 C) H0 : p 0.6 vs. Ha : p < 0.6

D) H0 : p = 0.6 vs. Ha : p 0.6

Objective: (7.2) Identify Rejection Region

39) Consider the following printout. HYPOTHESIS: VARIANCE X = x X = gpa SAMPLE MEAN OF X = 2.1646 SAMPLE VARIANCE OF X = .19000 SAMPLE SIZE OF X = 151 HYPOTHESIZED VALUE (x) = 2.3 VARIANCE X - x = -.1,354 z = -3.81707 Suppose we tested Ha : µ < 2.3. Find the appropriate rejection region if we used

A) Reject if z > 1.96 or z < -1.96. C) Reject if z < -1.96.

= .05.

B) Reject if z < -1.645. D) Reject if z > 1.645 or z < -1.645.

Objective: (7.2) Identify Rejection Region

Answer the question True or False. 40) A rejection region is established in each tail of the sampling distribution for a two-tailed test. A) True B) False Objective: (7.2) Identify Rejection Region

41) The rejection region for a two-tailed test with A) True

= .05 is -1.96 < z < 1.96. B) False

Objective: (7.2) Identify Rejection Region

For the given value of and observed significance level (p-value), indicate whether the null hypothesis would be rejected. 42) = 0.1, p-value = 0.09 A) Reject H0 B) Fail to reject H0 Objective: (7.3) Determine if Null Hypothesis is Rejected Given

43)

= 0.01, p-value = 0.10 A) Reject H0

and p-Value

B) Fail to reject H0

Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

Solve the problem. 44) Consider a test of H0 : µ = 55 performed with the computer. SPSS reports a two-tailed p-value of 0.0574. Make the appropriate conclusion for the given situation: Ha : µ < 55, z = -1.9,

A) Reject H0

= 0.05

B) Fail to reject H0

Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

45) Consider a test of H0 : µ = 45 performed with the computer. SPSS reports a two-tailed p-value of 0.0164. Make the appropriate conclusion for the given situation: Ha : µ > 45, z = -2.4,

A) Fail to reject H0

= 0.01

B) Reject H0

Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

46) Consider a test of H0 : µ = 90 performed with the computer. SPSS reports a two-tailed p-value of 0.2112. Make the appropriate conclusion for the given situation: Ha : µ > 90, z = 1.25,

A) Reject H0

= 0.10

B) Fail to reject H0

Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

47) Consider a test of H0 : µ = 90 performed with the computer. SPSS reports a two-tailed p-value of 0.0038. Make the appropriate conclusion for the given situation: Ha : µ 90, z = 2.9,

A) Reject H0

= 0.01

B) Fail to reject H0

Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

48) Given H0 : µ = 25, Ha : µ 25, and p = 0.029. Do you reject or fail to reject H0 at the .01 level of significance? A) fail to reject H0 B) reject H0 C) not sufficient information to decide Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

49) Given H0 : µ = 18, Ha : µ < 18, and p = 0.068. Do you reject or fail to reject H0 at the .05 level of significance? A) reject H0 B) fail to reject H0 C) not sufficient information to decide Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

50) A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 81 bottles and finds the average amount of liquid held by the bottles is 9.9145 ounces with a standard deviation of 0.45 ounce. Suppose the p-value of this test is 0.0436. State the proper conclusion. A) At = 0.10, fail to reject the null hypothesis. B) At = 0.05, reject the null hypothesis. C) At = 0.05, accept the null hypothesis. D) At = 0.025, reject the null hypothesis. Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

51) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. The information was entered into a spreadsheet and the following printout was obtained: One-Sample T Test Null Hypothesis: µ = 215 Alternative Hyp: µ > 215 95% Conf Interval Variable Mean SE Lower Upper T DF P Camera Price 245.23 15.620 212.740 277.720 1.94 21 0.0333 Cases Included 22 Use the p- value given above to determine which of the following conclusions is correct. A) At = 0.03, there is insufficient evidence to indicate that the mean price of all digital cameras exceeds $215.00 B) At = 0.05, there is insufficient evidence to indicate that the mean price of all digital cameras exceeds $215.00 C) At = 0.01, there is sufficient evidence to indicate that the mean price of all digital cameras exceeds $215.00 D) At = 0.10, there is insufficient evidence to indicate that the mean price of all digital cameras exceeds $215.00 Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

52) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used to create a confidence interval and to conduct a test of hypothesis, both of which are shown in the printout below. One-Sample Z Test Null Hypothesis: µ = 20 Alternative Hyp: µ > 20 95% Conf Interval Variable Mean SE Lower Upper Z P Camera Price 23.243 1.3133 20.669 25.817 2.47 0.0071 Cases Included 238 What conclusion can be made from the test of hypothesis conducted in this printout? Begin each answer with, "When testing at = 0.01…" A) …there is sufficient evidence to indicate that the average travel time of all students exceeds 20 minutes. B) …there is insufficient evidence to indicate that the average travel time of all students exceeds 20 minutes. C) …there is sufficient evidence to indicate that the average travel time of all students is equal to 20 minutes. D) …there is insufficient evidence to indicate that the average travel time of all students is equal to 20 minutes. Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 53) Based on the information in the screen below, what would you conclude in the test of H0 : µ 14, Ha : µ > 14. Use = .01.

Objective: (7.3) Determine if Null Hypothesis is Rejected Given

and p-Value

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 54) Consider the following printout. HYPOTHESIS: MEAN X = x X = gpa SAMPLE MEAN OF X = 3.0512 SAMPLE VARIANCE OF X = 0.230731 SAMPLE SIZE OF X = 167 HYPOTHESIZED VALUE (x) = 3 MEAN X - x = 0.0512 z = 1.3774 Suppose a two-tailed test is desired. Find the p-value for the test. A) p = 0.9162 B) p = 0.0838 C) p = 0.1676

D) p = 0.8324

Objective: (7.3) Find and Interpret p-Value

55) A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 19 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. To determine whether the site meets the organization's requirements, consider the test, H0 : µ = 19 vs. Ha : µ > 19, where µ is the true mean wind speed at the site and = .05. Suppose the observed significance level (p-value) of the test is calculated to be p = 0.4288. Interpret this result. A) The probability of rejecting the null hypothesis is 0.4288. B) Since the p-value greatly exceeds = .05, there is strong evidence to reject the null hypothesis. C) We are 57.12% confident that µ = 19. D) Since the p-value exceeds = .05, there is insufficient evidence to reject the null hypothesis. Objective: (7.3) Find and Interpret p-Value

56) If a hypothesis test were conducted using hypothesis to be rejected. A) 0.150 B) 0.110

= 0.10, to which of the following p-values would cause the null

C) 0.105

D) 0.090

Objective: (7.3) Find and Interpret p-Value

57) A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. Suppose a sample of 108 students produced a test statistic of z = -1.35. Find the p-value for the test of interest to the college. A) p = 0.9115 B) p = 0.4115 C) p = 0.0885 D) p = 0.1770 Objective: (7.3) Find and Interpret p-Value

58) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Suppose the large-sample test statistic was calculated to be z = 2.14. Find the p-value for this test of hypothesis. A) p = 0.9838 B) p = 0.0162 C) p = 0.0324 D) p = 0.4838 Objective: (7.3) Find and Interpret p-Value

Answer the question True or False. 59) The smaller the p-value in a test of hypothesis, the more significant the results are. A) True B) False Objective: (7.3) Find and Interpret p-Value

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 60) In a test of H0 : µ = 65 against Ha : µ > 65, the sample data yielded the test statistic z = 1.38. Find and interpret the p-value for the test.

Objective: (7.3) Find and Interpret p-Value

61) In a test of H0 : µ = 70 against Ha : µ 70, the sample data yielded the test statistic z = 2.11. Find and interpret the p-value for the test.

Objective: (7.3) Find and Interpret p-Value

62) In a test of H0 : µ = 12 against Ha : µ > 12, a sample of n = 75 observations possessed mean x = 13.1 and standard deviation s = 4.3. Find and interpret the p-value for the test. Objective: (7.3) Find and Interpret p-Value

63) In a test of H0 : µ = 250 against Ha : µ 250, a sample of n = 100 observations possessed mean x = 247.3 and standard deviation s = 11.4. Find and interpret the p-value for the test. Objective: (7.3) Find and Interpret p-Value

64) The scores on a standardized test are reported by the testing agency to have a mean of 75. Based on his personal observations, a school guidance counselor believes the mean score is much higher. He collects the following scores from a sample of 50 randomly chosen students who took the test. 39 71 79 85 90

48 71 79 86 91

55 73 79 86 92

63 74 80 88 92

66 76 80 88 93

68 76 82 88 95

68 76 83 88 96

69 77 83 89 97

70 78 83 89 97

71 79 85 89 99

Find and interpret the p-value for the test of H0 : µ = 75 against Ha : µ > 75. Objective: (7.3) Find and Interpret p-Value

65) A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the weight of the chicken. The store advertises that the average weight of their chickens is 4.6 pounds. A random sample of 30 of the store's chickens yielded the weights (in pounds) shown below. 4.4 4.7 4.6 4.4 4.5 4.3 4.6 4.5 4.6 4.9 4.6 4.8 4.3 4.4 4.7 4.5 4.2 4.3 4.1 4.0 4.5 4.6 4.2 4.4 4.7 4.8 5.0 4.2 4.1 4.5 Find and interpret the p-value in a test of H0 : µ = 4.6 against Ha : µ < 4.6. Objective: (7.3) Find and Interpret p-Value

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 66) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 67 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: x = 61, s = 16. Suppose the corresponding test statistic falls in the rejection region at = .05. What is the correct conclusion? A) At = .10, reject Ha . B) At = .05, reject H0 .

C) At

D) At

= .10, reject H0 .

= .05, accept Ha .

Objective: (7.4) Perform Hypothesis Test for Population Mean

67) We have created a 99% confidence interval for µ with the result (12, 17). What conclusion will we make if we test H0 : µ = 19 vs. Ha : µ 19 at = .01? A) Fail to reject H0 . B) Reject H0 in favor of Ha . C) Accept H0 rather than Ha . D) We cannot tell what our decision will be with the information given. Objective: (7.4) Perform Hypothesis Test for Population Mean

68) Suppose we wish to test H0 : µ = 20 vs. Ha : µ < 20. Which of the following possible sample results gives the most evidence to support Ha (i.e., reject H0)?

A) x = 18, s = 6

B) x = 16, s = 11

C) x = 17, s = 8

Objective: (7.4) Perform Hypothesis Test for Population Mean

69) Consider the following printout. HYPOTHESIS: VARIANCE X = x X = gpa SAMPLE MEAN OF X = 2.5886 SAMPLE VARIANCE OF X = .21000 SAMPLE SIZE OF X = 225 HYPOTHESIZED VALUE (x) = 2.7 VARIANCE X - x = -.1,114 z = -3.64642 State the proper conclusion when testing H0 : µ = 2.7 vs. Ha : µ < 2.7 at

A) Fail to reject H0 . B) Reject H0 . C) Accept H0 . D) We cannot determine from the information given. Objective: (7.4) Perform Hypothesis Test for Population Mean

= .05.

D) x = 16, s = 5

70) Consider the following printout. HYPOTHESIS: VARIANCE X = x X = gpa SAMPLE MEAN OF X = 2.7632 SAMPLE VARIANCE OF X = .24000 SAMPLE SIZE OF X = 219 HYPOTHESIZED VALUE (x) = 2.9 VARIANCE X - x = -.1,368 z = -4.13240 Is this a large enough sample for this analysis to work? A) Yes, since the population of GPA scores is approximately normally distributed. B) Yes, since the np > 15 and nq > 15. C) No. D) Yes, since n = 219, which is greater than 30. Objective: (7.4) Perform Hypothesis Test for Population Mean

71) A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 25 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of n = 34 wind speed recordings (taken at random intervals), the wind speed at the site averaged x = 25.9 mph, with a standard deviation of s = 3.8 mph. To determine whether the site meets the organization's requirements, consider the test, H0 : µ = 25 vs. Ha : µ > 25, where µ is the true mean wind speed at the site and = .01. Suppose the value of the test statistic were computed to be 1.38. State the conclusion. A) We are 99% confident that the site meets the organization's requirements. B) At = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph. C) We are 99% confident that the site does not meet the organization's requirements. D) At = .01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph. Objective: (7.4) Perform Hypothesis Test for Population Mean

72) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Find the large-sample rejection region for the test of interest to the college when using a level of significance of 0.05. A) Reject H0 if z > 1.645. B) Reject H0 if z < -1.96. C) Reject H0 if z < -1.645 or z > 1.645.

D) Reject H0 if z < -1.96 or z > 1.96.

Objective: (7.4) Perform Hypothesis Test for Population Mean

73) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Suppose the sample mean and sample standard deviation were calculated to be 23.2 and 20.26 minutes, respectively. Calculate the value of the test statistic to be used in the test. A) z = 37.59 B) z = 2.551 C) z = 0.173 D) z = 2.437 Objective: (7.4) Perform Hypothesis Test for Population Mean

74) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of n = 200 cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. Find the large-sample rejection region appropriate for this test if we are using = 0.05. A) Reject H0 if z < -1.645 or z > 1.645. B) Reject H0 if z < -1.96. C) Reject H0 if z < -1.96 or z > 1.96.

D) Reject H0 if z > 1.645.

Objective: (7.4) Perform Hypothesis Test for Population Mean

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 75) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 63 hours. In order to test whether the time to fill out the form has been reduced, a sample of 72 small business owners who annually complete the form was randomly chosen and their completion times recorded. The mean completion time for the sample was 62.4 hours with a standard deviation of 17 hours. State the rejection region for the desired test at = .05. Objective: (7.4) Perform Hypothesis Test for Population Mean

76) State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 890 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 890 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the .10 significance level. Suppose 58 bulbs were tested with the following results: x = 905 hours, s = 77 hours. Find the rejection region for the test of interest to the State University. Objective: (7.4) Perform Hypothesis Test for Population Mean

77) State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 1,000 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 1,000 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the .05 significance level. Suppose 121 bulbs were tested with the following results: x = 1,030 hours, s = 110 hours. Conduct the test using Objective: (7.4) Perform Hypothesis Test for Population Mean

= .05.

78) The scores on a standardized test are reported by the testing agency to have a mean of 70. Based on his personal observations, a school guidance counselor believes the mean score is much higher. He collects the following scores from a sample of 50 randomly chosen students who took the test. 39 71 79 85 90

48 71 79 86 91

55 73 79 86 92

63 74 80 88 92

66 76 80 88 93

68 76 82 88 95

68 76 83 88 96

69 77 83 89 97

Use the data to conduct a test of hypotheses at counselor's suspicions.

70 78 83 89 97

71 79 85 89 99

= .05 to determine whether there is any evidence to support the

Objective: (7.4) Perform Hypothesis Test for Population Mean

79) A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the weight of the chicken. The store advertises that the average weight of their chickens is 4.6 pounds. A random sample of 30 of the store's chickens yielded the weights (in pounds) shown below. 4.4 4.7 4.6 4.4 4.5 4.3 4.6 4.5 4.6 4.9 4.6 4.8 4.3 4.4 4.7 4.5 4.2 4.3 4.1 4.0 4.5 4.6 4.2 4.4 4.7 4.8 5.0 4.2 4.1 4.5 Test whether the population mean weight of the chickens is less than 4.6 pounds. Use

= .05.

Objective: (7.4) Perform Hypothesis Test for Population Mean

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 80) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 39 minutes. The owner has randomly selected 16 customers and delivered pizzas to their homes in order to test whether the mean delivery time actually exceeds 39 minutes. What assumption is necessary for this test to be valid? A) None. The Central Limit Theorem makes any assumptions unnecessary. B) The sample mean delivery time must equal the population mean delivery time. C) The population variance must equal the population mean. D) The population of delivery times must have a normal distribution. Objective: (7.5) Perform Hypothesis Test for Population Mean

81) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 39 minutes. The owner has randomly selected 19 customers and delivered pizzas to their homes in order to test whether the mean delivery time actually exceeds 39 minutes. Suppose the p-value for the test was found to be .0285. State the correct conclusion. A) At = .025, we fail to reject H0 . B) At = .05, we fail to reject H0 . C) At

D) At

= .03, we fail to reject H0 .

Objective: (7.5) Perform Hypothesis Test for Population Mean

= .02, we reject H0 .

82) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X = x X = land_value SAMPLE MEAN OF X = 48,417 SAMPLE VARIANCE OF X = 273,643,254 SAMPLE SIZE OF X = 25 x = 43,974 MEAN X - x = 4443 t = 1.34293 D.F. = 24 P-VALUE = 0.1918585 P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43 Suppose we are interested in testing whether the mean land value from this neighborhood differs from 43,974. Which hypotheses would you test? A) H0 : µ = 43,974 vs. Ha : µ 43,974 B) H0 : µ = 43,974 vs. Ha : µ < 43,974

C) H0 : µ = 43,974 vs. Ha : µ > 43,974

D) H0 : µ 43,974 vs. Ha : µ = 43,974

Objective: (7.5) Perform Hypothesis Test for Population Mean

83) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X = x X = land_value SAMPLE MEAN OF X = 51,215 SAMPLE VARIANCE OF X = 273,643,254 SAMPLE SIZE OF X = 25 x = 46,772 MEAN X - x = 4443 t = 1.34293 D.F. = 24 P-VALUE = 0.1918585 P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43 Find the p-value for testing whether the mean land value differs from $46,772. A) p = 0.808142 B) p = 0.0959288 C) p = 0.308142 Objective: (7.5) Perform Hypothesis Test for Population Mean

D) p = 0.1918585

84) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X = x X = land_value SAMPLE MEAN OF X = 50,927 SAMPLE VARIANCE OF X = 273,643,254 SAMPLE SIZE OF X = 25 x = 46,484 MEAN X - x = 4443 t = 1.34293 D.F. = 24 P-VALUE = 0.1918585 P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43 What is the correct conclusion when testing a greater-than alternative hypothesis at A) Fail to reject Ha . B) Fail to reject H0 . C) Reject H0 .

= .05?

D) Accept H0 .

Objective: (7.5) Perform Hypothesis Test for Population Mean

85) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X = x X = land_value SAMPLE MEAN OF X = 47,780 SAMPLE VARIANCE OF X = 273,643,254 SAMPLE SIZE OF X = 25 x = 43,337 MEAN X - x = 4443 t = 1.34293 D.F. = 24 P-VALUE = 0.1918585 P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43 What assumptions are necessary for any inferences derived from this printout to be valid? A) The sample was selected from an approximately normal population. B) The sampled data are approximately normal. C) The sampling distribution of the sample mean is approximately normal. D) None. The Central Limit Theorem makes any assumptions unnecessary. Objective: (7.5) Perform Hypothesis Test for Population Mean

86) An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 14 ounces printed on each cartridge. To check this claim, a sample of n = 22 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: x = 14.12 ounces, s = .22 ounce. To determine whether the supplier's claim is true, consider the test, H0 : µ = 14 vs. Ha : µ > 14, where µ is the true mean weight of the cartridges. Calculate the value of the test statistic. A) 0.545 B) 1.200

C) 12.000

D) 2.558

Objective: (7.5) Perform Hypothesis Test for Population Mean

87) An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 10 ounces printed on each cartridge. To check this claim, a sample of n = 10 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: x = 10.11 ounces, s = .30 ounce. To determine whether the supplier's claim is true, consider the test, H0 : µ = 10 vs. Ha : µ > 10, where µ is the true mean weight of the cartridges. Find the rejection region for the test using A) |z| > 2.58 C) t > 2.821, where t depends on 9 df

= .01.

B) z > 2.33 D) t > 3.25, where t depends on 9 df

Objective: (7.5) Perform Hypothesis Test for Population Mean

88) A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 22 bottles and finds the average amount of liquid held by the bottles is 9.6 ounces with a standard deviation of .3 ounce. Which of the following is the set of hypotheses the company wishes to test? A) H0 : µ = 10 vs. Ha : µ > 10 B) H0 : µ = 10 vs. Ha : µ 10 C) H0 : µ < 10 vs. Ha : µ = 10

D) H0 : µ = 10 vs. Ha : µ < 10

Objective: (7.5) Perform Hypothesis Test for Population Mean

89) A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 22 bottles and finds the average amount of liquid held by the bottles is 11.6 ounces with a standard deviation of .3 ounce. Calculate the appropriate test statistic. A) t = -3.425 B) t = -6.110 C) t = -6.254 D) t = -29.333 Objective: (7.5) Perform Hypothesis Test for Population Mean

90) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of n = 22 cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. Find a rejection region appropriate for this test if we are using = 0.05. A) Reject H0 if t > 1.725 B) Reject H0 if t > 1.717 C) Reject H0 if t > 2.080 or t < -2.080

D) Reject H0 if t > 1.721

Objective: (7.5) Perform Hypothesis Test for Population Mean

91) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. The information was entered into a spreadsheet and the following printout was obtained: One-Sample T Test Null Hypothesis: µ = 215 Alternative Hyp: µ > 215 95% Conf Interval Mean SE Lower Upper 245.23 15.620 212.740 277.720 1.94 21

Variable Camera Price

T DF 0.0333

Cases Included 22 Is a sample size n = 22 large enough to utilize the central limit theorem in this inferential procedure? A) Yes, since the central limit theorem works whenever means are used B) No, since n < 30 C) No, since either np or nq is less than 15 D) Yes, since both np and nq are greater than or equal to 15 Objective: (7.5) Perform Hypothesis Test for Population Mean

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 92) According to an advertisement, a strain of soybeans planted on soil prepared with a specified fertilizer treatment has a mean yield of 101 bushels per acre. Twenty farmers who belong to a cooperative plant the soybeans in soil prepared as specified. Each uses a 40-acre plot and records the mean yield per acre. The mean and variance for the sample of the 20 farms are x = 86 and s2 = 18,000. Find the rejection region used for determining if the mean yield for the soybeans is not equal to 101 bushels per acre. Use

= .05.

Objective: (7.5) Perform Hypothesis Test for Population Mean

93) A random sample of n = 12 observations is selected from a normal population to test H0 : µ = 22.1 against Ha : µ > 22.1 at

= .05. Specify the rejection region.

Objective: (7.5) Perform Hypothesis Test for Population Mean

94) A random sample of n = 18 observations is selected from a normal population to test H0 : µ = 145 against Ha : µ 145 at

= .10. Specify the rejection region.

Objective: (7.5) Perform Hypothesis Test for Population Mean

95) A random sample of n = 15 observations is selected from a normal population to test H0 : µ = 2.89 against Ha : µ < 2.89 at

= .01. Specify the rejection region.

Objective: (7.5) Perform Hypothesis Test for Population Mean

96) A sample of 6 measurements, randomly selected from a normally distributed population, resulted in the following summary statistics: x = 9.1, s = 1.5. Test the null hypothesis that the mean of the population is 10 against the alternative hypothesis µ < 10. Use = .05. Objective: (7.5) Perform Hypothesis Test for Population Mean

97) A sample of 8 measurements, randomly selected from a normally distributed population, resulted in the following summary statistics: x = 5.2, s = 1.1. Test the null hypothesis that the mean of the population is 4 against the alternative hypothesis µ 4. Use = .05. Objective: (7.5) Perform Hypothesis Test for Population Mean

98) A recipe submitted to a magazine by one of its subscribers states that the mean baking time for a cheesecake is 55 minutes. A test kitchen preparing the recipe before it is published in the magazine makes the cheesecake 10 times at different times of the day in different ovens. The following baking times (in minutes) are observed. 54

Assume that the baking times belong to a normal population. Test the null hypothesis that the mean baking time is 55 minutes against the alternative hypothesis µ > 55. Use = .05. Objective: (7.5) Perform Hypothesis Test for Population Mean

99) An ink cartridge for a laser printer is advertised to print an average of 10,000 pages. A random sample of eight businesses that have recently bought this cartridge are asked to report the number of pages printed by a single cartridge. The results are shown. 9771 9975

9811 10,079

9885 10,145

9914 10,214

Assume that the data belong to a normal population. Test the null hypothesis that the mean number of pages is 10,000 against the alternative hypothesis µ 10,000. Use = .10. Objective: (7.5) Perform Hypothesis Test for Population Mean

100) A random sample of 8 observations from an approximately normal distribution is shown below. 5

Find the observed level of significance for the test of H0 : µ = 5 against Ha : µ 5. Interpret the result. Objective: (7.5) Perform Hypothesis Test for Population Mean

101) Based on the information in the screen below, what would you conclude in the test of H0 : µ 14, Ha : µ > 14. Use = .01.

Objective: (7.5) Perform Hypothesis Test for Population Mean

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given binomial sample size and null-hypothesized value of p0 , determine whether the sample size is large enough to use the normal approximation methodology to conduct a test of the null hypothesis H0 : p = p0 .

102) n = 100, p0 = 0.3 A) No

B) Yes

Objective: (7.6) Perform Hypothesis Test for Population Proportion

103) n = 65, p0 = 0.8 A) No

B) Yes

Objective: (7.6) Perform Hypothesis Test for Population Proportion

104) n = 500, p0 = 0.02 A) No

B) Yes

Objective: (7.6) Perform Hypothesis Test for Population Proportion

105) n = 1,200, p0 = 0.99 A) No

B) Yes

Objective: (7.6) Perform Hypothesis Test for Population Proportion

Solve the problem. 106) The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 30%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 75 have laptops. Find the rejection region for the corresponding test using = .05. A) Reject H0 if z = 1.645. B) Reject H0 if z > 1.96 or z < -1.96. C) Reject H0 if z > 1.645.

D) Reject H0 if z < -1.645.

Objective: (7.6) Perform Hypothesis Test for Population Proportion

107) The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion differs from 25%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.4. Find the p-value for a two-tailed test of hypothesis. A) .4,836 B) .4,918 C) .0164 D) .0082 Objective: (7.6) Perform Hypothesis Test for Population Proportion

108) The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 30%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 85 have laptops. What assumptions are necessary for this test to be satisfied? A) The sample size n satisfies n 30. B) The sample proportion is close to .5. C) The population has an approximately normal distribution. D) The sample size n satisfies both np0 15 and nq0 15. Objective: (7.6) Perform Hypothesis Test for Population Proportion

109) A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of 100 doctors was chosen which resulted in 82 who indicate that they recommend this cough syrup. The test statistic in this problem is approximately: A) 2.67 B) -2.33 C) -2.17 D) -2.67 Objective: (7.6) Perform Hypothesis Test for Population Proportion

110) A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of doctors was taken. Suppose the test statistic is z = -1.75. Can we conclude that H0 should be rejected at the a) = .10, b) = .05, and c) = .01 level? A) a) no; b) no; c) yes

B) a) yes; b) yes; c) yes

C) a) no; b) no; c) no

D) a) yes; b) yes; c) no

Objective: (7.6) Perform Hypothesis Test for Population Proportion

111) A test of hypothesis was performed to determine if the true proportion of college students who preferred a particular brand of soda differs from .50. The ASP printout is supplied below. Note: All data refer to the proportion of students who preferred the brand of soda. HYPOTHESIS: PROPORTION X = x X = drink_(soda=1) SAMPLE PROPORTION OF X = .419162 SAMPLE SIZE OF X = 167 HYPOTHESIZED VALUE (x) = .5 SAMPLE PROPORTION X - x = -.080838 Z = -2.08932 P-VALUE = .0366 P-VALUE/2 = .0183 SD. ERROR = .0386912 State the proper conclusion if the test was conducted at = .10. A) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of soda differs from .50. B) There is insufficient evidence to indicate the true proportion of college students who prefer the brand of soda differs from .50. C) There is insufficient evidence to indicate the true proportion of college students who prefer the brand of soda is less than .50. D) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of soda is less than .50. Objective: (7.6) Perform Hypothesis Test for Population Proportion

112) A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. Find the large-sample rejection region for the test of interest to the college when using a level of significance of 0.01. A) Reject H0 if z < -1.28. B) Reject H0 if z < -2.33 or z > 2.33. C) Reject H0 if z < -2.33.

D) Reject H0 if z < -1.96.

Objective: (7.6) Perform Hypothesis Test for Population Proportion

113) A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. A sample of 108 students was randomly selected and the following printout was obtained: Hypothesis Test - One Proportion Sample Size Successes Proportion

108 16 0.14815

Null Hypothesis: Alternative Hyp:

P = 0.2 P < 0.2

Difference Standard Error -1.35 Z

-0.05185 0.03418 p-value

0.0885

Based on the information contained in the printout, what conclusion would be correct when testing at = 0.05. A) Reject H0 B) Accept HA C) Fail to reject H0 D) Accept H0 Objective: (7.6) Perform Hypothesis Test for Population Proportion

114) A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. The college decided to take a random sample of 108 of their current students to use in the analysis. Is the sample size of n = 108 large enough to use this inferential procedure? A) No B) Yes, since the central limit theorem works whenever proportions are used C) Yes, since n 30 D) Yes, since both np and nq are greater than or equal to 15 Objective: (7.6) Perform Hypothesis Test for Population Proportion

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 115) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 15% of women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 60 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 7. Calculate the test statistic used by the researchers for the corresponding test of hypothesis. Objective: (7.6) Perform Hypothesis Test for Population Proportion

116) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 20% of women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 80 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 9. Is the sample size sufficiently large to conduct this test of hypothesis? Explain. Objective: (7.6) Perform Hypothesis Test for Population Proportion

117) Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 85% of firms in the manufacturing sector still do not offer any child-care benefits. A random sample of 330 manufacturing firms is selected, and only 35 of them offer child-care benefits. Specify the rejection region that the union will use when testing at = .10. Objective: (7.6) Perform Hypothesis Test for Population Proportion

118) Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 85% of firms in the manufacturing sector still do not offer any child-care benefits. A random sample of 270 manufacturing firms is selected and asked if they offer child-care benefits. Suppose the p-value for this test was reported to be p = .1,186. State the conclusion of interest to the union. Use = .05. Objective: (7.6) Perform Hypothesis Test for Population Proportion

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 119) I want to test H0 : p = .7 vs. Ha : p .7 using a test of hypothesis. This test would be called a(n) ____________ test. A) two-tailed

B) upper-tailed

C) lower-tailed

D) one-tailed

Objective: (7.6) Perform Hypothesis Test for Population Proportion

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 120) A company reports that 80% of its employees participate in the company's stock purchase plan. A random sample of 50 employees was asked the question, "Do you participate in the stock purchase plan?" The answers are shown below. yes no no yes no

no yes yes no yes

yes yes no yes no

no no yes yes yes

no yes yes yes yes

yes no no yes yes

yes no yes yes yes

no yes yes no yes

no yes yes yes yes

Perform the appropriate test of hypothesis to investigate your suspicion that fewer than 80% of the company's employees participate in the plan. Use = .05. Objective: (7.6) Perform Hypothesis Test for Population Proportion

121) A random sample of 100 observations is selected from a binomial population with unknown probability of success, ^

p. The computed value of p is equal to .56. Find the observed levels of significance in a test of H0 : p = .5 against Ha : p > .5. Interpret the result. Objective: (7.6) Perform Hypothesis Test for Population Proportion

122) Identify the observed level of significance for the test summarized on the screen below and interpret its value.

Objective: (7.6) Perform Hypothesis Test for Population Proportion

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 123) Let

2 2 0 be a particular value of . Find the value of

A) 21.0642

B) 22.3621

2 2 0 such that P( >

2 0 ) = .10 for n = 14.

C) 19.8119

D) 7.0415

Objective: (7.7) Use Chi-Square Distribution

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 124) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .05 to ensure proper inoculation. A random sample of 49 injections resulted in a variance of .118. Calculate the test statistic for the test of interest. Objective: (7.7) Use Chi-Square Distribution

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 125) A random sample of n observations, selected from a normal population, is used to test the null hypothesis H0 : 2 = 155. Specify the appropriate rejection region. Ha : 2 < 155, n = 14, = .01 A) 2 < 4.10691 B) 2 < 27.6883

C) 2 < 29.1413

D) 2 < 4.66043

Objective: (7.7) Use Chi-Square Distribution

126) A random sample of n observations, selected from a normal population, is used to test the null hypothesis H0 : 2 = 155. Specify the appropriate rejection region. Ha : 2 155, n = 10, = .05 A) 2 < 3.32511 or 2 > 16.9190

B) 2 < 3.24697 or 2 > 20.4831 D) 2.70039 < 2 < 19.0228

C) 2 < 2.70039 or 2 > 19.0228

Objective: (7.7) Use Chi-Square Distribution

127) A random sample of n observations, selected from a normal population, is used to test the null hypothesis H0 : 2 = 155. Specify the appropriate rejection region. Ha : 2 > 155, n = 25, = .10 A) 2 > 36.4151 B) 2 > 33.1963

C) 2 > 34.3816

D) 2 > 15.6587

Objective: (7.7) Use Chi-Square Distribution

128) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 51 students and asked each to provide the amount of time they spent traveling to campus. The sample results found that the sample mean was 23.243 minutes and the sample standard deviation was 20.40 minutes. Find the rejection region for determining if the population standard deviation exceeds 20 minutes. Use = 0.05. A) Reject H0 if z > 1.645 B) Reject H0 if 2 > 71.4202 C) Reject H0 if 2 > 34.7642 D) Reject H0 if 2 > 67.5048 Objective: (7.7) Use Chi-Square Distribution

129) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 51 students and asked each to provide the amount of time they spent traveling to campus. The sample results found that the sample mean was 23.243 minutes and the sample standard deviation was 20.40 minutes. It is desired to determine if the population standard deviation exceeds 20 minutes. Calculate the test statistic for this test of hypothesis. A) 2 = 51 B) 2 = 58.11 C) 2 = 53.06 D) 2 = 52.02 Objective: (7.7) Perform Test of Hypothesis for Population Variance

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 130) An educational testing service designed an achievement test so that the range in student scores would be greater than 300 points. To determine whether the objective was achieved, the testing service gave the test to a random sample of 47 students and found that the sample mean and variance were 780 and 2,274, respectively. Specify the null and alternative hypotheses for determining whether the test achieved the desired dispersion in scores. Assume that range = 6 . Objective: (7.7) Perform Test of Hypothesis for Population Variance

131) An educational testing service designed an achievement test so that the range in student scores would be greater than 300 points. To determine whether the objective was achieved, the testing service gave the test to a random sample of 30 students and found that the sample mean and variance were 759 and 1943, respectively. Conduct the test for H0 : 2 = 2,500 vs. Ha : 2 > 2,500 using = .025. Assume the range is 6 . Objective: (7.7) Perform Test of Hypothesis for Population Variance

132) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .08 to ensure proper inoculation. A random sample of 31 injections resulted in a variance of .118. Specify the rejection region for the test. Use = .10. Objective: (7.7) Perform Test of Hypothesis for Population Variance

133) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .06 to ensure proper inoculation. A random sample of 25 injections was measured. Suppose the p-value for the test is p = .0085. State the proper conclusion using = .01. Objective: (7.7) Perform Test of Hypothesis for Population Variance

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 134) It is desired to test H0 : µ = 55 against Ha : µ < 55 using

= .10. The population in question is uniformly distributed

with a standard deviation of 20. A random sample of 64 will be drawn from this population. If µ is really equal to 50, what is the probability that the hypothesis test would lead the investigator to commit a Type II error? A) .2358 B) .2642 C) .7642 D) .4716 Objective: (7.8) Find and Interpret

135) It is desired to test H0 : µ = 12 against Ha : µ 12 using

= 0.05. The population in question is uniformly distributed

with a standard deviation of 2.0. A random sample of 100 will be drawn from this population. If µ is really equal to 11.9, what is the value of associated with this test? A) .0791 B) .9209 C) .4210 D) .0395 Objective: (7.8) Find and Interpret

136) It is desired to test H0 : µ = 50 against HA: µ 50 using

= 0.10. The population in question is uniformly

distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If µ is really equal to 48, what is the probability that the hypothesis test would lead the investigator to commit a Type II error? A) 0.8994 B) 0.7567 C) 0.2433 D) 0.1006 Objective: (7.8) Find and Interpret

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 137) It has been estimated that the G-car obtains a mean of 35 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects 36 G-cars and records the mileage obtained for each car over a driving course similar to that used to obtain the estimate. The following data resulted: x = 36.8 miles per gallon, s = 6 miles per gallon. Calculate the value of if the true value of the mean is 37 miles per gallon. Use = .025. Objective: (7.8) Find and Interpret

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 138) It is desired to test H0 : µ = 55 against Ha : µ < 55 using

= .10. The population in question is uniformly distributed

with a standard deviation of 15. A random sample of 49 will be drawn from this population. If µ is really equal to 50, what is the power of this test? A) .8531 B) .1469 C) .3531 D) .2938 Objective: (7.8) Find and Interpret Power of Test

139) It is desired to test H0 : µ = 50 against HA: µ 50 using

= 0.10. The population in question is uniformly

distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If µ is really equal to 45, what is the power of the test? A) 0.7544 B) 0.2456 C) 0.8959 D) 0.1041 Objective: (7.8) Find and Interpret Power of Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 140) It has been estimated that the G-car obtains a mean of 30 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects 64 G-cars and records the mileage obtained for each car over a driving course similar to that used to obtain the estimate. The following data resulted: x = 31.2 miles per gallon, s = 8 miles per gallon. Calculate the power of the test if the true value of the mean is 31 miles per gallon. Use a value of = .025. Objective: (7.8) Find and Interpret Power of Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 141) The null distribution is the distribution of the test statistic assuming the null hypothesis is true; it mound shaped and symmetric about the null mean µ0 . A) True

B) False

Objective: (7.8) Find and Interpret Power of Test

142) Type I errors and Type II errors are complementary events so that = P(Type I error) = 1 - P(Type II error) = 1 - . A) True B) False Objective: (7.8) Find and Interpret Power of Test

143) Under the assumption that µ = µa , where µa is the alternative mean, the distribution of x is mound shaped and symmetric about µa .

A) True

B) False

Objective: (7.8) Find and Interpret Power of Test

144) The value of

is the area under the bell curve for the distribution of x centered at µa for values of x that fall within

the acceptance region of the distribution of x centered at µ0 .

A) True

Objective: (7.8) Find and Interpret Power of Test

B) False

Answer Key Testname: SB14ECH7TEST

1) B 2) A 3) C 4) D 5) D 6) A 7) B 8) To determine if the new method is more accurate in detecting cancer than the old method, we test: H0 : p = .22 vs. Ha : p < .22 9) To determine if the mean yield for the soybeans differs from 459 bushels per acre, we test:

29)

31)

33)

30)

32)

H0 : µ = 459 vs. Ha : µ 459 10) A 11) D 12) C 13) D 14) B 15) B 16) B 17) D 18) A 19) C 20) B 21) C 22) A 23) B 24) B 25) B 26) B 27) B 28) C

34)

Answer Key Testname: SB14ECH7TEST

35)

36) B 37) B 38) B 39) B 40) A 41) B 42) A 43) B 44) A 45) A 46) B 47) A 48) A 49) B 50) B 51) A 52) A 53) Since the p-value, .00335, is less than .01, we reject the null hypothesis in favor of the alternative hypothesis. 54) C 55) D 56) D 57) C 58) C 59) A

60) p-value = P(z >1.38) = .5 - .4162 = .0838; The probability of a test statistic even more contradictory to the null hypothesis than the one observed is .0838. 61) p-value = P(z < -2.11 or z > 2.11) = 2(.5 .4826) = .0348; The probability of a test statistic even more contradictory to the null hypothesis than the one observed is .0348. 62) The z-statistic is z = 13.1 - 12 2.22. 4.3 / 75

64) x = 79.98, s = 12.34; z 79.98 - 75 = 2.85. 12.34 / 50 p-value = P(z >2.85) = .5 - .4978 = .0022; The probability of a test statistic even more contradictory to the null hypothesis than the one observed is .0022. 65) p = .0037; The probability of a test statistic even more contradictory than the one observed is .0037. 66) B 67) B 68) D 69) B 70) D 71) D 72) D 73) D 74) D 75) To determine whether the mean time has been reduced, we test:

p-value = P(z >2.22) = .5 - .4868 = .0132; The probability of a test statistic even more contradictory to the null hypothesis than the one observed is .0132. 63) The z-statistic is z = 247.3 - 250 -2.36. 11.4 / 100

H0 : µ = 63 vs. Ha : µ < 63

p-value = P(z < -2.36 or z > 2.36) = 2(.5 .4909) = .0182; The probability of a test statistic even more contradictory to the null hypothesis than the one observed is .0182.

The rejection region requires = .05 in the lower tail of the z distribution. From a z table, we find z.05 = 1.645. The rejection region is z < -1.645.

76) To determine if the mean exceeds 890 hours, we test: H0 : µ = 890 vs. Ha : µ > 890 The rejection region requires = .10 in the upper tail of the z distribution. From a z table, we find z.10 = 1.28. The rejection region is z > 1.28. 77) To determine if the mean life exceeds 1,000 hours, we test: H0 : µ = 1,000 vs. Ha : µ > 1,000 The test statistic is z = x - µ0

x - µ0

/ n

s/ n

1,030 - 1,000 = 3. 110/ 121 Since the test is greater than 1.645, H0 can be rejected. There is sufficient evidence to indicate the average life of the new bulbs exceeds 1,000 hours when testing at = .05.

Answer Key Testname: SB14ECH7TEST

78) H0 : µ = 70 vs. Ha : µ > 70; x = 79.98, s = 79.98 - 70 12.34; z = 12.34 / 50 5.72 Since 5.72 > 1.645, we reject the null hypothesis in favor of the alternative hypothesis. There is evidence to support the counselor's suspicions. 79) H0 : µ = 4.6; Ha : µ < 4.6; x = 4.48; s = .2455; z = 4.48 - 4.6 -2.677; .2455 / 30 rejection region: z < -1.645; Since the test statistic falls within the rejection region, we reject the null hypothesis in favor of the alternative hypothesis. There is evidence that the mean weight of the chicken is less than 4.6 pounds. 80) D 81) A 82) A 83) D 84) B 85) A 86) D 87) C 88) D 89) C 90) D 91) B

92) The rejection region requires /2 = .05/2 = .025 in both tails of the t distribution with df = n - 1 = 20 - 1 = 19. The rejection region is t > 2.093 or t < -2.093. 93) Using 11 degrees of freedom, t.05 = 1.796.

97) The test statistic is 5.2 - 4 t= 3.09. 1.1 / 8

= 1.740. The rejection region is t < -1.740 or t > 1.740. 95) Using 14 degrees of freedom, t.01 = 2.624.

98) x = 59.4, s = 3.24; The test statistic is 59.4 - 55 t= 4.29. 3.24 / 10

The rejection region is t < -2.365 or t > 2.365. Since the test statistic falls in the rejection region, we reject the null hypothesis in favor of the alternative hypothesis. We conclude that 4 is not the true population mean.

The rejection region is t > 1.796. 94) Using 17 degrees of freedom, t.10/2 = t.05

The rejection region is t > 1.833. Since the test statistic falls in the rejection region, we reject the null hypothesis in favor of the alternative hypothesis. We conclude that the true mean baking time is actually greater than 55 minutes.

The rejection region is t < -2.624. 96) The test statistic is 9.1 - 10 t= -1.47. 1.5 / 6

The rejection region is t < -2.015. Since the test statistic does not fall in the rejection region, we can not reject the null hypothesis in favor of the alternative hypothesis. We cannot conclude that the true population mean is actually less than 10.

99) x = 9974.25, s = 159.09; The test statistic is 9,974.25 - 10,000 t= 159.09 / 8 The rejection region is t < 1.895 or t > 1.895. Since the test statistic does not fall in the rejection region, we can not reject the null hypothesis in favor of the alternative hypothesis. We cannot conclude that the mean number of pages printed per cartridge is different than 10,000. 100) p = .649; The probability of a test statistic even more contradictory than the one observed is .649. 101) Since the p-value, .104, is greater than .01, we do not reject the null hypothesis. 102) B 103) A 104) A 105) A 106) C 107) C 108) D 109) D 110) D 111) A 112) C 113) C 114) D

-.458.

Answer Key Testname: SB14ECH7TEST

115) The test statistic is z = ^

p - p0 p 0 q0

where p =

n 7 = .1,167. 60 The test statistic is z = .1,167 - .15 = -.72. .15(.85) 60

116) To determine if the sample size is large enough for the test of hypothesis to work properly, we need to calculate np0 and nq0 . np0 = 80(.2) = 16 > 15 and nq0 = 80(.8) = 64 > 15 Since both quantities are greater than 15, the sample size is large enough for the test of hypothesis to work properly. 117) To determine if more than 85% of the firms do not offer any child-care benefits, we test: H0 : p = .85 vs. Ha : p > .85 The rejection region requires = .10 in the upper tail of the z distribution. The rejection region is z > z.10 = 1.28.

118) At = .05, < p-value = .1,186, so H0 cannot be

124) The test statistic is X2 (n - 1)s2 = = 2 0

rejected. There is insufficient evidence to indicate that more than 85% of the firms do not offer any child-care benefits. 119) A ^ 32 = .64; The test 120) p = 50

(49 - 1).118 = .05

113.280. 125) A 126) C 127) B 128) D 129) D statistic is 130) To determine if the .64 - .8 z= -2.828. test achieved the (.8)(.2) / 50 desired dispersion, The rejection region we test: is z < 1.645. Since the test statistic falls H0 : 2 = 2,500 vs. within the rejection region, we reject the Ha : 2 > 2,500 null hypothesis in favor of the alternative hypothesis and conclude that fewer than 80% of the company's employees participate in the stock plan. 121) The p-value is .115.; The probability of a test statistic even more contradictory than the one observed is .115. 122) The p-value is .010.; The probability of a test statistic even more contradictory than the one observed is .010. 123) C

131) We test H0: 2 = 2,500

Ha : 2 >

2,500 The test statistic is X2 (n -1)s2 = = 2 (30 -1)1943 = 22.539 2,500 The rejection region requires = .025 in the upper tail of the X2 distribution with

n - 1 = 30 - 1 = 29 df. So X2 .025 = 45.722. The rejection region is X2 > 45.722. Since the observed value of the test statistic does not fall in the rejection region (X2 = 22.539 45.722),

H0 cannot be rejected. There is insufficient evidence to indicate the variance is greater than 2,500 at = .025. 132) The rejection region requires = .10 in the upper tail of the X2 distribution with n - 1 = 31 - 1 = 30 df. From Table VII, Appendix B, X2 .10 = 40.256. The rejection region is X2 > 40.256.

Answer Key Testname: SB14ECH7TEST

133) Since = .01 > p = .00 85, H0 can be

140) Since the alternative hypothesis is Ha : µ >

rejected. There is sufficient evidence to indicate that the variance in the amount of serum injected exceeds .06. 134) A 135) B 136) B 137) Since the alternative hypothesis is Ha : µ >

30, the test is one-tailed. Thus, = .025 is required in the upper tail of the z distribution, and we have z.025 = 1.96. The

35, the test is one-tailed. Thus, = .025 is required in the upper tail of the z distribution, and we have z.025 = 1.96. The value of x on the border between the rejection region and the acceptance region is found using

value of x on the border between the rejection region and the acceptance region is found using x=z 1.96

1.96

+ 35

6 + 35 36

36.96 = P(x < 36.96, when µa = 37) = P z<

36.96 - 37 = P(z 6/ 36

8 + 30 64

31.96

= P(x < 31.96, when µa = 31) = P z<

x=z

+ 30

31.96 - 31 = P(z 8/ 64

< 0.96) = .5 + .3315 = .8315 The power is 1 - = 1 - .8315 = .1685. 141) A 142) B 143) A 144) A

< -.04) = .5 - .0160 = .4840 138) A 139) A

McClave Statistics for Business and Economics Chapter 8 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Which of the following represents the difference in two population means? A) p 1 + p 2 B) p 1 - p 2 C) µ1 - µ2

D) µ1 + µ2

Objective: (8.1) Identify Target Parameter

2) Which of the following represents the difference in two population proportions? 2 1 A) µ1 - µ2 B) p 1 - p 2 C) 2 2

D) p 1 + p 2

Objective: (8.1) Identify Target Parameter

3) Which of the following represents the ratio of variances? 2 p1 1 A) B) 2 p2 2

C) p 1 - p 2

µ1 µ2

Objective: (8.1) Identify Target Parameter

4) A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this particular manufacturer from one day to the next. Twenty-eight random working days were selected and each plan was monitored and the number of items produced each day was recorded. Some of the collected data is shown below: DAY PLAN 1 OUTPUT PLAN 2 OUTPUT 1 1234 units 1311 units 2 1355 units 1366 units 3 1300 units 1289 units What type of analysis will best allow the manufacturer to determine which plan is more effective? A) An independent samples comparison of population proportions. B) A test of a single population proportion. C) A paired difference comparison of population means. D) An independent samples comparison of population means. Objective: (8.1) Identify Target Parameter

5) When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex - males or females - is more likely to respond. Random, independent samples of 60 females and 100 males were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes between the male and female responses. What type of analysis should be used? A) An independent samples comparison of population proportions. B) A test of a single population proportion. C) An independent samples comparison of population means. D) A paired difference comparison of population means. Objective: (8.1) Identify Target Parameter

6) A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. What type of analysis should be used to compare the mean age of male and female purchasers? A) A test of a single population mean. B) A paired difference comparison of population means. C) An independent samples comparison of population means. D) An independent samples comparison of population proportions. Objective: (8.1) Identify Target Parameter

7) Calculate the degrees of freedom associated with a small-sample test of hypothesis for (µ1 - µ2 ), assuming 1 2 = 2 2 and n1 = n2 = 16. A) 33

B) 30

C) 15

D) 31

Objective: (8.2) Understand Process of Comparing Two Independent Means

8) Calculate the degrees of freedom associated with a small-sample test of hypothesis for (µ1 - µ2 ), assuming 1 2 = 2 2 and n1 = n2 = 12. A) 12

B) 11

C) 25

D) 23

Objective: (8.2) Understand Process of Comparing Two Independent Means

9) Calculate the degrees of freedom associated with a small-sample test of hypothesis for (µ1 - µ2 ), assuming 12 2 2 and n1 = n2 = 20. A) 15

B) 31

C) 30

D) 33

Objective: (8.2) Understand Process of Comparing Two Independent Means

10) Calculate the degrees of freedom associated with a small-sample test of hypothesis for (µ1 - µ2 ), assuming 12 2 2 and n1 = 13, n2 = 12, s1 = 1.3, s2 = 1.5. A) 12 B) 25

C) 11

Objective: (8.2) Understand Process of Comparing Two Independent Means

D) 23

11) Salary data were collected from CEOs in the consumer products industry and CEOs in the telecommunication industry. The data were analyzed using a software package in order to compare mean salaries of CEOs in the two industries. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM SALARY X = Consumer Products Y = Telecommunications SAMPLE MEAN OF X = 1761 SAMPLE VARIANCE OF X = 3.97555E6 SAMPLE SIZE OF X = 21 SAMPLE MEAN OF Y = 1093.5 SAMPLE VARIANCE OF Y = 103255 SAMPLE SIZE OF Y = 21 MEAN X - MEAN Y = test statistic = D. F. = P-VALUE = P-VALUE/2 = SD. ERROR =

667.5 1.47809 40 0.147626 0.0738131 451.597

What of the following assumptions is necessary to perform the test described above? A) The means of the two populations of salaries are equal. B) The standard deviations of the two populations of salaries are both large. C) The population of salaries for each of the two industries has an approximately normal distribution. D) None. The Central Limit Theorem takes care of all assumptions Objective: (8.2) Understand Process of Comparing Two Independent Means

12) In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below:

Adults (1) Children (2)

Sample Mean 77.5° F 74.5°F

Sample Variance 4.5 2.5

Find the standard error of the estimate for the difference in mean comfortable room temperatures between adults and children. A) 0.8367 B) 0.7000 C) 0.1871 D) 1.6279 Objective: (8.2) Understand Process of Comparing Two Independent Means

13) Consider the following set of salary data:

Sample Size Mean Standard Deviation

Men (1) Women (2) 100 80 $12,850 $13,000 $345 $500

What assumptions are necessary to perform a test for the difference in population means? A) The two samples were independently selected from the populations of men and women. B) The population variances of salaries for men and women are equal. C) Both of the target populations have approximately normal distributions. D) All of the above are necessary. Objective: (8.2) Understand Process of Comparing Two Independent Means

14) Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs in the low-tech industry with CEOs in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN industry 1 (low tech) (NUMBER = 15) industry 3 (consumer products) (NUMBER = 15) ___________________________________________________ X = industry1 Y = industry3 SAMPLE MEAN OF X = 157.286 SAMPLE VARIANCE OF X = 1563.45 SAMPLE SIZE OF X = 14 SAMPLE MEAN OF Y = 217.583 SAMPLE VARIANCE OF Y = 1601.54 SAMPLE SIZE OF Y = 12 MEAN X - MEAN Y = -60.2976 t = -4.23468 P-VALUE = 0.000290753 P-VALUE/2 = 0.000145377 SD. ERROR = 14.239 Using the printout, which of the following assumptions is not necessary for the test to be valid? A) The samples were randomly and independently selected. B) The population variances are equal. C) The population means are equal. D) Both populations have approximately normal distributions. Objective: (8.2) Understand Process of Comparing Two Independent Means

15) Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs in the low tech industry with CEOs in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN industry 1 (low tech) (NUMBER = 15) industry 3 (consumer products) (NUMBER = 15) _____________________________________________________________ X = industry1 Y = industry3 SAMPLE MEAN OF X = 157.286 SAMPLE VARIANCE OF X = 1563.45 SAMPLE SIZE OF X = 14 SAMPLE MEAN OF Y = 217.583 SAMPLE VARIANCE OF Y = 1601.54 SAMPLE SIZE OF Y = 12 MEAN X - MEAN Y = -60.2976 t = -4.23468 P-VALUE = 0.000290753 P-VALUE/2 = 0.000145377 SD. ERROR = 14.239 If we conclude that the mean return-to-pay ratios of the consumer products and low tech CEOs are equal when, in fact, a difference really does exist between the means, we would be making a __________. A) Type II error B) Type I error C) correct decision D) Type III error Objective: (8.2) Understand Process of Comparing Two Independent Means

16) A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here: Female: n = 10, Male: n = 10,

sample mean = 50.30, sample standard deviation = 13.215 sample mean = 39.80, sample standard deviation = 10.040

Which of the following assumptions must be true in order for the pooled test of hypothesis to be valid? I. Both the male and female populations of ages must possess approximately normal probability distributions. II. Both the male and female populations of ages must possess population variances that are equal. III. Both samples of ages must have been randomly and independently selected from their respective populations. A) I, II, and III B) II only C) I only D) III only Objective: (8.2) Understand Process of Comparing Two Independent Means

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 17) Independent random samples of 100 observations each are chosen from two normal populations with the following means and standard deviations. Population 1 µ1 = 15 1=3

Population 2 µ2 = 13 2=2

Find the mean and standard deviation of the sampling distribution of (x 1 - x 2 ). Objective: (8.2) Understand Process of Comparing Two Independent Means

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 18) A confidence interval for (µ1 - µ2 ) is (-5, 8). Which of the following inferences is correct? A) µ1 = µ2

B) µ1 < µ2

C) µ1 > µ2

D) no significant difference between means

Objective: (8.2) Construct and Interpret Confidence Interval

19) A confidence interval for (µ1 - µ2 ) is (5, 8). Which of the following inferences is correct? A) µ1 < µ2

B) µ1 = µ2

C) µ1 > µ2

D) no significant difference between means

Objective: (8.2) Construct and Interpret Confidence Interval

20) In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below:

Adults (1) Children (2)

Sample Mean 77.5° F 74.5°F

Sample Variance 4.5 2.5

Suppose that the psychologist decides to construct a 99% confidence interval for the difference in mean comfortable room temperatures instead of proceeding with a test of hypothesis. The 99% confidence interval turns out to be (-2.9, 3.1). Select the correct statement. A) It can be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults. B) It can be concluded at the 99% confidence level that the true mean room temperature for adults exceeds that for children. C) It cannot be concluded at the 99% confidence level that there is actually a difference between the true mean comfortable room temperatures for the two groups. D) It can be concluded at the 99% confidence level that the true mean comfortable room temperature is between -2.9 and 3.1. Objective: (8.2) Construct and Interpret Confidence Interval

21) University administrators are trying to decide where to build a new parking garage on campus. The state legislature has budgeted just enough money for one parking structure on campus. The administrators have determined that the parking garage will be built either by the college of engineering or by the college of business. To help make the final decision, the university has randomly and independently asked students from each of the two colleges to estimate how long they usually take to find a parking spot on campus (in minutes). Based on their sample, the following 95% confidence interval (for µe - µb) was created - (4.20, 10.20). What conclusion can the university make about the population mean parking times based on this confidence interval? A) They are 95% confident that the mean parking time of all business students equals the mean parking time of all engineering students. B) They are 95% confident that the mean parking time of all business students is less than the mean parking time of all engineering students. C) They are 95% confident that the mean parking time of all business students exceeds the mean parking time of all engineering students. Objective: (8.2) Construct and Interpret Confidence Interval

22) University administrators are trying to decide where to build a new parking garage on campus. The state legislature has budgeted just enough money for one parking structure on campus. The administrators have determined that the parking garage will be built either by the college of engineering or by the college of business. To help make the final decision, the university has randomly and independently asked students from each of the two colleges to estimate how long they usually take to find a parking spot on campus (in minutes). Suppose that the sample sizes selected by the university for the two samples were both n e = n b = 15. What critical value should be used by the university in the calculations for the 95% confidence interval for µe - µb? Assume that the university used the pooled estimate of the population variances in the calculation of the confidence interval. A) z = 1.645 B) t = 2.042 C) z = 1.96 D) t = 1.701 E) t = 2.048 Objective: (8.2) Construct and Interpret Confidence Interval

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 23) In order to compare the means of two populations, independent random samples of 144 observations are selected from each population with the following results. Sample 1

Sample 2

x 1 = 7,123

x 2 = 6,957

s1 = 175

s2 = 225

Use a 95% confidence interval to estimate the difference between the population means (µ1 - µ2 ). Interpret the confidence interval.

Objective: (8.2) Construct and Interpret Confidence Interval

24) Independent random samples selected from two normal populations produced the following sample means and standard deviations. Sample 1 n1 = 14

Sample 2 n2 = 11

x 1 = 7.1

x 2 = 8.4

s1 = 2.3

s2 = 2.9

Find and interpret the 95% confidence interval for (µ1 - µ2 ). Objective: (8.2) Construct and Interpret Confidence Interval

25) The screen below shows the 95% confidence interval for (µ1 - µ2 ).

What does the interval suggest about the relationship between µ1 and µ2? Objective: (8.2) Construct and Interpret Confidence Interval

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 26) The owners of an industrial plant want to determine which of two types of fuel (gas or electricity) will produce more useful energy at a lower cost. The cost is measured by plant investment per delivered quad ($ invested /quadrillion BTUs). The smaller this number, the less the industrial plant pays for delivered energy. Suppose we wish to determine if there is a difference in the average investment/quad between using electricity and using gas. Our null and alternative hypotheses would be: A) H0 : (µe - µg ) = 0 vs. Ha: (µe - µg ) < 0 B) H0 : (µe - µg ) = 0 vs. Ha: (µe - µg ) 0 C) H0 : (µe - µg ) = 0 vs. Ha: (µe - µg ) > 0

D) H0 : (µe - µg ) = 0 vs. Ha: (µe - µg ) = 0

Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

27) The owners of an industrial plant want to determine which of two types of fuel (gas or electricity) will produce more useful energy at a lower cost. The cost is measured by plant investment per delivered quad ($ invested /quadrillion BTUs). The smaller this number, the less the industrial plant pays for delivered energy. Random samples of 11 similar plants using electricity and 16 similar plants using gas were taken, and the plant investment/quad was calculated for each. In an analysis of the difference of means of the two samples, the owners were able to reject H0 in the test H0 : (µE - µG) = 0 vs. Ha: (µE - µG) > 0. What is our best interpretation of the result? A) The mean investment/quad for electricity is less than the mean investment/quad for gas. B) The mean investment/quad for electricity is different from the mean investment/quad for gas. C) The mean investment/quad for electricity is greater than the mean investment/quad for gas. D) The mean investment/quad for electricity is not different from the mean investment/quad for gas. Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

28) In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below:

Adults (1) Children (2)

Sample Mean 77.5° F 74.5°F

Sample Variance 4.5 2.5

If the psychologist wished to test the hypothesis that children prefer warmer room temperatures than adults, which set of hypotheses would he use? A) H0 : (µ1 - µ2 ) = 0 vs. H0 : (µ1 - µ2 ) > 0 B) H0 : (µ1 - µ2 ) = 0 vs. H0 : (µ1 - µ2 ) = 0

C) H0 : (µ1 - µ2 ) = 3 vs. H0 : (µ1 - µ2 )

D) H0 : (µ1 - µ2 ) = 0 vs. H0 : (µ1 - µ2 ) < 0

Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

29) Consider the following set of salary data:

Sample Size Mean Standard Deviation

Men (1) Women (2) 100 80 $12,850 $13,000 $345 $500

To determine if women have a higher mean salary than men, we would test: A) H0 : µ1 - µ2 = 0 vs. Ha : µ1 - µ2 < 0 B) H0 : µ1 - µ2 = 0 vs. Ha : µ1 - µ2 > 0

C) H0 : µ1 - µ2 = 0 vs. Ha : µ1 - µ2 0

D) H0 : µ1 - µ2 = 0 vs. Ha : µ1 - µ2 = 0

Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

30) Consider the following set of salary data:

Sample Size Mean Standard Deviation

Men (1) Women (2) 100 80 $12,850 $13,000 $345 $500

Calculate the appropriate test statistic for a test about µ1 - µ2 .

A) z = -2.45

B) z = -2.81

C) z = -2.28

D) z = -3.02

Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

31) Consider the following set of salary data:

Sample Size Mean Standard Deviation

Men (1) Women (2) 100 80 $12,850 $13,000 $345 $500

Suppose the test statistic turned out to be z = -1.20 (not the correct value). Find a two-tailed p-value for this test statistic. A) .6151 B) .1151 C) .2302 D) .3849 Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

32) Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs in the low-tech industry and CEOs in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN industry 1 (low tech) (NUMBER = 15) industry 3 (consumer products) (NUMBER = 15) ___________________________________________________ X = industry1 Y = industry3 SAMPLE MEAN OF X = 157.286 SAMPLE VARIANCE OF X = 1563.45 SAMPLE SIZE OF X = 14 SAMPLE MEAN OF Y = 217.583 SAMPLE VARIANCE OF Y = 1601.54 SAMPLE SIZE OF Y = 12 MEAN X - MEAN Y = -60.2976 t = -4.23468 P-VALUE = 0.000290753 P-VALUE/2 = 0.000145377 SD. ERROR = 14.239 Using the printout above, find the test statistic necessary for testing whether the mean return-to-pay ratio of low tech CEO's exceeds the return-to-pay ratio of consumer product CEOs. A) -60.2976 B) 14.239 C) .000145377 D) -4.23468 Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

33) Data were collected from CEOs in the consumer products industry and CEOs in the telecommunication industry. The data were analyzed using a software package in order to compare mean salaries of CEOs in the two industries. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM SALARY X = Consumer Products Y = Telecommunications SAMPLE MEAN OF X = 1761 SAMPLE VARIANCE OF X = 3.97555E6 SAMPLE SIZE OF X = 21 SAMPLE MEAN OF Y = 1093.5 SAMPLE VARIANCE OF Y = 103255 SAMPLE SIZE OF Y = 21 MEAN X - MEAN Y = test statistic = D. F. = P-VALUE = P-VALUE/2 = SD. ERROR =

667.5 1.47809 40 0.147626 0.0738131 451.597

Find the p-value for testing a two-tailed alternative hypothesis. A) 0.9261869 B) 0.295252 C) 0.0738131 Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

D) 0.147626

34) Data were collected from CEOs in the consumer products industry and the CEOs in the telecommunication industry. The data were analyzed using a software package in order to compare mean salaries of CEOs in the two industries. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM SALARY X = Consumer Products Y = Telecommunications SAMPLE MEAN OF X = 1761 SAMPLE VARIANCE OF X = 3.97555E6 SAMPLE SIZE OF X = 21 SAMPLE MEAN OF Y = 1093.5 SAMPLE VARIANCE OF Y = 103255 SAMPLE SIZE OF Y = 21 MEAN X - MEAN Y = test statistic = D. F. = P-VALUE = P-VALUE/2 = SD. ERROR =

667.5 1.47809 40 0.147626 0.0738131 451.597

Using = .05, give the rejection region for a two-tailed test. A) Reject H0 if t > 2.021.

C) Reject H0 if t > 1.684.

B) Reject H0 if t > 1.684 or t < -1.684. D) Reject H0 if t > 2.021 or t < -2.021.

Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

35) A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here: Female: n = 20, Male: n = 20,

sample mean = 50.30, sample standard deviation = 13.215 sample mean = 39.80, sample standard deviation = 10.040

Suppose the test statistic was calculated to be the value, t = 2.83. Use the rejection region to state the correct conclusion when testing at alpha = 0.05. A) We fail to reject H0 . B) We accept H0 . C) We reject H0 . Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

36) A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here: Female: n = 10, Male: n = 10,

sample mean = 50.30, sample standard deviation = 13.215 sample mean = 39.80, sample standard deviation = 10.040

Find the rejection region to state the correct conclusion when testing at alpha = 0.01. A) Reject H0 if t > 2.528 B) Reject H0 if t > 2.552

C) Reject H0 if t > 1.330

D) Reject H0 if t > 2.878

Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 37) In order to compare the means of two populations, independent random samples of 225 observations are selected from each population with the following results. Sample 1

Sample 2

x 1 = 478

x 2 = 481

s1 = 14.2

s2 = 11.2

Test the null hypothesis H0 : (µ1 - µ2 ) = 0 against the alternative hypothesis Ha : (µ1 - µ2 )

0 using

= .10. Give

the significance level, and interpret the result.

Objective: (8.2) Conduct Test of Hypothesis to Compare Two Independent Means

38) Assume that

1 2 = 2 2 = 2 . Calculate the pooled estimator of 2 for s1 2 = 50, s2 2 = 57, and n1 = n2 = 18.

Objective: (8.2) Conduct Pooled Hypothesis Test

39) Assume that

1 2 = 2 2 = 2 . Calculate the pooled estimator of 2 for s1 2 = .88, s2 2 = 1.01, n1 = 10, and n2 = 12.

Objective: (8.2) Conduct Pooled Hypothesis Test

40) Independent random samples from normal populations produced the results shown below. Sample 1: 5.8, 5.1, 3.9, 4.5, 5.4 Sample 2: 4.4, 6.1, 5.2, 5.7 a. b. c.

Calculate the pooled estimator of 2 . Test µ1 < µ2 using = .10.

Find a 90% confidence interval for (µ1 - µ2 ).

Objective: (8.2) Conduct Pooled Hypothesis Test

41) Independent random samples selected from two normal populations produced the following sample means and standard deviations. Sample 1 n1 = 14

Sample 2 n2 = 11

x 1 = 7.1

x 2 = 8.4

s1 = 2.3

s2 = 2.9

Conduct the test H0 : (µ1 - µ2 ) = 0 against. Ha: (µ1 - µ2 )

0, Use

= .05.

Objective: (8.2) Conduct Pooled Hypothesis Test

42) The screens below show the results of a test of H0 : (µ1 - µ2 ) = 0 against Ha: (µ1 - µ2 ) 0

Comment on the validity of the results. Objective: (8.2) Conduct Pooled Hypothesis Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 43) A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here: Female: n = 20, Male: n = 20,

sample mean = 50.30, sample standard deviation = 13.215 sample mean = 39.80, sample standard deviation = 10.040

Use the pooled estimate of the population standard deviation to calculate the value of the test statistic to use in this test of hypothesis. A) t = 2.17 B) t = 3.17 C) t = 2.83 D) t = 2.65 Objective: (8.2) Conduct Pooled Hypothesis Test

44) We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table:

Supermarket 1 2 3 4 5 6 7 8

Price Brand 1 Brand 2 $2.25 $2.30 2.47 2.45 2.38 2.44 2.27 2.29 2.15 2.25 2.25 2.25 2.36 2.42 2.37 2.40 x1 = 2.3125 x2 = 2.3500 s1 = 0.1007

s2 = 0.0859

Difference $-0.05 0.02 -0.06 -0.02 -0.10 0.00 -0.06 -0.03 d = -0.0375 sd = 0.0381

If the problem above represented a paired difference, what assumptions are needed for a confidence interval for the mean difference to be valid? A) The population of paired differences has an approximately normal distribution. B) The population variances are equal. C) The samples were independently selected from each population. D) All of the above are needed. Objective: (8.3) Understand Paired Difference Experiment

45) Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labeled A and B) and recorded the prices charged by each supermarket. The summary results are provided below: x A = 2.09

x B = 1.99

d = .10

sA = 0.22

sB = 0.19

sd = .03

Assuming a matched pairs design, which of the following assumptions is necessary for a confidence interval for the mean difference to be valid? A) None of these assumptions are necessary. B) The population variances must be equal. C) The samples are randomly and independently selected. D) The population of paired differences has an approximate normal distribution. Objective: (8.3) Understand Paired Difference Experiment

46) A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Based on the information provided, what type of analysis will yield the most useful information? A) Independent samples comparison of population proportions. B) Matched pairs comparison of population means. C) Matched pairs comparison of population proportions. D) Independent samples comparison of population means. Objective: (8.3) Understand Paired Difference Experiment

47) A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this particular manufacturer from one day to the next. Twenty-eight random working days were selected and each plan was monitored and the number of items produced each day was recorded. Some of the collected data is shown below: DAY PLAN 1 OUTPUT PLAN 2 OUTPUT 1 1234 units 1311 units 2 1355 units 1366 units 3 1300 units 1289 units What assumptions are necessary for the above test to be valid? A) Both populations must be approximately normally distributed. B) The population of paired differences must be approximately normally distributed. C) The population variances must be approximately equal. D) None of these listed, since the Central Limit Theorem can be applied. Objective: (8.3) Understand Paired Difference Experiment

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 48) The data for a random sample of six paired observations are shown below. Pair Observation 1 1 1 2 2 3 3 4 4 5 5 6 6

Observation 2 3 4 5 6 7 8

Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Use the differences to calculate sd 2 . b.

Calculate the standard deviations s1 2 and s2 2 of each column of observations. Then find pooled estimate of

the variance sp 2 . c.

Comparing sd 2 and sp 2 , explain the benefit of a paired difference experiment.

Objective: (8.3) Understand Paired Difference Experiment

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 49) The sample mean difference d is equal to the difference of the sample means x 1 - x 2 . A) True

B) False

Objective: (8.3) Understand Paired Difference Experiment

50) The sample standard deviation of differences sd is equal to the difference of the sample standard deviations s1 - s2 . A) True

B) False

Objective: (8.3) Understand Paired Difference Experiment

51) In order for the results of a paired difference experiment to be unbiased, the experimental units in each pair must be chosen independently of one another. A) True B) False Objective: (8.3) Understand Paired Difference Experiment

52) Using paired differences removes sources of variation that tend to inflate 2 . A) True B) False Objective: (8.3) Understand Paired Difference Experiment

Solve the problem. 53) We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table:

Supermarket 1 2 3 4 5 6 7 8

Price Brand 1 Brand 2 $2.25 $2.30 2.47 2.45 2.38 2.44 2.27 2.29 2.15 2.25 2.25 2.25 2.36 2.42 2.37 2.40 x1 = 2.3125 x2 = 2.3500 s1 = 0.1007

s2 = 0.0859

Difference $-0.05 0.02 -0.06 -0.02 -0.10 0.00 -0.06 -0.03 d = -0.0375 sd = 0.0381

Find a 98% confidence interval for the difference in mean price of brand 1 and brand 2. A) 0.0375 ± 0.0471 B) 0.0375 ± 0.1393 C) 0.0375 ± 0.0404 Objective: (8.3) Construct Confidence Interval

D) 0.0375 ± 0.0347

54) Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labeled A and B) and recorded the prices charged by each supermarket. The summary results are provided below: x A = 2.09

x B = 1.99

d = .10

sA = 0.22

sB = 0.19

sd = .03

Assuming the data represent a matched pairs design, calculate the confidence interval for comparing mean prices using a 95% confidence level. A) .10 ± .056975 B) .10 ± .004935 C) .10 ± .1255 D) .10 ± .00588 Objective: (8.3) Construct Confidence Interval

55) A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Suppose the following 95% confidence interval for µA - µB was calculated: (100, 2500). Which of the following inferences is correct? A) We are 95% confident that an engine using oil B has a higher mean number of hours of continuous use before breakdown than does an engine using oil A. B) We are 95% confident that an engine using oil A has a higher mean number of hours of continuous use before breakdown than does an engine using oil B. C) We are 95% confident that no significant differences exists in the mean number of hours of continuous use before breakdown of engines using oils A and B. D) We are 95% confident that the mean number of hours of continuous use of an engine using oil A is between 100 and 2500 hours. Objective: (8.3) Construct Confidence Interval

56) An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating improves the wear of the bicycle tires. The data and summary information is shown below: Bicycle Coated Tire (C) Non-Coated Tire (N) 1 1.452 0.785 2 1.634 0.844 50

1.211

Mean Std. Dev. Sample Size

0.954 Coated 1.38 0.12 50

Non-Coated 0.85 0.11 50

Difference 0.53 0.06 50

Use the summary data to construct a 90% confidence interval for the difference between the means. A) 0.53 ± 0.01663 B) 0.53 ± 0.04512 C) 0.53 ± 0.03787 D) 0.53 ± 0.01396 Objective: (8.3) Construct Confidence Interval

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 57) A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let µ1 be the true mean weight of individuals before starting the diet and let µ2 be the true mean weight of individuals after 3 weeks on the diet. Person 1 2 3 4 5

Weight Before Diet 149 194 187 196 203

Weight After Diet 142 189 184 190 199

Summary information is as follows: d = 5, sd = 1.58. Calculate a 90% confidence interval for the difference between the mean weights before and after the diet is used. Objective: (8.3) Construct Confidence Interval

58) The data for a random sample of five paired observations are shown below. Pair Observation 1 1 3 2 4 3 3 4 2 5 5 a.

Observation 2 5 4 4 5 6

Calculate the difference between each pair of observations by subtracting observation 2 from observation 1.

Use the differences to calculate d and sd. b. c.

Calculate the means x 1 and x 2 of each column of observations. Show that d = x 1 - x 2 . Form a 90% confidence interval for µD.

Objective: (8.3) Construct Confidence Interval

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 59) A paired difference experiment yielded n d pairs of observations. For the given case, what is the rejection region for testing H0 : µd = 9 against Ha: µd > 9? n d = 6,

= 0.025

A) t < 2.015

B) t > 2.447

C) t < 2.571

D) t > 2.571

Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

60) A paired difference experiment yielded n d pairs of observations. For the given case, what is the rejection region for testing H0 : µd = 15 against Ha: µd < 15? n d = 8,

= 0.1

A) t < 1.415

B) t < -1.415

C) t < 1.895

Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

D) t < -1.397

61) A paired difference experiment yielded n d pairs of observations. For the given case, what is the rejection region for testing H0 : µd = 9 against Ha: µd 9? n d = 23,

= 0.05

A) t > 1.717

B) t > 2.074

C) t > 2.069

D) t > 2.074

Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

62) An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating improves the wear of the bicycle tires. The data and summary information is shown below: Bicycle Coated Tire (C) Non-Coated Tire (N) 1 1.452 0.785 2 1.634 0.844 50

1.211

Mean Std. Dev. Sample Size

0.954 Coated 1.38 0.12 50

Non-Coated 0.85 0.11 50

Difference 0.53 0.06 50

Use the summary data to calculate the test statistic to determine if the new spray coating improves the mean wear of the bicycle tires. A) z = 23.02 B) z = 55.26 C) z = 34.25 D) z = 62.46 Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

63) An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating improves the wear of the bicycle tires. The data and summary information is shown below: Bicycle Coated Tire (C) Non-Coated Tire (N) 1 1.452 0.785 2 1.634 0.844 50

1.211

Mean Std. Dev. Sample Size

0.954 Coated 1.38 0.12 50

Non-Coated 0.85 0.11 50

Difference 0.53 0.06 50

Identify the correct null and alternative hypothesis for testing whether the new spray coating improves the mean wear of the bicycle tires (which would result in a larger amount of tread left on the tire). A) H0 : µd = 0 vs. Ha : µd 0 B) H0 : µd = 0 vs. Ha : µd < 0 C) H0 : µd = 0 vs. Ha : µd > 0 Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 64) A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let µ1 be the true mean weight of individuals before starting the diet and let µ2 be the true mean weight of individuals after 3 weeks on the diet. Person 1 2 3 4 5

Weight Before Diet 147 192 185 194 201

Weight After Diet 140 187 182 188 197

Summary information is as follows: d = 5, sd = 1.58. Test to determine if the diet is effective at reducing weight. Use

= .10.

Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

65) A paired difference experiment has 15 pairs of observations. What is the rejection region for testing Ha: µd > 0? Use

= .05.

Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

66) A paired difference experiment has 75 pairs of observations. What is the rejection region for testing Ha: µd > 0? Use

= .01.

Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

67) A paired difference experiment produced the following results. nd = 40, x 1 = 18.4, x2 = 19.7, d = -1.3, sd 2 = 5

Perform the appropriate test to determine whether there is sufficient evidence to conclude that µ1 < µ2 using = .10. Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

68) A paired difference experiment yielded the following results. nd = 50,

d = 967,

d 2 = 19,201

Test H0 : µd = 20 against Ha : µd 20 , where µd = µ1 - µ2 , using Objective: (8.3) Conduct Test of Hypothesis for Paired Difference

= .05.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 69) We sampled 100 men and 100 women and asked: "Do you think the environment is a major concern?" Of those sampled, 67 women and 53 men responded that they believed it is. For the confidence interval procedure to work properly, what additional assumptions must be satisfied? A) Both populations have approximate normal distributions. B) The population variances are equal. C) Both samples were randomly and independently selected from their respective populations. D) All of the above are necessary. Objective: (8.4) Understand Process of Comparing Two Proportions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 70) Determine whether the sample sizes are large enough to conclude that the sampling distributions are approximately normal. ^

n1 = 45, n2 = 52, p 1 = .3, p 2 = .6 Objective: (8.4) Understand Process of Comparing Two Proportions

71) Determine whether the sample sizes are large enough to conclude that the sampling distributions are approximately normal. ^

n1 = 48, n2 = 55, p 1 = .4, p 2 = .7 Objective: (8.4) Understand Process of Comparing Two Proportions

72) Independent random samples, each containing 500 observations were selected from two binomial populations. The samples from populations 1 and 2 produced 210 and 320 successes, respectively. Test H0 : (p 1 - p 2 ) = 0 against Ha : (p 1 - p 2 ) < 0. Use

= .05.

Objective: (8.4) Understand Process of Comparing Two Proportions

73) Independent random samples, each containing 1,000 observations were selected from two binomial populations. The samples from populations 1 and 2 produced 475 and 550 successes, respectively. Test H0 : (p 1 - p 2 ) = 0 against Ha : (p 1 - p 2 ) 0. Use

= .01.

Objective: (8.4) Understand Process of Comparing Two Proportions

74) Construct a 90% confidence interval for (p 1 - p2 ) when n1 = 400, n2 = 550, p 1 = .42, and p 2 = .63. Objective: (8.4) Understand Process of Comparing Two Proportions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 75) A cola manufacturer invited consumers to take a blind taste test. Consumers were asked to decide which of two sodas they preferred. The manufacturer was also interested in what factors played a role in taste preferences. Below is a printout comparing the taste preferences of men and women. HYPOTHESIS: PROP. X = PROP. Y SAMPLES SELECTED FROM soda(brand1,brand2) males females

(sex=0, males) (sex=1, females)

(NUMBER = 115) (NUMBER = 56) X = males Y = females

SAMPLE PROPORTION OF X = 0.422018 SAMPLE SIZE OF X = 109 SAMPLE PROPORTION OF Y = 0.25 SAMPLE SIZE OF Y = 52 PROPORTION X - PROPORTION Y = Z=

0.172018 2.11825

Suppose the manufacturer wanted to test to determine if the males preferred its brand more than the females. Using the test statistic given, compute the appropriate p-value for the test. A) .0170 B) .0340 C) .2119 D) .4681 Objective: (8.4) Perform Test of Hypothesis to Compare Two Proportions

76) When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex - males or females - is more likely to respond. Random, independent samples of 60 females and 100 males were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes of the male and female responses. Find the rejection region that would be used if it is desired to test to determine if a difference exists between the proportion of the females and males who responds to the call to donate blood. Use = 0.10. A) Reject H0 if z > 1.645. B) Reject H0 if z < -1.645 or z > 1.645. C) Reject H0 if z < -1.96.

D) Reject H0 if z < -1.96 or z > 1.96.

Objective: (8.4) Perform Test of Hypothesis to Compare Two Proportions

77) When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex - males or females - is more likely to respond. Random, independent samples of 60 females and 100 males were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes of the male and female responses. Suppose 45 of the females and 60 of the males responded that they were able to give blood. Find the test statistic that would be used if it is desired to test to determine if a difference exists between the proportion of the females and males who responds to the call to donate blood. A) z = 1.96 B) z = 1.645 C) z = 2.01 D) z = 1.93 Objective: (8.4) Perform Test of Hypothesis to Compare Two Proportions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 78) One indication of how strong the real estate market is performing is the proportion of properties that sell in less than 30 days after being listed. Of the condominiums in a Florida beach community that sold in the first six months of 2006, 75 of the 115 sampled had been on the market less than 30 days. For the first six months of 2007, 25 of the 85 sampled had been on the market less than 30 days. Test the hypothesis that the proportion of condominiums that sold within 30 days decreased from 2006 to 2007. Use = .01. Objective: (8.4) Perform Test of Hypothesis to Compare Two Proportions

79) In an exit poll, 42 of 75 men sampled supported a ballot initiative to raise the local sales tax to build a new football stadium. In the same poll, 41 of 85 women sampled supported the initiative. Find and interpret the p-value for the test of hypothesis that the proportions of men and women who support the initiative are different. Objective: (8.4) Perform Test of Hypothesis to Compare Two Proportions

80) A government housing agency is comparing home ownership rates among several immigrant groups. In a sample of 235 families who emigrated to the U.S. from Eastern Europe five years ago, 165 now own homes. In a sample of 195 families who emigrated to the U.S. from Pacific islands five years ago, 125 now own homes. Write a 95% confidence interval for the difference in home ownership rates between the two groups. Based on the confidence interval, can you conclude that there is a significant difference in home ownership rates in the two groups of immigrants? Objective: (8.4) Perform Test of Hypothesis to Compare Two Proportions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 81) The FDA is comparing the mean caffeine contents of two brands of cola. Independent random samples of 6-oz. cans of each brand were selected and the caffeine content of each can determined. The study provided the following summary information.

Sample size Mean Variance

Brand A 15 18 1.2

Brand B 10 20 1.5

How many cans of each soda would need to be sampled in order to estimate the difference in the mean caffeine content to within .5 with 95% reliability? A) n1 = n2 = 18 B) n1 = n2 = 42 C) n1 = n2 = 57 D) n1 = n2 = 21 Objective: (8.5) Determine Sample Size (Means)

82) The FDA is comparing the mean caffeine contents of two brands of cola. Independent random samples of 6-oz. cans of each brand were selected and the caffeine content of each can determined. The study provided the following summary information.

Sample size Mean Variance

Brand A 15 18 1.2

Brand B 10 20 1.5

How many cans of each soda would need to be sampled in order to estimate the difference in the mean caffeine content to within .10 with 90% reliability? A) n1 = n2 = 731 B) n1 = n2 = 74 C) n1 = n2 = 1038 D) n1 = n2 = 104 Objective: (8.5) Determine Sample Size (Means)

83) Suppose you want to estimate the difference between two population means correct to within 2.5 with probability 0.95. If prior information suggests that the population variances are both equal to the value 20, and you want to select independent random samples of equal size from the populations, how large should the sample sizes be? A) n 1 = n 2 = 25 B) n 1 = n 2 = 18 C) n 1 = n 2 = 62 D) n 1 = n 2 = 44 Objective: (8.5) Determine Sample Size (Means)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 84) An experiment has been conducted at a university to compare the mean number of study hours expended per week by student athletes with the mean number of hours expended by non athletes. A random sample of 55 athletes produced a mean equal to 20.6 hours studied per week and a standard deviation equal to 5.8 hours. A second random sample of 200 non athletes produced a mean equal to 23.5 hours per week and a standard deviation equal to 4 hours. How many students would need to be sampled in order to estimate the difference in means to within 2.5 hours with probability 95%? Objective: (8.5) Determine Sample Size (Means)

85) A new type of band has been developed for children who have to wear braces. The new bands are designed to be more comfortable, look better, and provide more rapid progress in realigning teeth. An experiment was conducted to compare the mean wearing time necessary to correct a specific type of misalignment between the old braces and the new bands. One hundred children were randomly assigned, 50 to each group. A summary of the data is shown in the table.

x s

Old Braces

New Bands

410 days 42 days

380 days 65 days

How many patients would need to be sampled to estimate the difference in means to within 27 days with probability 99%? Objective: (8.5) Determine Sample Size (Means)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 86) A consumer protection agency is comparing the work of two electrical contractors. The agency plans to inspect residences in which each of these contractors has done the wiring in order to estimate the difference in the proportions of residences that are electrically deficient. Suppose the proportions of residences with deficient work are expected to be about .8 for both contractors. How many homes should be sampled in order to estimate the difference in proportions using a 95% confidence interval of width .2? A) n1 = n2 = 123 B) n1 = n 2 = 246 C) n1 = n2 = 62 D) n1 = n2 = 615 Objective: (8.5) Determine Sample Size (Proportions)

87) Suppose you want to estimate the difference between two population proportions correct to within 0.03 with probability 0.90. If prior information suggests that p1 0.4 and p2 0.8, and you want to select independent random samples of equal size from the populations, how large should the sample sizes be? A) n 1 = n 2 = 1708 B) n 1 = n 2 = 963 C) n 1 = n 2 = 1203 D) n 1 = n 2 = 1925 Objective: (8.5) Determine Sample Size (Proportions)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 88) Two surgical procedures are widely used to treat a certain type of cancer. To compare the success rates of the two procedures, random samples of surgical patients were obtained and the numbers of patients who showed no recurrence of the disease after a 1-year period were recorded. The data are shown in the table. n 100 100

Procedure A Procedure B

Number of Successes 75 87

How large a sample would be necessary in order to estimate the difference in the true success rates to within .10 with 95% reliability? Objective: (8.5) Determine Sample Size (Proportions)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 89) Find F.05 where v 1 = 8 and v 2 = 11. A) 2.30

B) 3.66

C) 4.74

D) 2.95

C) 1.84

D) 1.71

C) 0.01

D) 0.025

C) 0.90

D) 0.95

C) 0.10

D) 0.025

Objective: (8.6) Use F-Distribution

90) Find F.10 where v 1 = 20 and v 2 = 40. A) 1.99

B) 1.61

Objective: (8.6) Use F-Distribution

91) Given v 1 = 9 and v 2 = 5, find P(F > 6.68). A) 0.10

B) 0.05

Objective: (8.6) Use F-Distribution

92) Given v 1 = 30 and v 2 = 60, find P(F < 1.68). A) 0.05

B) 0.10

Objective: (8.6) Use F-Distribution

93) Given v1 = 15 and v2 = 20, find P(F > 1.84). A) 0.01

B) 0.05

Objective: (8.6) Use F-Distribution

Specify the appropriate rejection region for testing H0 :

94) Ha :

2 1 >

2 2;

A) F > 3.15

2 1 =

2 2 in the given situation.

= 0.05, n 1 = 21, n 2 = 9

B) F > 3.15

C) F > 2.45

D) F > 2.94

Objective: (8.6) Perform Hypothesis Test to Compare Two Variances

95) Ha :

2 1 <

2 2;

A) F > 3.21

= 0.01, n 1 = 16, n 2 = 31

B) F > 3.21

C) F > 2.70

Objective: (8.6) Perform Hypothesis Test to Compare Two Variances

D) F > 2.64

96) Ha :

2 1

2 2;

= 0.10, n 1 = 10, n 2 = 16

2 2 Assume that s 2 > s 1 .

A) F > 3.01

B) F > 2.59

C) F > 2.34

D) F > 2.59

Objective: (8.6) Perform Hypothesis Test to Compare Two Variances

Solve the problem.

97) Identify the rejection region that should be used to test H0 : 1 2 = 2 2 against Ha : 1 2 = .05. A) F > 3.69 B) F > 6.63 C) F > 4.82

2 2 for v 1 = 5, v 2 = 8, and

D) F > 6.76

Objective: (8.6) Perform Hypothesis Test to Compare Two Variances

98) Identify the rejection region that should be used to test H0 : 1 2 = 2 2 against Ha : 1 2 > 2 2 for v 1 = 10, v 2 = 29, and = .10. A) F > 3.00 B) F > 2.53 C) F > 2.18 D) F > 1.83 Objective: (8.6) Perform Hypothesis Test to Compare Two Variances

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 99) Suppose it desired to compare two physical education training programs for preadolescent girls. A total of 62 girls are randomly selected, with 31 assigned to each program. After three 6-week periods on the program, each girl is given a fitness test that yields a score between 0 and 100. The means and variances of the scores for the two groups are shown in the table.

Program 1 Program 2

n 31 31

x 78.5 75.2

s2 201.3 259.6

Test to determine if the variances of the two programs differ. Use

= .05.

Objective: (8.6) Perform Hypothesis Test to Compare Two Variances

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 100) Independent random samples were selected from each of two normally distributed populations, n1 = 7 from population 1 and n2 = 9 from population 2. The data are shown below. Population 1:

2.5 3.1 2.3 1.8 4.2 3.5 3.9

Population 2:

2.9 1.7 4.6 3.5 3.7 2.8 4.6 3.4 1.9

Find the test statistic for the test of H0 : 1 2 = 2 2 against Ha : 1 2 22 . A) .857 B) 1.17 C) 1.36 Objective: (8.6) Perform Hypothesis Test to Compare Two Variances

D) .735

101) A marketing study was conducted to compare the variation in the age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. The sample data is shown here: Female: n = 31, Male: n = 21,

sample mean = 50.30, sample standard deviation = 13.215 sample mean = 39.80, sample standard deviation = 10.040

Identify the rejection region to that should be used to determine if the variation in the female ages exceeds the variation in the male ages when testing at = 0.05. A) F > 2.04 B) F > 1.74 C) F > 2.12 D) F > 1.93 Objective: (8.6) Perform Hypothesis Test to Compare Two Variances

102) A marketing study was conducted to compare the variation in the age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. The sample data is shown here: Female: n = 31, Male: n = 21,

sample mean = 50.30, sample standard deviation = 13.215 sample mean = 39.80, sample standard deviation = 10.040

Calculate the test statistics that should be used to determine if the variation in the female ages exceeds the variation in the male ages. A) F = 1.597 B) F = 1.316 C) F = 1.264 D) F = 1.732 Objective: (8.6) Perform Hypothesis Test to Compare Two Variances

Answer Key Testname: UNTITLED8

1) C 2) B 3) B 4) C 5) A 6) C 7) B 8) D 9) C 10) D 11) C 12) A 13) A 14) C 15) A 16) A 17) The mean is µ1 - µ2 = 15 - 13 = 2. The standard deviation is 12 22 + = n1 n2 32 22 + 100 100

.361.

34) D 35) C 36) B 37) The test statistic is z = 478 - 481 14.12 11.22 + 225 225

40) x 1 = 4.94, s1 = .75, n1 = 5, x 2 = 5.35, s2 = .73, n2 = 4 sp 2 = (5 - 1).752 + (4 - 1).732

(5 - 1) + (4 -1)

-2.50 38) sp 2 =

.550

(n1 - 1)s1 2 + (n2 - 1) s2 2 (n1 - 1) + (n2 -1)

= (18 - 1)50 + (18 - 1)57 (18 - 1) + (18 -1) = 53.5 39) sp 2 =

(n1 - 1)s1 2 + (n2 - 1) s2 2 (n1 - 1) + (n2 -1)

= (10 - 1).88 + (12 - 1)1.01 (10 - 1) + (12 -1) = .9515

The test statistic 4.94 - 5.35 is t = 1 1 .550 + 5 4 -.82. There are 7 degrees of freedom, so the rejection region for = .10 is t < 1.415. Since the test statistic does not fall within the rejection region, we have insufficient evidence to conclude that µ1 <

48) a.

The differences are all -2, so sd 2 = 0.

s1 2 = s2 2 = 3.5; 5(3.5) + 5(3.5) = sp 2 = 10 b.

3.5 c. For the paired difference experiment, the variance is much smaller. 49) A 50) B 51) B 52) A 53) C 54) D 55) B 56) D 57) The matched pairs confidence interval for µd is x d ± t /2 sd n

µ2 .

18) D 19) C 20) C 21) B 22) E 23) (7,123 - 6,957) ± 1.96 1752 2252 + 166 144 144

(4.94 - 5.35) ± 1 1 + 1.895 .550 5 4 .41 ± .943. 41) The observed level of significance is .223, which is not less than .05. There is no significant difference between the means. 42) The results are not valid because the sample sizes are too small to use a z-test. 43) C 44) A 45) A 46) B 47) B

± 46.56 24) The confidence interval is (-3.449, .849). There is no significant difference between the means. 25) µ1 > µ2

26) B 27) C 28) D 29) A 30) C 31) C 32) D 33) D

Confidence =1 coefficient .90 - .90 = .10. /2 = .10/2 = .05. t.05 = 2.132 with n - 1 = 5 - 1 = 4 df. The 90% confidence interval is: 5 ± 2.132

1.58 5

1.51 (3.49, 6.51) 58) a. The differences

are 2, 0, 1, 3, and 1; d = -1.4; sd = 1.14 b.

x 1 = 3.4, x 2 =

4.8, x 1 - x2 = 3.4 4.8 = - 1.4 = d c.

-1.4 ± 2.132

-1.4 ± 1.09 59) D

5±

1.14 5

Answer Key Testname: UNTITLED8

60) B 61) B 62) D 63) C 64) To determine if the diet is effective at reducing weight, we test: H0 : µD = 0 Ha : µD > 0 The test statistic is t = xd - 0 sd / n

5-0 = 7.07. 1.58 5

The rejection region requires = .10 in the upper tail of the t distribution with df = n - 1 = 5 - 1 = 4. t.10 = 1.533. The rejection region is t > 1.533. Since the observed value of the test statistic falls in the rejection region (t = 7.07 > 1.533), H0 is rejected. There is sufficient evidence to indicate that the diet is effective at reducing weight when testing at = .10. 65) The rejection region is t > 1.761. 66) The rejection region is z > 2.575.

67) The test statistic is z = -1.3 - 0 -3.677. 5 / 40

68) sd 2 =

19,201 - 9672 / 50 49

-7.15. The rejection region is z < 1.645. Since the test statistic falls in the rejection region, we reject the null hypothesis in favor of the alternative hypothesis that (p 1 -

5.43. The rejection region is z > 2.33. Since the test statistic falls in the rejection region, we reject the null hypothesis in favor of the alternative hypothesis that (p 1 -

that the proportion of condominiums that sold within 30 days was greater in the first half of 2006 than in the first half of 2007.

p 2 ) < 0.

10.188, so sd 3.19.

The test statistic is z = 19.34 - 20 -.1.46 3.19/ 50

73) p 1 = .475 and p 2 =

.550; The test statistic is z = (.475 - .550) - 0 .475(.525) .550(.45) + 1,000 1,000

The rejection region is z < -1.96 or z > 1.96. Since the test statistic does not fall in the rejection region, we have insufficient evidence to conclude that the mean difference is not 20. 69) C

-3.36. The rejection region is z < 2.575 or z > 2.575. Since the test statistic falls in the rejection region, we reject the null hypothesis in favor of the alternative hypothesis that (p 1 -

70) Since n1 p 1 = 45(.3) = 13.5 < 15, the sample size is not large enough.

p2 )

74) (.42 - .63) ± 1.645 .42(.58) .63(.37) + 400 550

71) Since n1 p 1 = 48(.4) = ^

19.2 > 15, n1 q1 =

-.21 ± .053. 75) A 76) B 77) D

48(.6) = 28.8 > 15, n2 ^

p 2 = 55(.7) = 38.5 > ^

15, and n2 q2 = 55(.3)

= 16.5 > 15, the sample sizes are large enough.

78) p 1 .65 and p 2 = .29;

The test statistic is z = (.42 - .64) - 0 .42(.58) .64(.36) + 500 500

The rejection region is z < -1.28. Since the test statistic does fall in the rejection region, we have sufficient evidence to conclude that µ1 < µ2.

72) p 1 = .42 and p 2 = .64;

The test statistic is z = (.65 - .29) - 0 .65(.35) .29(.71) + 115 85

p 2 ) > 0. We conclude

79) p 1 .56 and p 2 = .48;

The test statistic is z = (.56 - .48) - 0 .56(.44) .48(.52) + 75 85 1.01 The p-value is p = 2(.5 - .3438) = .3124. The probability of observing a value of z more contradictory to the null hypothesis is .3124.

Answer Key Testname: UNTITLED8

80) p 1 .70 and p 2 = .64;

The confidence interval is (.70 - .64) ± 1.96 .70(.30) .64(.36) + 235 195

.06 ± .089. Since the confidence interval includes 0, we cannot conclude that there is a difference in home ownership rates. 81) B 82) A 83) A 84) To determine the sample size necessary, we use n1 = n2 = z /2 2

2 1 +

2 2

(ME)2

Using confidence coefficient .95 = 1 = 1 - .95 = .05. /2 = .05/2 = .025. Thus z.025 = 1.96. n1 = n2 = (1.96)2 (5.82 + 4 2 ) 2.52

30.51 Round up to n1 = n2 = 31.

85) To determine the sample size necessary, we use n1

95) A 96) A 97) C 98) D 99) To determine if the variances of the two programs differ, we test:

= n2 = z /2 2

2 1 +

2 2

(ME)2

Using = .01, /2 = .01/2 = .005. Thus z.005 = 2.575. n1 = n2 = (2.575)2 (422 + 652 ) 272

H0 :

2 1 =

2 2

Ha :

2 1

2 2

The test statistic is F =

2 s2

54.47 Round up to n1 = n2

2 s1

= 55. 86) A 87) C 88) To determine the sample size necessary, we use n1

259.6 = 1.29. 201.3

This test requires /2 = .05/2 = .025 in the upper tail of the F distribution with v 1 = n2 - 1 = 30 and v 2 =

= n2 =

n2 - 1 = 30 df. From Table X, Appendix A, F.025 = 2.07. The

(z /2)2 (p 1 q1 + p 2 q2 ) (ME)2 Confidence coefficient .95 = 1 = 1 - .95 = .05. /2 = .05/2 = .025. z.025 =

rejection region is F > 2.07.

= 115.478496 Round up to n1 = n2

evidence to indicate the variances of the two programs differ when testing at = .05. 100) C 101) A 102) D

Since the observed value of the test 1.96. statistic does not fall in the rejection region n1 = n2 = (F = 1.29 2.07), H0 (1.96)2 [(0.75)(0.25) + (0.87)(0.13)]cannot be rejected. .102 There is insufficient

= 116. 89) D 90) B 91) D 92) D 93) C 94) A

McClave Statistics for Business and Economics 14e Chapter 9 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 12 recently hired sales trainees were randomly assigned to one of 3 different "home rooms" - four trainees per room. Each room is identical except for wall color, with 3 different colors used. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the 3 room colors. At the end of the training program, the attitude of each trainee was measured on a 100-pt. scale (the lower the score, the poorer the attitude). How many treatments are in this study? A) 4 B) 3 C) 12 D) 100 Objective: (9.1) Identify Elements of Designed Experiment

2) A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that primary specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 26 HMO physicians from each of four primary specialties-- General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP)-- and recorded the total per-member, per-month charges for each. Identify the treatments for this group. A) the four specialty groups GP, IM, PED, and FP B) the HMO C) the total per-member, per-month charges D) the 104 physicians Objective: (9.1) Identify Elements of Designed Experiment

3) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 17 physicians from each of the three certification levels Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I) and recorded the total per member per month charges for each (a total of 51 physicians). How many factors are present in this study? A) 17 B) 3 C) 1 D) 51 Objective: (9.1) Identify Elements of Designed Experiment

4) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 29 physicians from each of the three certification levels Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I) and recorded the total per-member, per-month charges for each (a total of 87 physicians). Identify the dependent (response) variable for this study. A) the three certifications groups C, E, and I B) the 87 physicians C) the HMO D) the total per-member, per-month charge Objective: (9.1) Identify Elements of Designed Experiment

5) A counselor obtains SAT averages for incoming freshmen each year for a period covering 12 years, with the objective of determining the relationship between the SAT score and the year the test was given. The averages are then subjected to analysis for the purpose of drawing a conclusion regarding a trend. Determine whether the study is observational or designed. A) observational B) designed Objective: (9.1) Identify Elements of Designed Experiment

6) An advertising firm conducts 11 different campaigns, each in 13 different cities, to promote a certain product, and tracks the product sales attributable to each campaign in each city. Determine whether the study is observational or designed. A) designed B) observational Objective: (9.1) Identify Elements of Designed Experiment

7) A city monitors ozone levels monthly over a 5 year period in order to relate the ozone levels to the seasons. Determine whether the study is observational or designed. A) designed B) observational Objective: (9.1) Identify Elements of Designed Experiment

8) Define the statistical term "treatments." A) assumptions that are satisfied exactly B) objects on which the responses are measured C) correlations among the factors used in an analysis of variance D) combinations of factor-levels employed in a designed study Objective: (9.1) Identify Elements of Designed Experiment

9) The variable measured in the study is called __________. A) the factor level C) the treatment

B) a sampling unit D) the response variable

Objective: (9.1) Identify Elements of Designed Experiment

10) The variables, quantitative or qualitative, whose effect on a response variable is of interest are called __________. A) factors B) the factor level C) the experimental units D) the treatments Objective: (9.1) Identify Elements of Designed Experiment

11) The intensity of a factor is called __________. A) the treatment C) a factor level

B) the design D) the experimental unit

Objective: (9.1) Identify Elements of Designed Experiment

12) __________ is a particular combination of levels of the factors involved in a study. A) An analysis of variance B) A treatment C) The factor level D) The sampling design Objective: (9.1) Identify Elements of Designed Experiment

13) In a study to determine the least amount of time necessary to clean an SUV while maintaining a high quality standard, the owner of a chain of car washes designed an experiment where 20 employees were divided into four groups, each with five members. Each member of each group was assigned an SUV to clean within a certain time limit. The time limits for the groups were 20 minutes, 25 minutes, 30 minutes, and 35 minutes. After the time limits for each group had expired, the owner inspected each SUV and rated the quality of the cleaning job on a scale of 1 to 10. What are the factor levels for this study? A) the number of groups: 4 B) the quality ratings: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 C) the number of employees in each group: 5 D) the time limits: 20 min, 25 min, 30 min, 35 min Objective: (9.1) Identify Elements of Designed Experiment

14) In a study to determine the least amount of time necessary to clean an SUV while maintaining a high quality standard, the owner of a chain of car washes designed an experiment where 20 employees were divided into four groups, each with five members. Each member of each group was assigned an SUV to clean within a certain time limit. The time limits for the groups were 20 minutes, 25 minutes, 30 minutes, and 35 minutes. After the time limits for each group had expired, the owner inspected each SUV and rated the quality of the cleaning job on a scale of 1 to 10. What are the possible values of the response variable? A) the number of groups: 4 B) the number of employees in each group: 5 C) the time limits: 20 min, 25 min, 30 min, 35 min D) the quality ratings: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Objective: (9.1) Identify Elements of Designed Experiment

15) A scientist is hoping to compare the mean levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he measures the amount of DDT toxin present. Ideally he will be able to rank the species based on the mean level of toxin found in each of the three species. How many factors are present in this study? A) 50 B) 1 C) 3 D) 6 Objective: (9.1) Identify Elements of Designed Experiment

16) A scientist is hoping to compare the mean levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he measures the amount of DDT toxin present. Ideally he will be able to rank the species based on the mean level of toxin found in each of the three species. Identify the treatments for this study. A) The scientist B) The three fish species C) The 50 fish D) The amount of DDT in a fish Objective: (9.1) Identify Elements of Designed Experiment

17) A scientist is hoping to compare the mean levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he measures the amount of DDT toxin present. Ideally he will be able to rank the species based on the mean level of toxin found in each of the three species. Identify the response variable in this study. A) The scientist B) The amount of DDT in a fish C) The three fish species D) The number of fish Objective: (9.1) Identify Elements of Designed Experiment

18) Use the appropriate table to find the following F value: F0.05, v 1 = 3, v 2 = 28 A) 2.92

B) 8.62

C) 2.95

D) 3.34

B) 0.99

C) 0.01

D) 0.005

B) 0.01

C) 0.98

D) 0.025

Objective: (9.2) Use F-Distribution

19) Find the following: P(F 4.10), for v 1 = 5, v 2 = 20 A) 0.995 Objective: (9.2) Use F-Distribution

20) Find the following: P(F > 4.24), for v 1 = 3, v 2 = 14 A) 0.97 Objective: (9.2) Use F-Distribution

21) Find the critical value F0 for a one-tailed test using A) 2.74

= 0.05, d.f.N = 6, and d.f.D = 16.

B) 2.19

C) 3.94

D) 2.66

Objective: (9.2) Use F-Distribution

22) Find the critical value F0 for a one-tailed test using

= 0.05, with 8 numerator degrees of freedom and 15

denominator degrees of freedom A) 3.22 B) 2.64

C) 3.20

D) 4.10

Objective: (9.2) Use F-Distribution

23) Given that the sum of squares for treatments (SST) for an ANOVA F-test is 9,000 and there are four total treatments, find the mean square for treatments (MST). A) 1,500 B) 3,000 C) 2,250 D) 1,800 Objective: (9.2) Use F-Distribution

24) Given that the sum of squares for error (SSE) for an ANOVA F-test is 12,000 and there are 40 total experimental units with eight total treatments, find the mean square for error (MSE). A) 300 B) 375 C) 400 D) 308 Objective: (9.2) Use F-Distribution

25) Given that the mean square for treatments (MST) for an ANOVA F-test is 5,000 and the mean square for error (MSE) is 3,750, find the value of the test statistic F. A) 1.25 B) .800 C) .750 D) 1.33 Objective: (9.2) Use F-Distribution

26) 307 diamonds were sampled and randomly sorted into three groups of diamonds. These diamonds were randomly assigned to one of the three organizations, or groups (HRD, GIA, or IGI), that certify the appraisal of diamonds. A study was conducted to determine if the average size of diamonds reported by these three certification groups differ. A completely randomized design was used and the resulting ANOVA table is shown below. One-Way AOV for CARAT by CERT Source DF SS MS F CERT 2 8.3265 4.16326 ??? Error 305 15.2604 0.05003 Total 307 23.5869 Find the F-value that is missing in the ANOVA table. A) 0.5000 B) 83.215 Objective: (9.2) Complete ANOVA Table

C) 0.5242

D) 0.0120

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 27) A partially completed ANOVA table for a completely randomized design is shown here. Source Time Error Total a. b. c.

SS 25.2

11 13

86.4

Complete the ANOVA table. How many treatments are involved in the experiment? Do the data provide sufficient evidence to indicate a difference among the population means? Test using = .05.

Objective: (9.2) Complete ANOVA Table

28) Complete the ANOVA table. Source Treatments Error Total

df 3 8

SS 857.1 372.8

Objective: (9.2) Complete ANOVA Table

29) In a completely randomized design experiment, 10 experimental units were randomly chosen for each of three treatment groups and a quantity was measured for each unit within each group. In the first steps of testing whether the means of the three groups are the same, the sum of squares for treatments was calculated to be 3,110 and the sum of squares for error was calculated to be 27,000. Complete the ANOVA table. Source Treatments Error Total

Objective: (9.2) Complete ANOVA Table

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 30) Which of the following is not a condition required for a valid ANOVA F-test for a completely randomized experiment? A) The samples are chosen from each population in an independent manner. B) The sample chosen from each of the populations is sufficiently large. C) The variances of all the sampled populations are equal. D) The sampled populations all have distributions that are approximately normal. Objective: (9.2) Perform One-Way ANOVA

31) An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different "home rooms" five trainees per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray, and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, the attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one-way analysis of variance. ONE-WAY ANOVA FOR ATTITUDE BY COLOR SOURCE DF SS MS F P BETWEEN 3 1678.15 559.3833 59.03782 0.0000 WITHIN 16 151.6 9.475 TOTAL 19 1829.75 SAMPLE GROUP COLOR MEAN SIZE Blue 50.400 5 Green 50.200 5 Gray 31.400 5 Red 32.600 5

STD DEV 4.3589 3.9623 1.5811 0.8367

Give the null hypothesis for the ANOVA F-test shown on the printout. A) H0 : µ1 = µ2 = µ3 = µ4 = µ5 , where the µi represent attitude means for the ith person in each room

B) H0 : µgreen = µblue = µgray = µred, where the µ's represent mean attitudes for the four rooms C) H0 : x 1 = x 2 = x 3 = x 4 , where the x's represent the room colors D) H0 : p green = p blue = p gray = p red, where the p's represent the proportion with the corresponding attitude Objective: (9.2) Perform One-Way ANOVA

32) Four different leadership styles used by Big-Six accountants were investigated. As part of a designed study, 15 accountants were randomly selected from each of the four leadership style groups (a total of 60 accountants). Each accountant was asked to rate the degree to which their subordinates performed substandard field work on a 10-point scale called the "substandard work scale". The objective is to compare the mean substandard work scales of the four leadership styles. The data on substandard work scales for all 60 observations were subjected to an analysis of variance. ONE-WAY ANOVA FOR SUBSTAND BY STYLE SOURCE BETWEEN WITHIN TOTAL

DF 3 56 59

SS MS F P 2,300.58 766.860 5.210 0.003 8,242.64 147.190 10,543.22

Interpret the results of the ANOVA F-test shown on the printout for = 0.05. A) At =.05, there is insufficient evidence of differences among the substandard work scale means for the four leadership styles. B) At = .05, there is no evidence of interaction. C) At =.05, nothing can be said. D) At = .05, there is sufficient evidence of differences among the substandard work scale means for the four leadership styles. Objective: (9.2) Perform One-Way ANOVA

33) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 17 physicians from each of the three certification levels Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I) and recorded the total per-member, per-month charges for each (a total of 17 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Write the null hypothesis tested by the ANOVA. A) H0 : µC = µE = µI B) H0 : µC = µE = µI = 0 C) H0 : p 1 = p 2 = p 3

D) H0 : 1 = 2 = 3 = 0

Objective: (9.2) Perform One-Way ANOVA

34) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 18 physicians from each of the three certification levels Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I) and recorded the total per-member, per-month charges for each (a total of 54 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Give the degrees of freedom appropriate for conducting the ANOVA F-test. A) numerator df = 52, denominator df = 2 B) numerator df = 2, denominator df = 51 C) numerator df = 3, denominator df = 51 D) numerator df = 52, denominator df = 3 Objective: (9.2) Perform One-Way ANOVA

35) A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 20 physicians from each of the three certification levels Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I) and recorded the total per member per month charges for each (a total of 60 physicians). In order to compare the mean charges for the three groups, the data were subjected to an analysis of variance. The results of the ANOVA are summarized in the following table. Take = 0.01 Source df SS MS F Value Prob > F Treatments 2 2,110.314 1,055.157 20.73 .0001 Error 57 2,901.3 50.9 Total 59 5,011.614 _____________________________________________________ Interpret the p-value of the ANOVA F-test. A) The model is not statistically useful (at = .01) for prediction purposes. B) The means of the total per member per month charges for the three groups of physicians are equal at = .01. C) The means of the total per member per month charges for the three groups of physicians differ at = .01. D) The variances of the total per number per month charges for the three groups of physicians differ at = .01. Objective: (9.2) Perform One-Way ANOVA

36) 307 diamonds were sampled and randomly sorted into three groups of diamonds. These diamonds were randomly assigned to one of the three organizations, or groups (HRD, GIA, or IGI), that certify the appraisal of diamonds. A study was conducted to determine if the average size of diamonds reported by these three certification groups differ. A completely randomized design was used and the resulting ANOVA table is shown below. One-Way AOV for CARAT by CERT Source DF SS MS CERT 2 8.3265 4.16326 Error 305 15.2604 0.05003 Total 307 23.5869

F 83.21

P 0.0000

Specify the null hypothesis for a test to compare the mean size of a diamond for the three certification groups (HRD, GIA, and IGI). A) H0 : µ = 0, where µ = mean carat weight.

B) H0 : µHRD = µGIA = µIGI = 0, where µj = mean carat weight for certification group i C) H0 : µHRD = µGIA = µIGI, where µj = mean carat weight for certification group i D) At least two of the population mean carat weights differ for the three certification groups. Objective: (9.2) Perform One-Way ANOVA

37) 307 diamonds were sampled and randomly sorted into three groups of diamonds. These diamonds were randomly assigned to one of the three organizations, or groups (HRD, GIA, or IGI), that certify the appraisal of diamonds. A study was conducted to determine if the average size of diamonds reported by these three certification groups differ. A completely randomized design was used and the resulting ANOVA table is shown below. One-Way AOV for CARAT by CERT Source DF SS MS CERT 2 8.3265 4.16326 Error 305 15.2604 0.05003 Total 307 23.5869

F 83.21

P 0.0000

Give a practical conclusion for the test in the words of the problem. Use = 0.10 to make your conclusion. A) There is sufficient evidence to indicate that the mean carat weight for the HRD group equals the mean carat weight for the IGI group. B) There is sufficient evidence to indicate that the mean carat weight for the GIA group is lower than the other two groups. C) There is insufficient evidence to indicate that differences exist among the mean carat weights for the three certification groups. D) There is sufficient evidence to indicate that differences exist among the mean carat weights for the three certification groups. Objective: (9.2) Perform One-Way ANOVA

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 38) A company that employs a large number of salespeople is interested in learning which of the salespeople sell the most: those strictly on commission, those with a fixed salary, or those with a reduced fixed salary plus a commission. The previous month's records for a sample of salespeople are inspected and the amount of sales (in dollars) is recorded for each, as shown in the table. Commissioned $492 $450 $532 $483 $466 $425

Fixed Salary $425 $443 $437 $432 $444

ANALYSIS OF VARIANCE SOURCE FACTOR ERROR TOTAL

Commission Plus Salary $507 $492 $470 $424

DF 2 12 14

SS 4195 7945 12140

MS 2097.7 662.1

F 3.17

Test to determine if a difference exists in the mean sale amounts among the three compensation systems. Test using = .025. Objective: (9.2) Perform One-Way ANOVA

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 39) A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. Rank the means from smallest to largest. Use solid lines to connect those means which are not significantly different. (µA - µB): (17, 35) (µA - µC): (7, 23) (µA - µD): (3, 21) (µB - µC): (-21, -1) (µB - µD): (-23, -5) (µC - µD): (-12, 0)

A) B C A D

C) B C D A

B) B C D A

Objective: (9.3) Understand Multiple Comparison Method

D) C D B A

40) A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. For each pair of means, indicate which mean is larger or indicate that there is no significant difference. (µA - µB): (20, 32) (µA - µC): (9, 21) (µA - µD): (5, 19) (µB - µC): (-19, -3) (µB - µD): (-24, -4) (µC - µD): (-9, 3)

A) µA < µB; µA < µC; µA < µD; µB > µC; µB > µD; no significant difference between µC and µD B) µA > µB; µA > µC; µA > µD; µB < µC; µB < µD; µC < µD C) µA > µB; µA > µC; µA > µD; µB < µC; µB < µD; no significant difference between µC and µD D) no significant difference between µA and µB; µA < µC; µA < µD; µB > µC; µB > µD; no significant difference between µC and µD Objective: (9.3) Understand Multiple Comparison Method

41) A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. Rank the means from smallest to largest. Use solid lines to connect those means which are not significantly different. (µ1 - µ2 ): (8, 20) (µ1 - µ3 ): (-6, 2) (µ1 - µ4 ): (8, 22) (µ2 - µ3 ): (-22, -10) (µ2 - µ4 ): (-4, 6) (µ3 - µ4 ): (10, 24)

A) 4 2 1 3

B) 2 4 1 3

C) 4 2 1 3

Objective: (9.3) Understand Multiple Comparison Method

D) 4 1 2 3

42) A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. For each pair of means, indicate which mean is larger or indicate that there is no significant difference. (µ1 - µ2 ): (10, 18) (µ1 - µ3 ): (-9, 5) (µ1 - µ4 ): (9, 21) (µ2 - µ3 ): (-23, -9) (µ2 - µ4 ): (-6, 8) (µ3 - µ4 ): (10, 24)

A) µ1 > µ2 ; no significant difference between µ1 and µ3 ; µ1 > µ4 ; µ2 < µ3 ; no significant difference between µ2 and µ4 ; µ3 > µ4

B) µ1 > µ2 ; µ1 < µ3 ; µ1 > µ4 ; µ2 < µ3 ; µ2 < µ4 ; µ3 > µ4 C) no significant difference between µ1 and µ2 ; no significant difference between µ1 and µ3 ; µ1 > µ4 ; µ2 < µ3 ; no significant difference between µ2 and µ4 ; µ3 > µ4

D) µ1 < µ2 ; no significant difference between µ1 and µ3 ; µ1 < µ4 ; µ2 > µ3 ; no significant difference between µ2 and µ4 ; µ3 < µ4 Objective: (9.3) Understand Multiple Comparison Method

43) Which procedure was specifically developed for pairwise comparisons when the sample sizes of the treatments are equal? A) Tukey B) Scheffé C) ANOVA D) Bonferroni Objective: (9.3) Understand Multiple Comparison Method

44) Which method generally produces wider confidence intervals? A) ANOVA B) Tukey C) Bonferroni

D) Scheffé

Objective: (9.3) Understand Multiple Comparison Method

45) Which of the following is not one of the multiple comparison method options available to compare treatment means? A) The Tukey Method B) The Bonferroni Method C) The Einstein Method D) The Scheffe Method Objective: (9.3) Understand Multiple Comparison Method

46) In an experiment with 10 treatments, how many pairs of means can be compared? A) 100 B) 90 C) 20

D) 45

Objective: (9.3) Understand Multiple Comparison Method

47) Consider a completely randomized design with k treatments. Assume all pairwise comparisons of treatment means are to be made using a multiple comparisons procedure. Determine the total number of treatment means to be compared for the value k = 9. A) 18 B) 45 C) 9 D) 36 Objective: (9.3) Understand Multiple Comparison Method

48) Consider a completely randomized design with five treatments. How many pairwise comparisons of treatments are made in a Bonferroni analysis? A) 5! = 120 B) 10 C) 20 D) 5 Objective: (9.3) Understand Multiple Comparison Method

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 49) The __________ in a designed experiment to compare k means is the probability of making at least one Type I error in a series of inferences about the population means, based on (1 - ) 100% confidence intervals. Objective: (9.3) Understand Multiple Comparison Method

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 50) A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that primary specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 20 HMO physicians from each of four primary specialties General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP) and recorded the total per-member, per-month charges for each. In order to compare the mean charges for the four specialty groups, the data were be subjected to a one-way analysis of variance. The results of the Tukey analysis are summarized below. Group IM GP FP PED

Sample Mean 55.9 41.4 39.90 22.20

Which primary specialties have significantly lower mean charges than Internal Medicine (IM)? A) PED and FP B) PED C) PED, FP, and GP D) none Objective: (9.3) Perform Multiple Comparison Procedure

51) An appliance manufacturer is interested in determining whether the brand of laundry detergent used affects the average amount of dirt removed from standard household laundry loads. An experiment is set up in which 10 laundry loads are randomly assigned to each of four laundry detergents-Brands A, B, C, and D (a total of 40 loads in the experiment). The amount of dirt removed, y, (measured in milligrams) for each load is recorded and subjected to an ANOVA analysis, including a follow-up Tukey analysis. Which of the following inferences concerning the Tukey results below is incorrect? Brands D C B A

Sample Means 182 174 142 131

A) µD > µA

B) µC < µD

C) µA < µC

Objective: (9.3) Perform Multiple Comparison Procedure

D) µB < µD

52) An article in a journal examined the attitudes of three groups of professionals on the condition of the environment, and quantified their responses on a seven-point scale (1 = no problem to 7 = disaster very likely). The mean scores for the groups are: A: 5.60 , B: 5.30 , and C: 5.29 . Using an experimentalwise error rate of = .05, Tukey's minimum significance for comparing means is 0.21. Use this information to conduct a multiple comparisons of the means. A) There is no significant difference in any of the means. B) The highest mean differs significantly from the other two, but there is no significant difference in the other two means. C) All means are significantly different. D) The lowest mean differs significantly from the other two, but there is no significant difference in the other two means. Objective: (9.3) Perform Multiple Comparison Procedure

53) 307 diamonds were sampled and randomly sorted into three groups of diamonds. These diamonds were randomly assigned to one of the three organizations, or groups (HRD, GIA, or IGI), that certify the appraisal of diamonds. A study was conducted to determine if the average size of diamonds reported by these three certification groups differ. A completely randomized design was used and the Bonferroni multiple comparison results are shown below. Bonferroni All-Pairwise Comparisons Test of CARAT by CERT CERT HRD GIA IGI

Mean 0.8129 0.6723 0.3665

Bonferroni Groups A B C

Alpha 0.05 Give the population mean(s) which are in the statistically largest group. A) µHRD B) µGIA C) µHRD & µGIA Objective: (9.3) Perform Multiple Comparison Procedure

D) µIGI

54) An economist is investigating the impact of today's economy on workers in the manufacturing industry who have been laid off. A sample of 50 workers was randomly selected from all workers in manufacturing that have been laid off in the past year. The following variables were measured for each laid off worker: length of time jobless (number of weeks) and tax status (single, married, or married/head of household). The data for the 50 workers were entered into the computer and analyzed to determine if the mean number of weeks jobless differed for the three tax status groups. The Tukey multiple comparison printout is shown below: Tukey HSD All-Pairwise Comparisons Test of JOBLESS by STATUS STATUS Married Single Mar/Head

Mean 50.375 48.000 33.789

Tukey Groups A A B

Alpha 0.1

Critical Q Value 2.975

Give the population mean(s) which are in the statistically smallest group. A) µMarried B) µSingle

C) µMar/Head

D) µMarried & µSingle

Objective: (9.3) Perform Multiple Comparison Procedure

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 55) The results of a Tukey multiple comparison are summarized below. Treatment B C A a. b. c.

Sample Mean 35.4 31.5 20.7

How many pairwise comparisons of the three treatments are there? Which treatments are significantly different from each other? Which treatments are not significantly different from each other?

Objective: (9.3) Perform Multiple Comparison Procedure

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 56) An experiment was conducted to compare the mean iron content in iron ore pieces determined by three different methods: (1) mechanical, (2) manual, and (3) laser. Five 1-meter long pieces of iron ore were removed from a conveyor belt, and the iron content of each piece was determined using each of the three methods. The data are shown below. How should the data be analyzed? Piece Mechanical Manual Laser 1 65.46 66.49 65.43 2 70.56 71.06 71.58 3 65.44 65.50 66.78 4 63.46 63.49 63.33 5 58.32 57.34 59.28

A) randomized block design with five treatments and three blocks B) 3 × 5 factorial design C) completely randomized design with three treatments D) randomized block design with three treatments and five blocks Objective: (9.4) Understand Randomized Block Design

57) Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in the table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 330 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 How should the data be analyzed? A) Randomized block design with eight treatments and four blocks B) Randomized block design with four treatments and eight blocks C) 4 × 8 factorial design D) Completely randomized design with four treatments Objective: (9.4) Understand Randomized Block Design

58) Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in the table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 330 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 Identify the response variable in this experiment. A) The average distance hit C) The brand of bat

B) A batter D) The brand of baseball

Objective: (9.4) Understand Randomized Block Design

59) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket.

1) 2) 3) | 59) 60)

Item A paper towels 1.22 cereal 2.75 floor cleaner 5.90 | | shaving cream 0.95 canned green beans 0.45

B 1.42 3.20 5.78 | 0.85 0.6

C 1.37 2.95 6.79 | 0.91 0.37

Identify the treatments for this experiment. A) the day on which the data were collected C) the 60 × 3 = 180 prices

B) the three supermarkets D) the 60 grocery items

Objective: (9.4) Understand Randomized Block Design

60) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket.

1) 2) 3) | 59) 60)

Item A paper towels 1.23 cereal 2.74 floor cleaner 5.97 | | shaving cream 1.03 canned green beans 0.52

B 1.43 3.19 5.85 | 0.93 0.67

C 1.38 2.94 6.86 | 0.99 0.44

Identify the dependent (response) variable for this experiment. A) the prices of the grocery items B) the supermarkets C) the mean prices of the grocery items at each supermarket D) the grocery items Objective: (9.4) Understand Randomized Block Design

61) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket.

1) 2) 3) | 59) 60)

Item A paper towels 1.29 cereal 2.84 floor cleaner 5.98 | | shaving cream 0.96 canned green beans 0.40

B 1.49 3.29 5.86 | 0.86 0.55

C 1.44 3.04 6.87 | 0.92 0.32

Identify the blocks for this experiment. A) the 60 × 3 = 180 prices C) the day on which the data were collected

B) the 60 grocery items D) the three supermarkets

Objective: (9.4) Understand Randomized Block Design

Answer the question True or False. 62) When a variable is identified as reducing variation in the response variable, but no additional knowledge concerning the variable is desired, it should be used as the blocking factor in the randomized block design. A) True B) False Objective: (9.4) Understand Randomized Block Design

63) The randomized block design is an extension of the matched pairs comparison of µ1 and µ2 . A) True

B) False

Objective: (9.4) Understand Randomized Block Design

Solve the problem. 64) Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in the table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 330 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 A partial ANOVA table is shown below. Source Batter Brand Error Total

DF 7 3 21 31

MS 946.77

500.9 11245.9

Find the F-value in the table above for testing whether the average distance hit for the four brands of baseball bats differ. A) 2.8 B) 39.7 C) 57.6 D) 23.9 Objective: (9.4) Complete ANOVA Table

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 65) An experiment was conducted using a randomized block design. The data from the experiment are displayed in the following table. TREATMENT BLOCK 1 2 3 1 15 20 13 2 14 23 13 3 17 19 14 Fill in the missing entries for an ANOVA table. SOURCE df SS MS F ________________________________________________ Treatments 86.22 Blocks Error ________________________________________________ Total 100.22 Objective: (9.4) Complete ANOVA Table

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 66) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. The results of the ANOVA test are summarized in the following table. Source Supermkt Item Error Corrected Total

df 2 59 118 179

Anova SS 2.6412678 215.5949311 3.9725322 222.2087311

Mean Square 1.3206399 3.6541514 0.0336655

F Value 39.23 108.54

Pr > F 0.0001 0.0001

What is the value of the test statistic for determining whether the three supermarkets have the same average prices? A) 1.3206 B) 108.54 C) 39.23 D) 0.0001 Objective: (9.4) Interpret Two-Way ANOVA Results

67) Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in the table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 330 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 The ANOVA table output is shown here: Source Batter Brand Error Total

DF 7 3 21 31

SS MS F P 6227.4 946.77 39.70 0.0000 4117.6 1372.54 57.55 0.0000 500.9 23.85 11245.9

Identify the test statistic that should be used for testing whether the average distance hit for the four brands of baseball bats differ. A) 57.55 B) 23.85 C) 39.7 D) 0.0000 Objective: (9.4) Interpret Two-Way ANOVA Results

68) Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in the table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 330 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 The ANOVA table output is shown here: Source Batter Brand Error Total

DF 7 3 21 31

SS MS F P 6227.4 946.77 39.70 0.0000 4117.6 1372.54 57.55 0.0000 500.9 23.85 11245.9

Based on the p-value for this test, make the proper conclusion about the treatments in this experiment. A) There is insufficient evidence (at = 0.01) to indicate differences among the mean distances for the eight batters. B) There is sufficient evidence (at = 0.01) to indicate differences among the mean distances for the four brands of baseball bats. C) There is insufficient evidence (at = 0.01) to indicate differences among the mean distances for the four brands of baseball bats. D) There is sufficient evidence (at = 0.01) to indicate differences among the mean distances for the eight batters. Objective: (9.4) Interpret Two-Way ANOVA Results

69) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. The results of the ANOVA are summarized in the following table. Source Supermkt Item Error Corrected Total

df 2 59 118 179

Anova SS 2.6412678 215.5949311 3.9725322 222.2087311

Mean Square 1.3206399 3.6541514 0.0336655

F Value 39.23 108.54

Pr > F 0.0001 0.0001

Based on the p-value of the test, make the proper conclusion. A) No conclusions can be drawn from the given information. B) There is insufficient evidence (at = .01) to indicate differences among the mean prices of grocery items at the three supermarkets. C) There is sufficient evidence (at = .01) to indicate differences among the mean prices of grocery items at the three supermarkets. D) There is sufficient evidence (at = .01) to indicate that the mean prices of grocery items at the three supermarkets are identical. Objective: (9.4) Interpret Two-Way ANOVA Results

70) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. The results of a Bonferroni analysis are summarized below. ___________ Supermarket A B C Mean Price 1.665 1.919 1.925 Interpret the Bonferroni analysis results. A) C has a significantly larger mean price than either of the other two supermarkets. B) A has a significantly smaller mean price than either of the other two supermarkets. C) B and C have significantly different mean prices. D) A has a significantly larger mean price than either of the other two supermarkets. Objective: (9.4) Interpret Two-Way ANOVA Results

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 71) A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. The results of the Bonferroni analysis are summarized below. ___________________ ________________ Supermarket A B C Mean Price 1.66 1.80 1.94 Fully interpret the Bonferroni analysis. Objective: (9.4) Interpret Two-Way ANOVA Results

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 72) Suppose an experiment utilizing a random block design has 4 treatments and 8 blocks for a total of 32 observations. Assume that the total Sum of Squares for the response is SS(Total) = 600. If the Sum of Squares for Treatments (SST) is 50% of SS(Total), and the Sum of Squares for Blocks (SSB) is 10% of SS (Total), find the F values for this experiment. A) treatments: F = 15.83; blocks: F = 6.79 B) treatments: F = 6.56; blocks: F = 0.66 C) treatments: F = 8.75; blocks: F = 0.75 D) treatments: F = 12.92; blocks: F = 1.11 Objective: (9.4) Conduct Two-Way ANOVA

73) Suppose a company makes 4 different frozen dinners, and tests their ability to attract customers. They test the frozen dinners in 13 different stores in order to account for any extraneous sources of variation. The company records the number of customers who purchase each product at each store. What assumptions are necessary for the validity of the F statistic for comparing the response means of the 4 frozen dinners? A) The means of the observations corresponding to all the block-treatment combinations are equal, and the variances of all the probability distributions are equal. B) The probability distributions of observations corresponding to all the block-treatment combinations are normal, and the sampling distributions of the variances of all the block-treatment combinations are normally distributed. C) The probability distributions of observations corresponding to all the block-treatment combinations are normal, and the variances of all the probability distributions are equal. D) None. The Central Limit Theorem eliminates the need for any assumptions. Objective: (9.4) Conduct Two-Way ANOVA

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 74) A market research firm is interested in the possible success of new flavors of ice cream. A study was conducted with three different flavors peach, almond, and coconut. Three participants were given a sample of each ice cream, in random order, and asked to rate the flavors on a 100-point scale. The results are given in the table below. FLAVOR PARTICIPANT Peach Almond Coconut 1 68 76 66 2 73 91 71 3 76 82 67 a.

What is the purpose of blocking on participants in this study?

Construct an ANOVA summary table using the information given.

Is there sufficient evidence of a difference in the mean ratings for the three flavors? Use

= 0.05.

Objective: (9.4) Conduct Two-Way ANOVA

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 75) A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that both primary specialty and whether the physician is a foreign or USA medical school graduate are an important factors in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 40 HMO physicians, half foreign graduates and half USA graduates, from each of four primary specialties General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP) and recorded the total per-member, per-month charges for each. Thus, information on charges were obtained for a total of n = 160 doctors. The sample mean charges for each of the eight categories are shown in the table. Primary Specialty Foreign Grad USA Grad GP 39.80 42.20 IM 55.80 53.50 PED 23.30 25.10 FP 31.10 34.90 What type of design was used for this experiment? A) completely randomized design with two treatments B) 4 x 2 factorial design with 20 replications C) completely randomized design with eight treatments D) 2 x 2 factorial design with 160 replications Objective: (9.5) Understand Factorial Experiment

76) Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been named the "MUM effect." To investigate the cause of the MUM effect, undergraduates at a university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Fifteen subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions. Then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) What type of experimental design was employed in this study? A) randomized block design with four treatments and 15 blocks B) 2 x 2 factorial design with 15 replications C) completely randomized design with four treatments D) 4 x 20 factorial design with no replications Objective: (9.5) Understand Factorial Experiment

77) The goal of an experiment is to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, we want to determine whether the effect of directional aid (wall signs or map) on travel time depends on starting room location (interior or exterior). Three visitors were assigned to each of the combinations of directional aid and starting room location, and the travel times of each (in seconds) to reach the goal destination room were recorded. DIRECTIONAL STARTING ROOM AID Interior Exterior Wall signs 131 227 105 338 240 134 Map

135 110 252

231 332 136

Explain how to properly analyze these data. A) ANOVA F-test for interaction in a 2 x 2 factorial design with 3 replications B) ANOVA F-test for a randomized block design with two treatments C) Chi-square test for a 2 x 2 factorial design D) ANOVA F-test for a completely randomized design with four treatments Objective: (9.5) Understand Factorial Experiment

78) An appliance manufacturer is interested in determining whether the brand of laundry detergent used affects the average amount of dirt removed from standard household laundry loads. An experiment is set up in which 26 laundry loads are randomly assigned to each of four laundry detergents-- Brands A, B, C, and D. (A total of 40 loads in the experiment.) A manufacturer of Brand A claims that the design of the experiment is flawed. According to the manufacturer, Brand A is better in cold water than in hot water. If all 104 loads in the above experiment were run in hot water, the results will be biased against Brand A. Explain how to redesign the experiment so that the main effects of both brand and water temperature (hot or cold) on amount of dirt removed, and their possible interaction, can be investigated. A) Randomly select two brands (say, A and B) and wash 26 loads in with each brand in cold water. Use hot water in all loads washed by the remaining two brands (say, C and D). B) For each of the 104 loads, randomly select one of the detergent brands and randomly select hot or cold water. C) Consider all eight combinations of brand and temperature (e.g., A-hot, A-cold, B-hot, B-cold, etc.). Randomly assign 13 loads to each of the eight combinations. D) Use one detergent brand (Brand A). Put 52 loads in hot water and 52 loads in cold water, and compare the results. Objective: (9.5) Understand Factorial Experiment

79) A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket) and display level (normal display space, normal display space plus end-of-aisle display, and twice the normal display space) were tested to determine if they had any effect on the weekly sales of a particular supermarket product. Each of the combinations of price level and display level were put in place for a randomly selected week and the weekly sales of the product was recorded. Each combination was used three times over the course of the experiment. The results of the study are shown here:

Identify the treatments used in this experiment. A) The weekly sales collected for each of the weeks. B) The three display levels used by the supermarket. C) The three price levels used by the supermarket. D) The nine combinations of price level and display level used by the supermarket. Objective: (9.5) Understand Factorial Experiment

80) A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket) and display level (normal display space, normal display space plus end-of-aisle display, and twice the normal display space) were tested to determine if they had any effect on the weekly sales of a particular supermarket product. Each of the combinations of price level and display level were put in place for a randomly selected week and the weekly sales of the product was recorded. Each combination was used three times over the course of the experiment. The results of the study are shown here:

Identify the response variable used in this experiment. A) The weekly sales collected for each of the weeks. B) The three price levels used by the supermarket. C) The three display levels used by the supermarket. D) The nine combinations of price level and display level used by the supermarket. Objective: (9.5) Understand Factorial Experiment

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 81) A beverage distributor wanted to determine the combination of advertising agency (two levels) and advertising medium (three levels) that would produce the largest increase in sales per advertising dollar. Each of the advertising agencies prepared ads as required for each of the media-- newspaper, radio, and television. Twelve small towns of roughly the same size were selected for the experiment, and two each were randomly assigned to receive an advertisement prepared and transmitted by each of the six agency-medium combinations. The dollar increases in sales per advertising dollar, based on a 1-month sales period, are shown in the table. Advertising Medium Newspaper Radio Television Agency 1 15.3, 12.7 17.4, 20.1 16.2, 12.7 Agency 2 22.4, 18.9 24.3, 28.8 9.4, 12.5 The SPSS analysis is shown below. _____________________________________________________________________ ***ANALYSIS OF VARIANCE*** SALES BY AGENCY MEDIUM

Source of Variation

Sum of Squares

Mean Square

Signif of F

Main Effects AGENCY MEDIUM

238.299 39.967 198.332

3 1 2

79.433 39.967 99.166

13.934 7.011 17.395

.004 .038 .003

77.345

38.672

6.784

.029

315.644 34.205 349.849

5 6 11

63.129 5.701 31.804

11.074

.005

AGENCY*MEDIUM Explained Residual Total

(Note: SPSS uses "Explained" instead of "Treatment" in the factorial analysis. Also, SPSS uses "Residual" instead of "Error.") Would you test the main effects factors, agency and medium, in this example? Explain why or why not. Objective: (9.5) Understand Factorial Experiment

82) Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been named the "MUM effect." To investigate the cause of the MUM effect, undergraduates at a university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Fifteen subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions. Then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) Describe the experiment, including the response variable, factors, factor levels, replications, and treatments. Objective: (9.5) Understand Factorial Experiment

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 83) A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket) and display level (normal display space, normal display space plus end-of-aisle display, and twice the normal display space) were tested to determine if they had any effect on the weekly sales of a particular supermarket product. Each of the combinations of price level and display level were put in place for a randomly selected week and the weekly sales of the product was recorded. Each combination was used three times over the course of the experiment. The results of the study are shown here:

The ANOVA table is shown below: Source Display Price Display*Price Error Total

DF 2 2 4 18 26

SS MS 1691393 845696 3089054 1544527 510705 127676 8905 495 5300057

Find the test statistic for determining whether the interaction between Price and Display is significant. A) 495 B) 3121.89 C) 1709.37 D) 257.93 Objective: (9.5) Complete ANOVA Table

84) A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket) and display level (normal display space, normal display space plus end-of-aisle display, and twice the normal display space) were tested to determine if they had any effect on the weekly sales of a particular supermarket product. Each of the combinations of price level and display level were put in place for a randomly selected week and the weekly sales of the product was recorded. Each combination was used three times over the course of the experiment. The results of the study are shown here:

The ANOVA table is shown below: Source Display Price Display*Price Error Total

DF 2 2 4 18 26

SS MS F P 1691393 845696 1709.37 0.0000 3089054 154427 3121.89 0.0000 510705 127676 258.07 0.0000 8905 495 5300057

Which of the following tests should be conducted first? A) A test of the Price Main Effect. B) A test of the Weekly Sales Main Effect. C) A test of the interaction between Price and Display. D) A test of the Display Main Effect. Objective: (9.5) Complete ANOVA Table

85) A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket) and display level (normal display space, normal display space plus end-of-aisle display, and twice the normal display space) were tested to determine if they had any effect on the weekly sales of a particular supermarket product. Each of the combinations of price level and display level were put in place for a randomly selected week and the weekly sales of the product was recorded. Each combination was used three times over the course of the experiment. The results of the study are shown here:

The ANOVA table is shown below: Source Display Price Display*Price Error Total

DF 2 2 4 18 26

SS MS F P 1691393 845696 1709.37 0.0000 3089054 154427 3121.89 0.0000 510705 127676 258.07 0.0000 8905 495 5300057

Based on the results found in the ANOVA table, should the Main Effects tests for either Display or Price be conducted? A) Yes. The main effects tests are both significant and should be tested. B) No. The interaction of Display and Price indicates that the Main Effects should not be tested. C) It depends on whether the main effects tests will be significant or not. D) Yes. The interaction of Display and Price indicates that the Main Effects should be tested. Objective: (9.5) Complete ANOVA Table

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 86) Complete the ANOVA table. Source A B AB ERROR Total

df 3 1

SS 519.90

5,600.10

MS 490.50 118.10

Objective: (9.5) Complete ANOVA Table

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 87) A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that both primary specialty and whether the physician is a foreign or USA medical school graduate are an important factors in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 40 HMO physicians, half foreign graduates and half USA graduates, from each of four primary specialties General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP) and recorded the total per-member, per-month charges for each. Thus, information on charges were obtained for a total of n = 160 doctors. The ANOVA results are summarized in the following table. Source Specialty Medschool Interaction Error Total

df 3 1 3 152 159

SS 22855 105 890 18950 42800

MS 7618 105 297 125

F Value 60.94 0.84 2.38

Prob > F .0001 .6744 .1348

Interpret the test for interaction shown in the ANOVA table. Use = 0.1. A) There is sufficient evidence at the = 0.1 level to say that primary specialty and medical school interact. B) There is sufficient evidence at the = 0.1 level to say that primary specialty and medical school do not interact. C) There is insufficient evidence at the = 0.1 level to say that primary specialty and medical school interact. D) It is impossible to make conclusions about primary specialty and medical school interaction based on the given information. Objective: (9.5) Conduct Factorial Analysis

88) A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that both primary specialty and whether the physician is a foreign or USA medical school graduate are an important factors in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 40 HMO physicians, half foreign graduates and half USA graduates, from each of four primary specialties General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physician (FP) and recorded the total per-member, per-month charges for each. Thus, information on charges were obtained for a total of n = 160 doctors. The ANOVA results are summarized in the following table. Source Specialty Medschool Interaction Error Total

df 3 1 3 152 159

SS 22855 105 890 18950 42800

MS 7618 105 297 125

F Value 60.94 0.84 2.38

Prob > F .0001 .6744 .1348

Assuming no interaction, is there evidence of a difference between the mean charges of USA and foreign medical school graduates? Use = 0.025. A) Yes, the test for the main effect for medical school is significant at = 0.025. B) No, the test for the main effect for medical school is not significant at = 0.025. C) No, because the test for the interaction is not significant at = 0.025, the test for the main effect for medical school is not valid. D) It is impossible to make conclusions about the main effect of medical school based on the given information Objective: (9.5) Conduct Factorial Analysis

89) Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been named the "MUM effect." To investigate the cause of the MUM effect, 40 undergraduates at a certain university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) The data was subject to an analysis of variance, with the following results: Source df SS MS F PR > F ___________________________________________________________________ Subject visibility 1 1,325.16 1,325.16 4.09 0.50 Test taker success 1 1,380.24 1,380.24 4.26 0.046 Visibility x success 1 3385.80 3385.80 10.45 .002 Error 36 11,664.00 324.00 ___________________________________________________________________ Total 39 17,755.20 Which conclusion can you draw from the analysis? Use = .01. A) At = .01, there is sufficient evidence to indicate that subject visibility and test taker success interact. B) At = .01, neither subject visibility nor test taker success are important predictors of latency to feedback. C) At = .01, there is no evidence of interaction between subject visibility and test taker success. D) At = .01, the model is not useful for predicting latency to feedback. Objective: (9.5) Conduct Factorial Analysis

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 90) Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been named the "MUM effect." To investigate the cause of the MUM effect, 40 undergraduates at a university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) The data was subject to an analysis of variance, with the following results: Source df SS MS F PR > F ___________________________________________________________________ Subject visibility 1 1,325.16 1,325.16 4.09 0.50 -1,316.81 Test taker success 1 1,380.24 1,380.24 0.046 Visibility x success 1 3385.80 3385.80 10.45 .002 Error 36 11,664.00 324.00 ___________________________________________________________________ Total 39 17,755.20 Is there evidence to indicate that subject visibility and test taker success interact? Use Objective: (9.5) Conduct Factorial Analysis

= .01.

91) FACTOR A

Level 1 2

FACTOR B 1 4.1, 4.1 5.8, 5.6

2 5.0, 5.2 5.4, 5.0

3 6.4, 6.0 8.8, 9.0

Calculate the mean response for each treatment

The MINITAB ANOVA printout is shown here. Test for interaction at the

Analysis of variance for response. Source df SS MS F __________________________________________________________ A 1 0.53777 0.53777 0.11851 B 2 5.02708 2.51334 0.55391 AB 2 13.49334 6.74667 1.48678 Error 6 27.22667 4.53778 __________________________________________________________ Total 11 46.28486 c.

Does the result warrant tests of the two factor mean effects?

Objective: (9.5) Conduct Factorial Analysis

= 0.05 level of significance.

Answer Key Testname: SB14ECH9TEST

1) B 2) A 3) C 4) D 5) A 6) A 7) B 8) D 9) D 10) A 11) C 12) B 13) D 14) D 15) B 16) B 17) B 18) C 19) B 20) D 21) A 22) B 23) B 24) B 25) D 26) B 27) a.

T E T

28)

29)

Source

F Treatments

7 000

.6 Total

00 Total

1 9.9 12.6 5.56

55 Error

2.8

25.2 61.2 86.4

13 Error

2 11 13

5.7

df SS MS F

7.1

Source

122

110

2.26

b. 3 c. No; F = 2.26 is less than F.05 = 3.98

30) B 31) B 32) D 33) A 34) B 35) C 36) C 37) D

with df = 2 and 11.

d S

38) To determine if a difference exists in the mean sale amounts among the three compensation systems, we test:

H0 : µ1 = µ2 = µ3 vs. Ha : At lea .

3,1 1,5 1.5

2 27,

1,0

2 30,

The test statistic is F = 3.17. The rejection region requires = .025 in the upper tail of the F distribution with v 1 = p - 1 = 3 - 1 = 2 df and v 2 = n - p = 15 - 3 = 12 df . So F.025 = 5.10, and the rejection region is F > 5.10. Since the observed value of the test statistic does not fall in the rejection region (F = 3.17 5.10), H0 cannot be rejected. There is insufficient evidence to indicate a difference in the mean sale amounts among the three compensation systems when testing at = .025. 39) C 40) C 41) C 42) A 43) A 44) D 45) C 46) D 47) D 48) B 49) experimentwise error rate

Answer Key Testname: SB14ECH9TEST

50) B 51) B 52) B 53) A 54) C 55) a. 3 b. A and C; A and B c. B and C 56) D 57) B 58) A 59) B 60) A 61) B 62) A 63) A 64) C 65) SOURCE df SS MS F ___________________ ___________________ ___________ Treatments 2 86.22 43.11 13.15 Blocks 2 0.889 0.444 0.136 Error 4 13.11 3.28 ___________________ ___________________ ___________ Total 8 100.22 66) C 67) A 68) B 69) C 70) B

71) Supermarkets connected by a line cannot be determined to have significantly different mean prices. From the Bonferroni Summary, we can conclude only that µA < µC.

reject the null hypothesis of equal means. There is sufficient statistical evidence that the three flavors of ice cream have different mean ratings. 75) B 76) B 77) A 78) C 79) D 80) A 81) The main effect factors, agency and medium, would not be tested since the interaction of these factors is a significant factor. 82) The data were collected using a 2 x 2 factorial design with 15 replications. The two factors in the experiment are subject visibility (levels: visible and not visible) and test taker success (levels: top 20% and bottom 20%). The treatments are the 2 x 2 = 4 combinations of the factor levels:

72) C 73) C 74) a. Blocking on participants controls possible participant-to-partici pant variation in rating the ice cream flavors. b. SOURCE

df SS MS F ___________________ ___________________ ______________ Flavors 2 357.5 6 178.7 8 12.98 Participants 2 105.5 6 52.78 3.83 Error 4 55.11 1 13.78 ___________________ ___________________ _______________ Total 8 518.2 3

Visible, Top 20% Visible, Bottom 20% Not Visible, Top 20% Not Visible, Bottom 20% The response variable is the latency to feedback times. 83) D 84) C

c. Yes. Since F = 12.98 > F.05 = 6.94 (df1 = 2, df2 = 4), we

85) B 86) Source f S

d S

MS F ___________________ ___________________ ___________________ ____________ A 3 1,471.5 490.50 2.41 B 1 519.90 519.90 2.56 AB 3 354.30 118.10 0.58 ERROR 16 3,254.40 203.40 ___________________ ___________________ ___________________ ____________ Total 23 5,600.10

87) C 88) B 89) A

Answer Key Testname: SB14ECH9TEST

90) To determine if subject visibility and test taker success interact, we test: H0 : Subject visibility and test taker success do not interact. Ha : Subject visibility and test taker success do interact. The test statistic is F = 10.45. The p-value for this test is p = .002. Since = .01 > p = .002, H0 is rejected. There is sufficient evidence to indicate that subject visibility and test taker success interact. 91) a. FACTOR B Level 1 2 3 FACTOR A 1 4.1 5.1 6.2 2 5.7 5.2 8.9 b. Since F = 1.48678 < F.05 = 5.14 (df1 = 2, df2 = 6), we do not reject the null hypothesis of no interaction. No, there is not significant evidence of interaction. c. Yes, since the null hypothesis of no interaction was not rejected, we should test the main effects.

McClave Statistics for Business and Economics 14e Chapter 10 Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 1) What are characteristics of the trials in a multinomial experiment? Objective: (10.1) Understand Categorical Data and Multinomial Experiment

2) Describe probabilities of the k outcomes of the multinomial experiment trials. Objective: (10.1) Understand Categorical Data and Multinomial Experiment

3) What is categorical data? Objective: (10.1) Understand Categorical Data and Multinomial Experiment

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) Use the appropriate table to find the following chi-square value: A) 5.229

B) 4.660

2 .990 for df = 15.

C) 5.812

D) 30.578

Objective: (10.2) Use Chi-Square Distribution

5) Use the appropriate table to find the following probability: P( 2 16.75) for df = 5. A) 0.005 B) 0.995 C) 0.990

D) 0.010

Objective: (10.2) Use Chi-Square Distribution

6) Find the rejection region for a one-dimensional chi-square test of a null hypothesis concerning p 1 , p 2 , . . . p k if k = 7 and

= .005. 2 > 20.278 A)

B) 2 > 0.676

C) 2 > 21.955

Objective: (10.2) Use Chi-Square Distribution

D) 2 > 18.548

7) Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE Agree Strongly Agree Somewhat Disagree Somewhat Disagree Strongly

NUMBER 60 110 80 50

In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. Use the chi-square distribution to determine the rejection region when testing at = .05. A) Reject H0 if 2 > 7.81473 B) Reject H0 if 2 > 0.351846 C) Reject H0 if 2 > 0.710721 D) Reject H0 if 2 > 9.48773 Objective: (10.2) Use Chi-Square Distribution

8) Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE Agree Strongly Agree Somewhat Disagree Somewhat Disagree Strongly

NUMBER 60 110 80 50

In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. As part of that analysis, a 95% confidence interval for the multinomial probability associated with the "Agree Strongly" response was desired. Which of the following confidence intervals should be used? A) (0.145, 0.255) B) (0.141, 0.259) C) (0.162, 0.238) D) (0.155, 0.245) Objective: (10.2) Use Chi-Square Distribution

9) Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE Agree Strongly Agree Somewhat Disagree Somewhat Disagree Strongly

NUMBER 60 110 80 50

In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. As part of that analysis, a 90% confidence interval for the multinomial probability associated with the "Disagree Somewhat" response was desired. Which of the following confidence intervals should be used? A) (0.216, 0.317) B) (0.225, 0.309) C) (0.206, 0.327) D) (0.201, 0.332) Objective: (10.2) Use Chi-Square Distribution

10) A survey of entrepreneurs focused on their job characteristics, work habits, social activities, leisure time, etc. One question put to each entrepreneur was, "What make of car (U.S., Europe, or Japan) do you drive?" The responses (number in each category) for a sample of 100 entrepreneurs are summarized below. The goal of the analysis is to determine if the proportions of entrepreneurs who drive American, European, and Japanese cars differ. U.S. 40

Europe 35

Japan 25

In order to determine whether the true proportions in each response category differ, a one-way chi-square analysis should be conducted. Use the chi-square distribution to determine the rejection region when testing at 0.025. A) Reject H0 if 2 > 7.37776 B) Reject H0 if 2 > 9.34840 C) Reject H0 if 2 > 9.21034 D) Reject H0 if 2 > 11.1433 Objective: (10.2) Use Chi-Square Distribution

11) An adverse drug effect (ADE) is an unintended injury caused by prescribed medication. The table summarizes the proximal cause of 95 ADEs that resulted from a dosing error at a Boston hospital. WRONG DOSAGE USE NUMBER OF ADEs (1) Lack of knowledge of drug 29 (2) Rule violation 17 (3) Faulty dose checking 13 (4) Slips 9 (5) Other 27 TOTAL 95 In order to determine whether the true percentages of ADEs in the five "cause" categories differ, a chi-square analysis was conducted. Use the chi-square distribution to determine the rejection region when testing at = 0.025. A) Reject H0 if 2 > 9.48773 B) Reject H0 if 2 > 12.8325 C) Reject H0 if 2 > 14.4494 D) Reject H0 if 2 > 11.1433 Objective: (10.2) Use Chi-Square Distribution

12) A multinomial experiment with k = 4 cells and n = 400 produced the data shown in the following table.

Cell 1 2 46 216

3 100

4 38

Previous studies in this area have shown that p 1 = p 2 = p 3 = p 4 = .25. Construct a 95% confidence interval for the multinomial probability associated with cell 2. A) (0.084, 0.146) B) (0.491, 0.589)

C) (0.499, 0.581)

D) (0.498, 0.582)

Objective: (10.2) Construct Confidence Interval

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 13) A multinomial experiment with k = 3 cells and n =100 has been conducted and the results are shown in the table.

Cell 1 2

Construct a 99% confidence interval for the multinomial probability associated with cell 2. Objective: (10.2) Construct Confidence Interval

14) A multinomial experiment with k = 4 cells and n = 300 produced the data shown in the following table.

Cell 1 2 65 69

3 80

4 86

Do these data provide sufficient evidence to contradict the null hypothesis that p 1 = .20, p 2 = .20, p 3 = .30, and p 4 = .30? Test using = .05. Objective: (10.2) Perform One-Way Chi Square Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 15) Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The table displays the starting positions for the winners of 240 competitions. Calculate the chi-square test statistic 2 used to test the claim that the probability of winning is the same regardless of starting position..

Starting Position Number of Wins A) 6.750

1 2 3 4 5 6 50 44 33 36 32 45 B) 12.592

C) 9.326

D) 15.541

Objective: (10.2) Perform One-Way Chi Square Test

16) Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The table displays the starting positions for the winners of 240 competitions. Find the rejection region used to test the claim that the probability of winning is the same regardless of starting position. Use = 0.05. The results are based on 240 wins. Starting Position Number of Wins A) 2 > 12.833

1 2 3 4 5 6 45 36 33 44 50 32 B) 2 > 15.086

C) 2 > 11.070

D) 2 > 9.236

Objective: (10.2) Perform One-Way Chi Square Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 17) Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The table displays the starting positions for the winners of 240 competitions. Test the claim that the probability of winning is the same regardless of starting position. Use = 0.05. The results are based on 240 wins. Starting Position Number of Wins

1 2 3 4 5 6 45 36 33 50 44 32

Objective: (10.2) Perform One-Way Chi Square Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 18) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Calculate the chi-square test statistic 2 used to test the claim that the probabilities show no preference.

Brand 1 2 3 4 5 Customers 18 65 32 30 55 A) 55.63 B) 48.91

C) 37.45

Objective: (10.2) Perform One-Way Chi Square Test

D) 45.91

19) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Find the rejection region used to test the claim that the probabilities show no preference. Use = 0.01. Brand 1 2 3 4 5 Customers 55 32 30 18 65 A) 2 > 9.488 B) 2 > 11.143

C) 2 > 13.277

D) 2 > 14.860

Objective: (10.2) Perform One-Way Chi Square Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 20) A new coffeehouse wishes to see whether customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Test the claim that the probabilities show no preference. Use 0.01.

Brand 1 2 3 4 5 Customers 18 55 32 30 65 Objective: (10.2) Perform One-Way Chi Square Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 21) A teacher finds that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following grades were recorded. Calculate the chi-square test statistic 2 used to determine if the grade distribution for the department is different than expected. Use = 0.01. Grade A B C D F Number 36 42 60 14 8 A) 4.82

B) 3.41

C) 6.87

D) 5.25

Objective: (10.2) Perform One-Way Chi Square Test

22) A teacher finds that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following grades were recorded. Find the rejection region used to determine if the grade distribution for the department is different than expected. Use = 0.01. Grade A B C D F Number 36 42 60 14 8 A) 2 > 7.779

B) 2 > 13.277

C) 2 > 11.143

D) 2 > 9.488

Objective: (10.2) Perform One-Way Chi Square Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 23) A teacher finds that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following grades were recorded. Determine if the grade distribution for the department is different than expected. Use = 0.01. Grade A B C D F Number 36 42 60 14 8 Objective: (10.2) Perform One-Way Chi Square Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 24) A random sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Calculate the chi-square test statistic 2 used to test the claim that all ages have crash rates proportional to their driving rates. Age Under 26 26 - 45 46 - 65 Over 65 Drivers 66 39 25 30 A) 101.324 B) 85.123

C) 95.431

D) 75.101

Objective: (10.2) Perform One-Way Chi Square Test

25) A random sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Find the rejection region used to test the claim that all ages have crash rates proportional to their number of drivers. Use = 0.05. Age Under 26 26 - 45 46 - 65 Over 65 Drivers 66 39 25 30 A) 2 > 6.251 B) 2 > 7.815

C) 2 > 9.348

D) 2 > 11.143

Objective: (10.2) Perform One-Way Chi Square Test

26) Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE Agree Strongly Agree Somewhat Disagree Somewhat Disagree Strongly

NUMBER 60 110 80 50

Specify the null hypothesis for testing whether the true proportions of Internet users in each response category are equal. A) H0 : Internet users and Government scanning are independent

B) H0 : µ1 = µ2 = µ3 = µ4 , where µi represents the average number of Internet users in one of the found response categories C) H0 : p1 = 60, p2 = 110, p3 = 80, p4 = 50, where pi represents the proportion of Internet users in one of the four response categories D) H0 : p1 = p2 = p3 = p4 = 0.25, where pi represents the proportion of Internet users in one of the four response categories Objective: (10.2) Perform One-Way Chi Square Test

27) Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE Agree Strongly Agree Somewhat Disagree Somewhat Disagree Strongly

NUMBER 60 110 80 50

In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. When calculating the test statistic, what values for the expected counts should be used in the calculation? A) E1 = 0.25, E2 = 0.25, E3 = 0.25, E4 = 0.25 B) E1 = 60, E2 = 110, E3 = 80, E4 = 50

C) E1 = 300, E2 = 300, E3 = 300, E4 = 300

D) E1 = 75, E2 = 75, E3 = 75, E4 = 75

Objective: (10.2) Perform One-Way Chi Square Test

28) Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE Agree Strongly Agree Somewhat Disagree Somewhat Disagree Strongly

NUMBER 60 110 80 50

In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. Calculate the value of the test statistic for the desired analysis. A) 2 = 0.25 B) 2 = 75 C) 2 = 22.54 D) 2 = 28.0 Objective: (10.2) Perform One-Way Chi Square Test

29) A survey of entrepreneurs focused on their job characteristics, work habits, social activities, leisure time, etc. One question put to each entrepreneur was, "What make of car (U.S., Europe, or Japan) do you drive?" The responses (number in each category) for a sample of 100 entrepreneurs are summarized below. The goal of the analysis is to determine if the proportions of entrepreneurs who drive American, European, and Japanese cars differ. U.S. 40

Europe 35

Japan 25

In order to determine whether the true proportions in each response category differ, a one-way chi-square analysis should be conducted. When calculating the test statistic, what values for the expected counts should be used in the calculation? A) E1 = 33.33, E2 = 33.33, E3 = 33.33 B) E1 = 100, E2 = 100, E3 = 100

C) E1 = 46, E2 = 44, E3 = 9

D) E1 = 0.45, E2 = 0.46, E3 = 0.09

Objective: (10.2) Perform One-Way Chi Square Test

30) A survey of entrepreneurs focused on their job characteristics, work habits, social activities, leisure time, etc. One question put to each entrepreneur was, "What make of car (U.S., Europe, or Japan) do you drive?" The responses (number in each category) for a sample of 100 entrepreneurs are summarized below. The goal of the analysis is to determine if the proportions of entrepreneurs who drive American, European, and Japanese cars differ. U.S. 40

Europe 35

Japan 25

In order to determine whether the true proportions in each response category differ, a one-way chi-square analysis should be conducted. As part of that analysis, a 95% confidence interval for the multinomial probability associated with the "Europe" response was desired. Which of the following confidence intervals should be used? A) (0.227, 0.473) B) (0.271, 0.428) C) (0.265, 0.440) D) (0.257, 0.443) Objective: (10.2) Perform One-Way Chi Square Test

31) A survey of entrepreneurs focused on their job characteristics, work habits, social activities, leisure time, etc. One question put to each entrepreneur was, "What make of car (U.S., Europe, or Japan) do you drive?" The responses (number in each category) for a sample of 100 entrepreneurs are summarized below. The goal of the analysis is to determine if the proportions of entrepreneurs who drive American, European, and Japanese cars differ. U.S. 40

Europe 35

Japan 25

In order to determine whether the true proportions in each response category differ, a one-way chi-square analysis should be conducted. Suppose the p-value for the test was calculated to be p = 0.1738. What is the appropriate conclusion to make when testing at = 0.10? A) There is insufficient evidence to indicate the proportion of entrepreneurs driving the three makes of car differ. B) There is sufficient evidence to indicate the proportion of entrepreneurs driving the three makes of car differ. C) There is sufficient evidence to indicate the proportion of entrepreneurs driving the three makes of car are equal. D) There is sufficient evidence to indicate the proportion of entrepreneurs driving Japanese cars is less than the proportion driving U.S. cars. Objective: (10.2) Perform One-Way Chi Square Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 32) A random sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 46-65 group, and 12% for the group over 65. Test the claim that all ages have crash rates proportional to their number of drivers. Use = 0.05. Age Under 26 26 - 45 46 - 65 Over 65 Drivers 66 39 25 30 Objective: (10.2) Perform One-Way Chi Square Test

33) A multinomial experiment with k = 3 cells and n =30 has been conducted and the results are shown in the table.

Cell 1 2

Explain why the sample size is not large enough to test whether p 1 = .55, p 2 = .40, and p 3 = .05. Objective: (10.2) Perform One-Way Chi Square Test

34) The null hypothesis for a test of data resulting from a multinomial experiment is given as p1 = p 2 = p 3 = p 4 = .25. What is the alternative hypothesis for the test?

Objective: (10.2) Perform One-Way Chi Square Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 35) Find the rejection region for a test of independence of two classifications where the contingency table contains r = 2 rows and c = 4 columns and = .10. A) 2 > 22.307 B) 2 > 13.362 C) 2 > 6.251 D) 2 > 15.507 Objective: (10.3) Use Chi-Square Distribution

36) The contingency table below shows the results of a random sample of 500 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliations. Assuming the row and column classifications are independent, find an estimate for the expected cell count E22. Opinion Party Approve Disapprove No Opinion Republican 105 50 35 Democrat 125 60 45 Independent 25 40 15 A) 117.3 B) 57

C) 43.7

D) 69

Objective: (10.3) Use Chi-Square Distribution

37) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Assuming the row and column classifications are independent, find an estimate for the expected cell count of cell E22. Football Basketball Soccer Baseball Home team wins 39 156 25 83 Visiting team wins 30 97 20 76 A) 25.9 B) 19.1 Objective: (10.3) Use Chi-Square Distribution

C) 107.3

D) 145.7

38) A drug company developed a honey-based liquid medicine designed to calm a child's cough at night. To test the drug, 105 children who were ill with an upper respiratory tract infection were randomly selected to participate in a clinical trial. The children were randomly divided into three groups - one group was given a dosage of the honey drug, the second was given a dosage of liquid DM (an over-the-counter cough medicine), and the third (control group) received a liquid placebo (no dosage at all). After administering the medicine to their coughing child, parents rated their children's cough diagnosis as either better or worse. The results are shown in the table below: Diagnosis Treatment Better Worse Total Control 4 33 37 DM 12 21 33 Honey 24 11 35 Total 40 65 105 In order to determine whether the treatment group is independent of the coughing diagnosis, a two-way chi-square test was conducted. Use the chi-square distribution to determine the rejection region for this test when testing at = 0.025. A) Reject H0 if 2 > 9.34840 B) Reject H0 if 2 > 7.37776 C) Reject H0 if 2 > 7.81473 D) Reject H0 if 2 > 5.99147 Objective: (10.3) Use Chi-Square Distribution

39) Economists at USF are researching the problem of absenteeism at U.S. firms. A random sample of 100 U.S. organizations was selected to participate in a 1-year study. As part of the study, the economists had collected data on the following two variables for each company: shiftwork available (Yes or No), and union-management relationship (Good or Poor). As part of their analyses, the economists wanted to determine whether or not a company makes shiftwork available depends on the relationship between union and management. The collected data are shown below: Relation Shiftwork Good Bad No 11 22 Yes 25 42 Total 36 64

Total 33 67 100

Use the chi-square distribution to determine the rejection region for this test when testing at A) Reject H0 if 2 > 5.99147 B) Reject H0 if 2 > 3.84146 C) Reject H0 if 2 > 7.81473 D) Reject H0 if 2 > 5.02389 Objective: (10.3) Use Chi-Square Distribution

= 0.05.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 40) Test the null hypothesis of independence of the two classifications, A and B, of the 3 × 3 contingency table shown below. Test using = .10.

B B2

A1 A2

Objective: (10.3) Perform Chi-Square Test of Independence

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 41) The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliations. Use = 0.05. Opinion Party Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Find the rejection region used to test the claim of independence. A) 2 > 11.143 B) 2 > 9.488 C) 2 > 13.277

D) 2 > 7.779

Objective: (10.3) Perform Chi-Square Test of Independence

42) The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Opinion Party Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Find the chi-square test statistic 2 used to test the claim of independence. A) 7.662 B) 11.765 C) 8.030 Objective: (10.3) Perform Chi-Square Test of Independence

D) 9.483

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 43) The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliations. Opinion Party Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Test the claim of independence. Use

= .05.

Objective: (10.3) Perform Chi-Square Test of Independence

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 44) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Find the rejection region used to test the claim that the number of home team and visiting team wins is independent of the sport. Use = 0.01. Football Basketball Soccer Baseball Home team wins 39 156 25 83 Visiting team wins 31 98 19 75 2 2 > 12.838 > 7.815 A) B)

C) 2 > 11.345

D) 2 > 9.348

Objective: (10.3) Perform Chi-Square Test of Independence

45) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Calculate the chi-square test statistic 2 used to test the claim that the number of home team and visiting team wins is independent of the sport. Use

= 0.01.

Football Basketball Soccer Baseball Home team wins 39 156 25 83 Visiting team wins 31 98 19 75 A) 2.919 B) 4.192 Objective: (10.3) Perform Chi-Square Test of Independence

C) 5.391

D) 3.290

46) A drug company developed a honey-based liquid medicine designed to calm a child's cough at night. To test the drug, 105 children who were ill with an upper respiratory tract infection were randomly selected to participate in a clinical trial. The children were randomly divided into three groups - one group was given a dosage of the honey drug, the second was given a dosage of liquid DM (an over-the-counter cough medicine), and the third (control group) received a liquid placebo (no dosage at all). After administering the medicine to their coughing child, parents rated their children's cough diagnosis as either better or worse. The results are shown in the table below: Diagnosis Treatment Better Worse Total Control 4 33 37 DM 12 21 33 Honey 24 11 35 Total 40 65 105 In order to determine whether the treatment group is independent of the coughing diagnosis, a two-way chi-square test was conducted. Calculate the value of the test statistic for the desired analysis. A) 2 = 9.72 B) 2 = 25.51 C) 2 = 15.79 D) 2 = 28.54 Objective: (10.3) Perform Chi-Square Test of Independence

47) A drug company developed a honey-based liquid medicine designed to calm a child's cough at night. To test the drug, 105 children who were ill with an upper respiratory tract infection were randomly selected to participate in a clinical trial. The children were randomly divided into three groups - one group was given a dosage of the honey drug, the second was given a dosage of liquid DM (an over-the-counter cough medicine), and the third (control group) received a liquid placebo (no dosage at all). After administering the medicine to their coughing child, parents rated their children's cough diagnosis as either better or worse. The results are shown in the table below: Diagnosis Treatment Better Worse Total Control 4 33 37 DM 12 21 33 Honey 24 11 35 Total 40 65 105 In order to determine whether the treatment group is independent of the coughing diagnosis, a two-way chi-square test was conducted. Suppose the p-value for the test was calculated to be p = 0.0016. What is the appropriate conclusion to make when testing at = 0.05? A) There is insufficient evidence to indicate the treatment group is independent of the coughing diagnosis. B) There is insufficient evidence to indicate the treatment group is dependent on the coughing diagnosis. C) There is sufficient evidence to indicate the treatment group is independent of the coughing diagnosis. D) There is sufficient evidence to indicate the treatment group is dependent on the coughing diagnosis. Objective: (10.3) Perform Chi-Square Test of Independence

48) A business professor conducted a campus survey to estimate demand among all students for a protein supplement for smoothies and other nutritional drinks. Each of 113 students, randomly selected from all students on campus, provided the following information: (1) How health conscious are you? (Very, Moderately, Slightly, Not very) (2) Do you prefer protein supplements in your smoothies? (Yes, No) As part of his analysis, the professor claims that whether or not the student prefers a protein supplement in smoothies is independent of health consciousness level (Very, Moderate, Slightly, or Not very). Identify the appropriate alternative hypothesis that the professor should use in the test of hypothesis he desires. A) HA: Preference and Health Consciousness level are dependent variables.

B) HA: There is interaction between the Preference and Health Consciousness variables. C) HA: Preference and Health Consciousness level are independent variables. D) HA: Preference and Health Consciousness level are mutually exclusive variables. Objective: (10.3) Perform Chi-Square Test of Independence

49) A business professor conducted a campus survey to estimate demand among all students for a protein supplement for smoothies and other nutritional drinks. Each of 113 students, randomly selected from all students on campus, provided the following information: (1) How health conscious are you? (Very, Moderately, Slightly, Not very) (2) Do you prefer protein supplements in your smoothies? (Yes, No) As part of his analysis, the professor claims that whether or not the student prefers a protein supplement in smoothies is independent of health consciousness level (Very, Moderate, Slightly, or Not very). Use the chi-square distribution to determine the rejection region for this test when testing at = 0.05. A) Reject H0 if 2 > 9.34840 B) Reject H0 if 2 > 5.99147 C) Reject H0 if 2 > 7.81473 D) Reject H0 if 2 > 9.48773 Objective: (10.3) Perform Chi-Square Test of Independence

50) Economists at USF are researching the problem of absenteeism at U.S. firms. A random sample of 100 U.S. organizations was selected to participate in a 1-year study. As part of the study, the economists had collected data on the following two variables for each company: shiftwork available (Yes or No), and union-management relationship (Good or Poor). As part of their analyses, the economists wanted to determine whether or not a company makes shiftwork available depends on the relationship between union and management. The collected data are shown below: Relation Shiftwork Good Bad No 11 22 Yes 25 42 Total 36 64

Total 33 67 100

In order to determine whether the shiftwork responses depend on the relationship responses, a two-way chi-square analysis should be conducted. When calculating the test statistic, what values for the expected counts should be used in the calculation? A) E11 = 0.065, E12 = 0.036, E21 = 0.032, E22 = 0.018 B) E11 = 36, E12 = 33, E21 = 64, E22 = 67

C) E11 = 11.88, E12 = 21.12, E21 = 24.12, E22 = 42.88 Objective: (10.3) Perform Chi-Square Test of Independence

D) E11 = 11, E12 = 22, E21 = 25, E22 = 42

51) Economists at USF are researching the problem of absenteeism at U.S. firms. A random sample of 100 U.S. organizations was selected to participate in a 1-year study. As part of the study, the economists had collected data on the following two variables for each company: shiftwork available (Yes or No), and union-management relationship (Good or Poor). As part of their analyses, the economists wanted to determine whether or not a company makes shiftwork available depends on the relationship between union and management. The collected data are shown below: Relation Shiftwork Good Bad No 11 22 Yes 25 42 Total 36 64

Total 33 67 100

In order to determine whether the shiftwork responses depend on the relationship responses, a two-way chi-square analysis should be conducted. Calculate the value of the test statistic for the desired analysis. A) 2 = 0.70 B) 2 = 11.88 C) 2 = 0.07 D) 2 = 0.15 Objective: (10.3) Perform Chi-Square Test of Independence

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 52) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Test the claim that the number of home team and visiting team wins is independent of the sport. Use = 0.01.

Home team wins Visiting team wins

Football Basketball Soccer Baseball 39 156 25 83 31 98 19 75

Objective: (10.3) Perform Chi-Square Test of Independence

53) The data below show the age and favorite type of music of 779 randomly selected people. Test the claim that age and preferred music type are independent. Use = 0.05. Age Country Rock Pop Classical 15 - 21 21 45 90 33 21 - 30 68 55 42 48 30 - 40 65 47 31 57 40 - 50 60 39 25 53 Objective: (10.3) Perform Chi-Square Test of Independence

54) A professor chose a random sample of 50 recent graduates of an MBA program and recorded the gender of each graduate (M or F) and whether the graduate chose to complete his or her degree requirements by completing a research project (RP) or by taking comprehensive exams (CE). The results are shown below. M, CE F, CE F, CE F, RP M, RP F, CE F, CE M, CE F, RP M, RP a.

M, RP F, RP, M, RP M, RP F, CE M, RP F, RP, M, RP M, RP F, CE

F, RP M, CE F, RP F, CE F, RP F, RP M, CE F, RP M, CE F, RP

M, CE M, RP F, CE M, CE M, CE M, CE M, RP F, CE M, CE M, CE

M, CE F, RP M, RP M, CE M, CE M, CE F, RP M, RP M, CE F, CE

Create a contingency table for the data. Perform a 2 -test to determine if there is any evidence that gender and choice of research project or

b. comprehensive exams are not independent. Use

= 0.05.

Objective: (10.3) Perform Chi-Square Test of Independence

55) Consider the accompanying contingency table.

Row 1 2

1 13 19

Column 2 15 26

3 16 11

a. Convert the values in row 1 to percentages by calculating the percentage of each column total falling in row 1. b. Create a bar graph with row 1 percentage on the vertical axis and column number on the horizontal axis. c. What pattern do you expect to see if the rows and columns are not independent? Is this pattern present in your graph? Objective: (10.3) Perform Chi-Square Test of Independence

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 56) When using any procedure to perform a hypothesis test, the user should always be certain that the experiment satisfies the assumptions given with the procedure. A) True B) False Objective: (10.4) Understand Assumptions of Chi-Square Tests

57) The sampling distribution for 2 works well when expected counts are very small. A) True B) False Objective: (10.4) Understand Assumptions of Chi-Square Tests

58) In a test of independence, it is safe to conclude that the events are independent when the value of 2 is very small. A) True B) False Objective: (10.4) Understand Assumptions of Chi-Square Tests

59) The 2 -test for independence is a useful tool for establishing a causal relationship between two factors. A) True B) False Objective: (10.4) Understand Assumptions of Chi-Square Tests

Solve the problem. 60) Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE Agree Strongly Agree Somewhat Disagree Somewhat Disagree Strongly

NUMBER 60 110 80 50

In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. Which of the following statements is not necessary for the analysis to be valid? A) The probabilities for the four response outcomes remain the same from one internet user to the next. B) The 300 internet users sampled are independent from one another. C) The expected cell counts all must be 30 or more. Objective: (10.4) Understand Assumptions of Chi-Square Tests

Answer Key Testname: SB14ECH10TEST

1) The trials are independent; there are k possible outcomes to each trial; the experiment consists of n identical trials. 2) The probabilities of the k outcomes remain the same from trial to trial and sum to 1. 3) data that represent the counts for each category of a multinomial experiment 4) A 5) B 6) D 7) A 8) D 9) B 10) A 11) D 12) B ^

13) p 2 = .32; The

confidence interval is .32(.68) .32 ± 2.575 100

.32 ± .12. 14) Since 2 = 3.056 < 2 .05 = 7.815 (df = 3), we do not reject the null hypothesis. There is not sufficient evidence that the cell proportions differ from those given in the null hypothesis. 15) A 16) C

17) The rejection region is 2 >11.070;

32) The rejection region is 2 > 7.815;

fail to reject H0;

reject H0; There is

chi-square test statistic is 2 6.750;

chi-square test statistic is 2 75.101;

There is not sufficient evidence to reject the claim of equal probabilities of winning in the six lanes. 18) C 19) C 20) The rejection region is 2 > 13.277;

sufficient evidence to reject the claim that the crash rates are proportional to the number of drivers. 33) E(n3 ) = .05(30) = 1.5 <

5, so the sample size is too small. 34) The alternative hypothesis is that at least two of the proportions differ from .25. 35) C 36) D 37) C 38) B 39) B 40) Since 2 = 42.8567 >

chi-square test statistic is 2 37.45; reject H0; There is

sufficient evidence to reject the claim that customers show no preference for the brands. 21) D 22) B 23) The rejection region is 2 > 13.277;

2 .10 = 7.779, we reject the null hypothesis. There is sufficient evidence to reject the claim that A and B are independent. 41) B 42) C 43) The rejection region is 2 > 9.488;

chi-square test statistic is 2 5.25; fail to reject H0;

There is not sufficient evidence to reject the claim that the grade distribution matches the expected one. 24) D 25) B 26) D 27) D 28) D 29) A 30) D 31) A

chi-square test statistic is 2 8.030; fail to reject H0;

There is not sufficient evidence to reject the claim of independence. 44) C 45) D 46) B 47) D

48) A 49) C 50) C 51) D 52) The rejection region is 2 > 11.345;

chi-square test statistic is 2 3.290; fail to reject H0;

There is not sufficient evidence to reject the claim of independence. 53) The rejection region is 2 > 16.919;

chi-square test statistic is 2 91.097; reject H0; There is

sufficient evidence to reject the claim of independence. 54) a. RP CE Total M 12 16 28 F 12 10 22 Total 24 26 50 b.

The rejection region is 2 >

3.84146; the test statistic is 2 .6743;

we cannot reject thee null hypothesis. There is no evidence that gender and choice of research project or comprehensive exams are not independent.

Answer Key Testname: SB14ECH10TEST

55) a. 40.6%, 36.6%, 59.3% b.

c. One bar would be much taller or much shorter than the others. Yes, the bar for column 3 is much taller than the other two bars. 56) A 57) B 58) B 59) B 60) C

McClave Statistics for Business and Economics 14e Chapter 11 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the line that passes through the given points. 1) (0, 6) and (6, 0)

Objective: (11.1) Graph Line

2) (-10, -10) and (5, 5)

Objective: (11.1) Graph Line

3) (-8, 0) and (-5, -1)

Objective: (11.1) Graph Line

4) (2, -4) and (-1, 2)

Objective: (11.1) Graph Line

5) (4, 8) and (-9, -1)

Objective: (11.1) Graph Line

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 6) Plot the line y = 3x. Then give the slope and y-intercept of the line. Objective: (11.1) Graph Line

7) Plot the line y = 4 - 2x. Then give the slope and y-intercept of the line. Objective: (11.1) Graph Line

8) Plot the line y = 1.5 + .5x. Then give the slope and y-intercept of the line. Objective: (11.1) Graph Line

9) The equation for a (deterministic) straight line is y = 0 + 1 x. If the line passes through the points (2, 5) and (3, 8), find the values of 0 and 1, respectively. Objective: (11.1) Graph Line

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the linear regression model: E(y) = 0 + 1 x, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following result was obtained: ^

y = 74.80 + 19.72x Which of the following statements concerning the deterministic model, E(y) = 0 + 1 x is true? A) In theory, a plot of the mean appraised value E(y) against the number of rooms x for the entire population of houses in east Meadow would result in a straight line. B) All of the above statements are true. C) In theory, if the appraised values y and number of rooms x for the entire population of houses in East Meadow were obtained and the (x, y) data points plotted, the points would fall in a straight line. ^

D) A plot of the predicted appraised values y against the number of rooms x for the sample of houses in East Meadow would not result in a straight line. Objective: (11.1) Understand Probabilistic Models

11) Is there a relationship between the raises administrators at County University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the linear regression model E(y) = 0 + 1 x. The faculty group obtained the following prediction equation: ^

y = 14,000 - 2,000x Which of the following statements about the model E(y) = 0 + 1 x is correct? A) The model hypothesizes that, on average, administrators make more money than professors. B) The model hypothesizes a line of means; as rating (x) increases, the mean raise E(y) moves up or down along a straight line. C) The model hypothesizes that knowing an administrator's rating (x) will determine exactly the administrator's raise (y). D) The model hypothesizes that the raises for the administrators fall in a perfect straight line. Objective: (11.1) Understand Probabilistic Models

Answer the question True or False. 12) The probabilistic model allows the E(y) values to fall around the regression line while the actual values of y must fall on the line. A) True B) False Objective: (11.1) Understand Probabilistic Models

Solve the problem. 13) Consider the data set shown below. Find the estimate of the slope of the least squares regression line. y 0 x -2

3 0

2 2

3 4

A) 1.49045

8 10 11 6 8 10

B) 0.94643

C) 0.9003

D) 1.5

Objective: (11.2) Perform Calculations and Find Least Squares Line

14) Consider the data set shown below. Find the estimate of the y-intercept of the least squares regression line. y 0 x -2

3 0

A) 1.49045

2 2

3 4

8 10 11 6 8 10

B) 0.9003

C) 1.5

Objective: (11.2) Perform Calculations and Find Least Squares Line

D) 0.94643

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 15) In a comprehensive road test for new car models, one variable measured is the time it takes the car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TIME60: y = Elapsed time (in seconds) from 0 mph to 60 mph MAX: x = Maximum speed attained (miles per hour) The simple linear model E(y) = 0 + 1 x was fit to the data. Computer printouts for the analysis are given below: NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60 PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T P CONSTANT 18.7171 0.63708 29.38 0.0000 -0.08365 -17.05 MAX 0.00491 0.0000 R-SQUARED ADJUSTED R-SQUARED SOURCE REGRESSION RESIDUAL TOTAL

DF 1 127 128

0.6960 0.6937

SS 374.285 163.443 537.728

RESID. MEAN SQUARE (MSE) STANDARD DEVIATION MS 374.285 1.28695

F 290.83

1.28695 1.13444

P 0.0000

CASES INCLUDED 129 MISSING CASES 0 ^

Find and interpret the estimate 1 in the printout above. Objective: (11.2) Perform Calculations and Find Least Squares Line

16) Is the number of games won by a major league baseball team in a season related to the team's batting average? Data from 14 teams were collected and the summary statistics yield: y = 1,134,

x = 3.642,

y 2 = 93,110,

x 2 = .948622, and

xy = 295.54

Find the least squares prediction equation for predicting the number of games won, y, using a straight-line relationship with the team's batting average, x. Objective: (11.2) Perform Calculations and Find Least Squares Line

17) To investigate the relationship between yield of potatoes, y, and level of fertilizer application, x, a researcher divides a field into eight plots of equal size and applies differing amounts of fertilizer to each. The yield of potatoes (in pounds) and the fertilizer application (in pounds) are recorded for each plot. The data are as follows: x y

1 25

1.5 31

2 27

2.5 28

3 36

3.5 35

4 32

4.5 34

Summary statistics yield SSxx = 10.5, SSyy = 112, SSxy = 25, x = 2.75, and y = 31. Find the least squares prediction equation.

Objective: (11.2) Perform Calculations and Find Least Squares Line

18) In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in the 15 minute period following the addition of food. The data showing the number of grunts and and the age of the warthog (in days) are listed below: Number of Grunts 83 61 32 37 56 33 55 10 13

Age (days) 118 134 148 153 160 167 176 182 188

a. Write the equation of a straight-line model relating number of grunts (y) to age (x). b. Give the least squares prediction equation. c.

Give a practical interpretation of the value of 0 , if possible.

d. Give a practical interpretation of the value of

1 , if possible.

Objective: (11.2) Perform Calculations and Find Least Squares Line

19) a.

Complete the table.

Totals b. c.

2 5 3 8

3 2 4 0

xi =

yi =

xi2

x iy i

xi2 =

xiy i =

Find SSxy, SSxx, 1 , x, y, and 0 . Write the equation of the least squares line.

Objective: (11.2) Perform Calculations and Find Least Squares Line

20) Consider the following pairs of measurements: x y a. b. c. d.

1 3

3 6

4 8

6 12

7 13

Construct a scattergram for the data. What does the scattergram suggest about the relationship between x and y? Find the least squares estimates of 0 and 1 .

Plot the least squares line on your scattergram. Does the line appear to fit the data well?

Objective: (11.2) Plot Least Squares Line with Scattergram

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 21) A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = 0 + 1 x, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 123 houses in East Meadow, the following results were obtained: ^

y = 123.80 + 19.72x ^

What are the properties of the least squares line, y = 123.80 + 19.72x? A) All 123 of the sample y-values fall on the line. B) It is normal, mean 0, constant variance, and independent. C) Average error of prediction is 0, and SSE is minimum. D) It will always be a statistically useful predictor of y. Objective: (11.2) Interpret Least Squares Line

22) A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = 0 + 1 x, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained: ^

y = 74.80 + 18.80x Give a practical interpretation of the estimate of the slope of the least squares line. A) For each additional room in the house, we estimate the appraised value to increase $74,800. B) For a house with 0 rooms, we estimate the appraised value to be $74,800. C) For each additional dollar of appraised value, we estimate the number of rooms in the house to increase by 18.80. D) For each additional room in the house, we estimate the appraised value to increase $18,800. Objective: (11.2) Interpret Least Squares Line

23) A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = 0 + 1 x, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained: ^

y = 74.80 + 19.72x Give a practical interpretation of the estimate of the y-intercept of the least squares line. A) For each additional room in the house, we estimate the appraised value to increase $19,720. B) We estimate the base appraised value for any house to be $74,800. C) There is no practical interpretation, since a house with 0 rooms is nonsensical. D) For each additional room in the house, we estimate the appraised value to increase $74,800. Objective: (11.2) Interpret Least Squares Line

24) Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model E(y) = 0 + 1 x. Using the method of least squares, the faculty group obtained the following prediction equation: ^

y = 14,000 - 2,000x Interpret the estimated slope of the line. A) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $2,000. B) For a $1 increase in an administrator's raise, we estimate the administrator's rating to decrease 2,000 points. C) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to decrease $2,000. D) For an administrator with a rating of 1.0, we estimate his/her raise to be $2,000. Objective: (11.2) Interpret Least Squares Line

25) Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model E(y) = 0 + 1 x. Using the method of least squares, the faculty group obtained the following prediction equation: ^

y = 14,000 - 2,000x Interpret the estimated y-intercept of the line. A) There is no practical interpretation, since rating of 0 is nonsensical and outside the range of the sample data. B) The base administrator raise at State University is $14,000. C) For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000. D) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000. Objective: (11.2) Interpret Least Squares Line

26) A large national bank charges local companies for using its services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict the service charge to a company is the company's sales revenue (x), measured in $ million. Data for 21 companies who use the bank's services were used to fit the model E(y) = 0 + 1 x. The results of the simple linear regression are provided below. ^

y = 2,700 + 20x Interpret the estimate of 0 , the y-intercept of the line. A) All companies will be charged at least $2,700 by the bank. B) There is no practical interpretation since a sales revenue of $0 is a nonsensical value. C) About 95% of the observed service charges fall within $2,700 of the least squares line. D) For every $1 million increase in sales revenue, we expect a service charge to increase $2,700. Objective: (11.2) Interpret Least Squares Line

27) An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT was created from a set of 25 data points. Which of the following is not an assumption required for the simple linear regression analysis to be valid? A) The errors of predicting SALARY are normally distributed. B) The errors of predicting SALARY have a mean of 0. C) The errors of predicting SALARY have a variance that is constant for any given value of GMAT. D) SALARY is independent of GMAT. Objective: (11.2) Interpret Least Squares Line

28) What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Constant Size

Coefficient -2298.36 11598.9

R-Squared Adjusted R-Squared

Std Error 158.531 230.111

P -14.50 0.0000 50.41 0.0000

0.8925 Resid. Mean Square (MSE) 0.8922 Standard Deviation

1248950 1117.56

Interpret the estimated slope of the regression line. A) For every 2298.36-carat decrease in the size of a diamond, we estimate that the price of the diamond will increase by $11,598.90. B) For every $1 decrease in the price of the diamond, we estimate that the size of the diamond will increase by 11,598.9 carats. C) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $11,598.90. D) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will decrease by $2298.36. Objective: (11.2) Interpret Least Squares Line

29) What is the relationship between diamond price and carat size? 307 diamonds were sampled (ranging in size from 0.18 to 1.1 carats) and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Constant Size

Coefficient -2298.36 11598.9

R-Squared Adjusted R-Squared

Std Error 158.531 230.111

P -14.50 0.0000 50.41 0.0000

0.8925 Resid. Mean Square (MSE) 0.8922 Standard Deviation

1248950 1117.56

Interpret the estimated y-intercept of the regression line. A) When a diamond is 0 carats in size, we estimate the price of the diamond to be $11,598.90. B) When a diamond is 0 carats in size, we estimate the price of the diamond to be $2298.36. C) No practical interpretation of the y-intercept exists since a diamond of 0 carats cannot exist and falls outside the range of the carat sizes sampled. D) When a diamond is 11598.9 carats in size, we estimate the price of the diamond to be $2298.36. Objective: (11.2) Interpret Least Squares Line

30) A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000’s) of graduates of the program based on the amount of tuition (in $1000’s) charged by the program. The results of a simple linear regression analysis are shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Size

Coefficient 18.1849 1.47494

Std Error 10.3336 0.14017

T 1.76 10.52

R-Squared 0.6027 Resid. Mean Square (MSE) Adjusted R-Squared 0.5972 Standard Deviation

P 0.0826 0.0000 532.986 23.0865

Interpret the estimated slope of the regression line. A) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $1474.94. B) For every $1474.94 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $18,184.90. C) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will decrease by $1474.94. D) For every $1000 increase in the average starting salary, we estimate that the tuition charged by the MBA program will increase by $1474.94. Objective: (11.2) Interpret Least Squares Line

Answer the question True or False. 31) The Method of Least Squares specifies that the regression line has an average error of 0 and has an SSE that is minimized. A) True B) False Objective: (11.2) Interpret Least Squares Line

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 32) A company keeps extensive records on its new salespeople on the premise that sales should increase with experience. A random sample of seven new salespeople produced the data on experience and sales shown in the table. Months on Job 2 4 8 12 1 5 9

Monthly Sales y ($ thousands) 2.4 7.0 11.3 15.0 .8 3.7 12.0

Summary statistics yield SSxx = 94.8571, SSxy = 124.7571, SSyy = 176.5171, x = 5.8571, and y = 7.4571. State the assumptions necessary for predicting the monthly sales based on the linear relationship with the months on the job. Objective: (11.2) Interpret Least Squares Line

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 33) What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Constant Size

Coefficient -2298.36 11598.9

R-Squared Adjusted R-Squared

Std Error 158.531 230.111

P -14.50 0.0000 50.41 0.0000

0.8925 Resid. Mean Square (MSE) 0.8922 Standard Deviation

1248950 1117.56

Which of the following assumptions is not stated correctly? A) The probability distribution of is normal. B) The variance of the probability distribution of is constant for all settings of the independent variable. C) The mean of the probability distribution of is 0. D) The values of associated with any two observations are dependent on one another. Objective: (11.3) Understand Model Assumptions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 34) State the four basic assumptions about the general form of the probability distribution of the random error . Objective: (11.3) Understand Model Assumptions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 35) If a least squares line were determined for the data set in each scattergram, which would have the smallest variance? A) B)

Objective: (11.3) Interpret Scattergram

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 36) Calculate SSE and s2 for n = 30, SSyy = 100, SSxy = 60, and 1 = .8. ^

Objective: (11.3) Find and Interpret s^2 and s

37) Calculate SSE and s2 for n = 25,

y2 = 950,

y = 65, SSxy = 3000, and 1 = .2.

Objective: (11.3) Find and Interpret s^2 and s

38) Suppose you fit a least squares line to 22 data points and the calculated value of SSE is .678. a. Find s2 , the estimator of 2 .

b. Find s, the estimator of . c. What is the largest deviation you might expect between any one of the 22 points and the least squares line? Objective: (11.3) Find and Interpret s^2 and s

39) Suppose you fit a least squares line to 21 data points and the calculated value of SSE is 0.428. a. Find s2 , the estimator of 2 .

b. What is the largest deviation you might expect between any one of the 21 points and the least squares line? Objective: (11.3) Find and Interpret s^2 and s

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 40) Consider the data set shown below. Find the standard deviation of the least squares regression line. y 0 3 x -2 0 A) 0.9003

2 2

3 4

8 10 11 6 8 10 B) 1.49045

C) 1.5

D) 0.94643

Objective: (11.3) Find and Interpret s^2 and s

41) What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Constant Size

Coefficient -2298.36 11598.9

R-Squared Adjusted R-Squared

Std Error 158.531 230.111

P -14.50 0.0000 50.41 0.0000

0.8925 Resid. Mean Square (MSE) 0.8922 Standard Deviation

1248950 1117.56

Interpret the standard deviation of the regression model. A) We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model. B) We expect most of the sampled diamond prices to fall within $1117.56 of their least squares predicted values. C) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. D) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values. Objective: (11.3) Find and Interpret s^2 and s

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 42) In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in the 15 minute period following the addition of food. The data showing the number of grunts and the age of the warthog (in days) are listed below: Number of Grunts 127 105 76 81 100 77 99 54 59 a. b.

Age (days) 155 171 185 190 197 204 213 219 225

Find SSE, s2 , and s. Interpret the value of s.

Objective: (11.3) Find and Interpret s^2 and s

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 43) A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = 0 + 1 x, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained: ^

y = 74.80 + 19.72x

R = 0.539

R 2 = 0.290

s = 58.031

Give a practical interpretation of the estimate of , the standard deviation of the random error term in the model. A) About 29% of the total variation in the sample of y-values can be explained by the linear relationship between appraised value and number of rooms. B) We expect 95% of the observed appraised values to lie on the least squares line. C) We expect to predict the appraised value of an East Meadow house to within about $29,000 of its true value. D) We expect to predict the appraised value of an East Meadow house to within about $58,000 of its true value. Objective: (11.3) Find and Interpret s^2 and s

44) The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's Business School graduates are selected at random, and data on GPA (x) and starting salary (y, in $thousands) for each graduate were used to fit the model E(y) = 0 + 1 x The results of the simple linear regression are provided below. ^

y = 4.25 + 2.75x,

SSxy = 5.15, SSxx = 1.87 SSyy = 15.17, SSE = 1.0075

Compute an estimate of , the standard deviation of the random error term. A) .048 B) 0.219 C) .689

D) 1.0075

Objective: (11.3) Find and Interpret s^2 and s

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 45) Is the number of games won by a major league baseball team in a season related to the team's batting average? Data from 14 teams were collected and the summary statistics yield: y = 1,134,

x = 3.642,

y 2 = 93,110,

x 2 = .948622, and

Assume 1 = 455.27. Estimate and interpret the estimate of . Objective: (11.3) Find and Interpret s^2 and s

xy = 295.54

46) A breeder of Thoroughbred horses wishes to model the relationship between the gestation period and the length of life of a horse. The breeder believes that the two variables may follow a linear trend. The information in the table was supplied to the breeder from various thoroughbred stables across the state. Horse

1 2 3 4

Gestation period x (days) 416 279 298 307

Life Length y (years) 24 25.5 20 21.5

Horse

Gestation period x (days) 356 403 265

5 6 7

Life Length y (years) 22 23.5 21

Summary statistics yield SSxx = 21,752, SSxy = 236.5, SSyy = 22, x = 332, and y = 22.5. Calculate SSE, s2 , and s. Objective: (11.3) Find and Interpret s^2 and s

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 47) Locate the values of SSE, s2 , and s on the printout below. Model Summary Model 1

R .859

Model 1

Regression Residual Total

Adjusted R Square .689

R Square .737

ANOVA Sum of df Squares 4512.024 1 1678.115 12 6190.139 13

Std. Error of the Estimate 11.826

Mean Square

Sig.

4512.024 139.843

32.265

.001

A) SSE = 4512.024; s2 = 139.843; s = 11.826 C) SSE = 6190.139; s2 = 4512.024; s = 32.265

B) SSE = 4512.024; s2 = 4512.024; s = 32.265 D) SSE = 1678.115; s2 = 139.843; s = 11.826

Objective: (11.3) Find and Interpret s^2 and s

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 48) Consider the following pairs of measurements: x y

5 6.2

8 3.4

3 7.5

4 8.1

9 3.2

a. Construct a scattergram for the data. b. Use the method of least squares to model the relationship between x and y. c. Calculate SSE, s2 , and s. ^

d. What percentage of the observed y-values fall within 2s of the values of y predicted by the least squares model? Objective: (11.3) Find and Interpret s^2 and s

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 49) Consider the data set shown below. Find the 95% confidence interval for the slope of the regression line. y 0 x -2

3 0

2 2

3 4

A) 0.94643 ± 0.33306

8 10 11 6 8 10

B) 0.94643 ± 0.28377

C) 0.94643 ± 0.36203

D) 0.94643 ± 0.27603

Objective: (11.4) Construct Confidence Interval for 1

50) A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (x), measured in $ million. Data for 21 companies who use the bank's services were used to fit the model E(y) = 0 + 1 x. Suppose a 95% confidence interval for 1 is (15, 25). Interpret the interval. A) We are 95% confident that the mean service charge will fall between $15 and $25 per month. B) We are 95% confident that service charge (y) will decrease between $15 and $25 for every $1 million increase in sales revenue (x). C) We are 95% confident that service charge (y) will increase between $15 and $25 for every $1 million increase in sales revenue (x). D) We are 95% confident that sales revenue (x) will increase between $15 and $25 million for every $1 increase in service charge (y). Objective: (11.4) Construct Confidence Interval for 1

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 51) Construct a 90% confidence interval for

1 when 1 = 49, s = 4, SSxx = 55, and n = 15.

Objective: (11.4) Construct Confidence Interval for 1

52) Construct a 95% confidence interval for

1 when 1 = 49, s = 4, SSxx = 55, and n = 15.

Objective: (11.4) Construct Confidence Interval for 1

53) The data for n = 62 points were subjected to a simple linear regression with the results: a. Test whether the two variables, x and y, are positively linearly related. Use b. Construct and interpret a 90% confidence interval for 1 . Objective: (11.4) Perform Hypothesis Test for Linearity

= .05.

1 = 0.84 and s ^ = 0.14. 1

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 54) In a comprehensive road test on new car models, one variable measured is the time it takes a car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TIME60: MAX:

y = Elapsed time (in seconds) from 0 mph to 60 mph x = Maximum speed attained (miles per hour)

The simple linear model E(y) = 0 + 1 x was fit to the data. Computer printouts for the analysis are given below: NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60 PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T P CONSTANT 18.7171 0.63708 29.38 0.0000 -0.08365 -17.05 MAX 0.00491 0.0000 R-SQUARED ADJUSTED R-SQUARED SOURCE REGRESSION RESIDUAL TOTAL

DF 1 127 128

0.6960 0.6937

SS 374.285 163.443 537.728

RESID. MEAN SQUARE (MSE) STANDARD DEVIATION MS 374.285 1.28695

F 290.83

1.28695 1.13444

P 0.0000

CASES INCLUDED 129 MISSING CASES 0 Fill in the blank: "At =.05, there is ________________ between maximum speed and acceleration time." A) insufficient evidence of a negative linear relationship B) sufficient evidence of a positive linear relationship C) insufficient evidence of a linear relationship D) sufficient evidence of a negative linear relationship Objective: (11.4) Perform Hypothesis Test for Linearity

55) A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect drums in the future. The manufacturer collected a random sample of 35 boilers and measured the following two variables: MANHRS: PRESSURE:

y = Number of man-hours required to erect the drum x 1 = Boiler design pressure (pounds per square inch, i.e., psi)

The simple linear model E(y) = 0 + 1 x was fit to the data. A printout for the analysis appears below: UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS PREDICTOR VARIABLES CONSTANT PRESSURE

COEFFICIENT 1.88059 0.00321

STUDENT'S T 3.22 2.17

P 0.0028 0.0300

R-SQUARED 0.4342 ADJUSTED R-SQUARED 0.4176

RESID. MEAN SQUARE (MSE) STANDARD DEVIATION

4.25460 2.06267

SOURCE REGRESSION RESIDUAL TOTAL

MS 111.008 4.25160

DF 1 34 35

SS 111.008 144.656 255.665

STD ERROR 0.58380 0.00163

F 5.19

P 0.0300

Fill in the blank. At =.01, there is ____________ between man-hours and pressure. A) sufficient evidence of a positive linear relationship B) sufficient evidence of a linear relationship C) insufficient evidence of a positive linear relationship D) sufficient evidence of a negative linear relationship Objective: (11.4) Perform Hypothesis Test for Linearity

56) A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = 0 + 1 x, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. What set of hypotheses would you test to determine whether appraised value is positively linearly related to number of rooms? A) H0 : 1 = 0 vs. Ha : 1 > 0 B) H0 : 1 < 0 vs. Ha : 1 > 0

C) H0 : 1 = 0 vs. Ha : 1 0

D) H0 : 1 = 0 vs. Ha : 1 < 0

Objective: (11.4) Perform Hypothesis Test for Linearity

57) A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (x), measured in $ million. Data for 21 companies who use the bank's services were used to fit the model E(y) = 0 + 1 x. The results of the simple linear regression are provided below. ^

y = 2,700 + 20x, s = 65, 2-tailed p-value = .064 (for testing 1 ) Interpret the p-value for testing whether 1 exceeds 0. A) There is sufficient evidence (at = .05) to conclude that service charge (y) is positively linearly related to sales revenue (x) . B) Sales revenue (x) is a poor predictor of service charge (y). C) For every $1 million increase in sales revenue (x), we expect a service charge (y) to increase $.064. D) There is insufficient evidence (at = .05) to conclude that service charge (y) is positively linearly related to sales revenue (x). Objective: (11.4) Perform Hypothesis Test for Linearity

58) The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's Business School graduates are selected at random, and data on GPA (x) and starting salary (y, in $thousands) for each graduate were used to fit the model E(y) = 0 + 1 x. The value of the test statistic for testing 1 is 17.169. Select the proper conclusion. A) There is insufficient evidence (at = .05) to conclude that GPA is positively linearly related to starting salary. B) At any reasonable , there is no relationship between GPA and starting salary. C) There is sufficient evidence (at = .05) to conclude that GPA is positively linearly related to starting salary. D) There is insufficient evidence (at = .10) to conclude that GPA is a useful linear predictor of starting salary. Objective: (11.4) Perform Hypothesis Test for Linearity

59) An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below. ^

0 = -92040

1 = 228 s = 3213 df = 23 t = 6.67

Set up the null and alternative hypotheses for testing whether a linear relationship exists between SALARY and GMAT. ^

A) H0 : 1 > 0 vs. Ha : 1 < 0

B) H0 : 1 = 228 vs. Ha : 1 > 228

C) H0 : 1 = 0 vs. Ha : 1 0

D) H0 : 1 = 0 vs. Ha : 1 > 0

Objective: (11.4) Perform Hypothesis Test for Linearity

60) Consider the following model y = 0 + 1 x + , where y is the daily rate of return of a stock, and x is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard & Poor's (S&P) 500 Composite Index. Using a random sample of n = 12 days from 2007, the least squares lines shown in the table ^

below were obtained for four firms. The estimated standard error of 1 is shown to the right of each least squares prediction equation. Firm

Estimated Market Model

Company A Company B Company C Company D

y = .0010 + 1.40x y = .0005 - 1.21x y = .0010 + 1.62x y = .0013 + .76x

Estimated Standard Error of 1 .03 .06 1.34 .15

Calculate the test statistic for determining whether the market model is useful for predicting daily rate of return of Company A's stock. A) 161.6 B) 1.40 C) 1.40 ± .067 D) 46.7 Objective: (11.4) Perform Hypothesis Test for Linearity

61) Consider the following model y = 0 + 1 x + , where y is the daily rate of return of a stock, and x is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard & Poor's (S&P) 500 Composite Index. Using a random sample of n = 12 days from 1980, the least squares lines shown in the table ^

below were obtained for four firms. The estimated standard error of 1 is shown to the right of each least squares prediction equation. Firm

Estimated Market Model

Company A Company B Company C Company D

y = .0010 + 1.40x y = .0005 - 1.21x y = .0010 + 1.62x y = .0013 + .76x

Estimated Standard Error of 1 .03 .06 1.34 .15

For which of the three stocks, Companies B, C, or D, is there evidence (at = .05) of a positive linear relationship between y and x? A) Company C only B) Companies B and D only C) Company D only D) Companies B and C only Objective: (11.4) Perform Hypothesis Test for Linearity

62) What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Constant Size

Coefficient -2298.36 11598.9

R-Squared Adjusted R-Squared

Std Error 158.531 230.111

P -14.50 0.0000 50.41 0.0000

0.8925 Resid. Mean Square (MSE) 0.8922 Standard Deviation

1248950 1117.56

Which of the following conclusions is correct when testing to determine if the size of the diamond is a useful positive linear predictor of the price of a diamond? A) There is insufficient evidence to indicate that the price of the diamond is a useful positive linear predictor of the size of a diamond when testing at = 0.05. B) The sample size is too small to make any conclusions regarding the regression line. C) There is sufficient evidence to indicate that the size of the diamond is a useful positive linear predictor of the price of a diamond when testing at = 0.05. D) There is insufficient evidence to indicate that the size of the diamond is a useful positive linear predictor of the price of a diamond when testing at = 0.05. Objective: (11.4) Perform Hypothesis Test for Linearity

63) A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000’s) of graduates of the program based on the amount of tuition (in $1000’s) charged by the program. The results of a simple linear regression analysis are shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Size

Coefficient 18.1849 1.47494

Std Error 10.3336 0.14017

T 1.76 10.52

R-Squared 0.6027 Resid. Mean Square (MSE) Adjusted R-Squared 0.5972 Standard Deviation

P 0.0826 0.0000 532.986 23.0865

Fill in the blank. At = 0.05, there is _________________ between the amount of tuition charged by an MBA program and the average starting salary of graduates of the program. A) …sufficient evidence of a positive linear relationship… B) …insufficient evidence of a positive linear relationship… C) …sufficient evidence of a negative linear relationship… Objective: (11.4) Perform Hypothesis Test for Linearity

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 64) Operations managers often use work sampling to estimate how much time workers spend on each operation. Work sampling which involves observing workers at random points in time was applied to the staff of the catalog sales department of a clothing manufacturer. The department applied regression to data collected for 40 randomly selected working days. The simple linear model E(y) = 0 + 1 x was fit to the data. The printouts for the analysis are given below: TIME:

y = Time spent (in hours) taking telephone orders during the day

ORDERS:

x = Number of telephone orders received during the day

UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T P CONSTANT 10.1639 1.77844 5.72 0.0000 ORDERS 0.05836 0.00586 9.96 0.0000 R-SQUARED 0.7229 ADJUSTED R-SQUARED 0.7156

RESID. MEAN SQUARE (MSE) STANDARD DEVIATION

SOURCE REGRESSION RESIDUAL TOTAL

MS 1151.55 11.6175

DF 1 38 39

SS 1151.55 441.464 1593.01

F 99.12

11.6175 3.40844

P 0.0000

CASES INCLUDED 40 MISSING CASES 0 Conduct a test of hypothesis to determine if time spent (in hours) taking telephone orders during the day and the number of telephone orders received during the day are positively linearly related. Use = .01. Objective: (11.4) Perform Hypothesis Test for Linearity

65) Is the number of games won by a major league baseball team in a season related to the team's batting average? Data from 14 teams were collected and the summary statistics yield: y = 1,134, ^

x = 3.642,

y 2 = 93,110,

x 2 = .948622, and

xy = 295.54

Assume 1 = 455.27 and = 9.18. Conduct a test of hypothesis to determine if a positive linear relationship exists between team batting average and number of wins. Use = .05. Objective: (11.4) Perform Hypothesis Test for Linearity

66) A breeder of Thoroughbred horses wishes to model the relationship between the gestation period and the length of life of a horse. The breeder believes that the two variables may follow a linear trend. The information in the table was supplied to the breeder from various thoroughbred stables across the state. Horse

1 2 3 4

Gestation period x (days) 416 279 298 307

Life Length y (years) 24 25.5 20 21.5

Horse

5 6 7

Gestation period x (days) 356 403 265

Life Length y (years) 22 23.5 21

Summary statistics yield SSxx = 21,752, SSxy = 236.5, SSyy = 22, x = 332, and y = 22.5. Test to determine if a linear relationship exists between the gestation period and the length of life of a horse. Use estimate of .

= .05 and use s = 1.97 as an

Objective: (11.4) Perform Hypothesis Test for Linearity

67) Consider the following pairs of observations: x y

2 1.3

3 1.6

5 2.1

5 2.2

6 2.7

a. Construct a scattergram for the data. Does the scattergram suggest that y is positively linearly related to x? b. Find the slope of the least squares line for the data and test whether the data provide sufficient evidence that y is positively linearly related to x. Use = .05. Objective: (11.4) Perform Hypothesis Test for Linearity

68) A realtor collected the following data for a random sample of ten homes that recently sold in her area. House A B C D E F G H I J

Asking Price $114,500 $149,900 $154,700 $159,900 $160,000 $165,900 $169,700 $171,900 $175,000 $289,900

Days on Market 29 16 59 42 72 45 12 39 81 121

a. Construct a scattergram for the data. b. Find the least squares line for the data and plot the line on your scattergram. c. Test whether the number of days on the market, y, is positively linearly related to the asking price, x. Use = .05. Objective: (11.4) Perform Hypothesis Test for Linearity

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 69) The coefficient of correlation is a useful measure of the linear relationship between two variables. A) True B) False Objective: (11.5) Interpret Correlation Coefficient

70) A high value of the correlation coefficient r implies that a causal relationship exists between x and y. A) True B) False Objective: (11.5) Interpret Correlation Coefficient

71) A low value of the correlation coefficient r implies that x and y are unrelated. A) True B) False Objective: (11.5) Interpret Correlation Coefficient

Solve the problem. 72) An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below. ^

0 = -92040

2 1 = 228 s = 3213 r = .66 r = .81 df = 23 t = 6.67

Give a practical interpretation of r = .81. A) There appears to be a positive correlation between SALARY and GMAT. B) We can predict SALARY correctly 81% of the time using GMAT in a straight-line model. C) 81% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. D) We estimate SALARY to increase 81% for every 1-point increase in GMAT. Objective: (11.5) Interpret Correlation Coefficient

73) A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000’s) of graduates of the program based on the amount of tuition (in $1000’s) charged by the program. The results of a simple linear regression analysis are shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Size

Coefficient 18.1849 1.47494

Std Error 10.3336 0.14017

T 1.76 10.52

R-Squared 0.6027 Resid. Mean Square (MSE) Adjusted R-Squared 0.5972 Standard Deviation

P 0.0826 0.0000 532.986 23.0865

In addition, we are told that the coefficient of correlation was calculated to be r = 0.7763. Interpret this result. A) There is a fairly strong positive linear relationship between the amount of tuition charged and the average starting salary variables. B) There is a fairly strong negative linear relationship between the amount of tuition charged and the average starting salary variables. C) There is a very weak positive linear relationship between the amount of tuition charged and the average starting salary variables. D) There is almost no linear relationship between the amount of tuition charged and the average starting salary variables. Objective: (11.5) Interpret Correlation Coefficient

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 74) In team-teaching, two or more teachers lead a class. A researcher tested the use of team-teaching in mathematics education. Two of the variables measured on each teacher in a sample of 192 mathematics teachers were years of teaching experience x and reported success rate y (measured as a percentage) of team-teaching mathematics classes. The correlation coefficient for the sample data was reported as r = -0.29. Interpret this result. Objective: (11.5) Interpret Correlation Coefficient

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 75) Consider the data set shown below. Find the coefficient of correlation for between the variables x and y. y 0 x -2

A) 0.9489

3 0

2 2

3 4

8 10 11 6 8 10

B) 0.9383

C) 0.8804

Objective: (11.5) Calculate Correlation Coefficient

D) 0.9003

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 76) To investigate the relationship between yield of potatoes, y, and level of fertilizer application, x, a researcher divides a field into eight plots of equal size and applies differing amounts of fertilizer to each. The yield of potatoes (in pounds) and the fertilizer application (in pounds) are recorded for each plot. The data are as follows: x y

1 25

1.5 31

2 27

2.5 28

3 36

3.5 35

4 32

4.5 34

Summary statistics yield SSxx = 10.5, SSyy = 112, SSxy = 25, and SSE = 52.476. Calculate the coefficient of correlation.

Objective: (11.5) Calculate Correlation Coefficient

77) In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in the 15 minute period following the addition of food. The data showing the number of grunts and and the age of the warthog (in days) are listed below: Number of Grunts 90 68 39 44 63 40 62 17 20

Age (days) 125 141 155 160 167 174 183 189 195

Find and interpret the value of r. Objective: (11.5) Calculate Correlation Coefficient

78) Consider the following pairs of observations: x y

2 1.3

3 1.6

5 2.1

5 2.2

6 2.7

Find and interpret the value of the coefficient of correlation. Objective: (11.5) Calculate Correlation Coefficient

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 79) A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000’s) of graduates of the program based on the amount of tuition (in $1000’s) charged by the program. We are told that the coefficient of correlation was calculated to be r = 0.7763. Use this information to calculate the test statistic that would be used to determine if a positive linear relationship exists between the two variables. A) t = 1.760 B) t = 0.6027 C) t = 1.475 D) t = 10.52 Objective: (11.5) Perform Correlation Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 80) In team-teaching, two or more teachers lead a class. An researcher tested the use of team-teaching in mathematics education. Two of the variables measured on each sample of 178 mathematics teachers were years of teaching experience x and reported success rate y (measured as a percentage) of team-teaching mathematics classes. a. The researcher hypothesized that mathematics teachers with more years of experience will report higher perceived success rates in team-taught classes. State this hypothesis in terms of the parameter of a linear model relating x to y. b. The correlation coefficient for the sample data was reported as r = -0.34. Interpret this result. c. Does the value of r support the hypothesis? Test using = .05. Objective: (11.5) Perform Correlation Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 81) Consider the data set shown below. Find the coefficient of determination for the simple linear regression model. y 0 x -2

3 0

2 2

A) 0.9003

3 4

8 10 11 6 8 10

B) 0.9383

C) 0.9489

D) 0.8804

Objective: (11.5) Calculate Coefficient of Determination

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 82) In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in the 15 minute period following the addition of food. The data showing the number of grunts and and the age of the warthog (in days) are listed below: Number of Grunts 83 61 32 37 56 33 55 10 13

Age (days) 118 134 148 153 160 167 176 182 188

Find and interpret the value of r2 . Objective: (11.5) Calculate Coefficient of Determination

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 83) The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's Business School graduates are selected at random, and data on GPA (x) and starting salary (y, in $thousands) for each graduate were used to fit the model E(y) = 0 + 1 x The results of the simple linear regression are provided below. ^

y = 4.25 + 2.75x,

SSxy = 5.15, SSxx = 1.87 SSyy = 15.17, SSE = 1.0075

Calculate the value of r2 , the coefficient of determination. A) 0.661 B) 0.339

C) 0.934

D) 0.872

Objective: (11.5) Calculate Coefficient of Determination

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 84) A company keeps extensive records on its new salespeople on the premise that sales should increase with experience. A random sample of seven new salespeople produced the data on experience and sales shown in the table. Months on Job

Monthly Sales y ($ thousands) 2.4 7.0 11.3 15.0 .8 3.7 12.0

2 4 8 12 1 5 9

Summary statistics yield SSxx = 94.8571, SSxy = 124.7571, SSyy = 176.5171, x = 5.8571, and y = 7.4571. Using SSE = 12.435, find and interpret the coefficient of determination. Objective: (11.5) Calculate Coefficient of Determination

85) To investigate the relationship between yield of potatoes, y, and level of fertilizer application, x, a researcher divides a field into eight plots of equal size and applies differing amounts of fertilizer to each. The yield of potatoes (in pounds) and the fertilizer application (in pounds) are recorded for each plot. The data are as follows: x y

1 25

1.5 31

2 27

2.5 28

3 36

3.5 35

4 32

4.5 34

Summary statistics yield SSxx = 10.5, SSyy = 112, SSxy = 25, and SSE = 52.476. Calculate the coefficient of determination.

Objective: (11.5) Calculate Coefficient of Determination

86) Consider the following pairs of observations: x y

2 1.3

3 1.6

5 2.1

5 2.2

6 2.7

Find and interpret the value of the coefficient of determination. Objective: (11.5) Calculate Coefficient of Determination

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 87) In a comprehensive road test on new car models, one variable measured is the time it takes the car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TIME60: MAX

y = Elapsed time (in seconds) from 0 mph to 60 mph x = Maximum speed attained (miles per hour)

DF 1 127 128

0.6960 0.6937

SS 374.285 163.443 537.728

RESID. MEAN SQUARE (MSE) STANDARD DEVIATION MS 374.285 1.28695

F 290.83

1.28695 1.13444

P 0.0000

CASES INCLUDED 129 MISSING CASES 0 Approximately what percentage of the sample variation in acceleration time can be explained by the simple linear model? A) 0% B) 8% C) 70% D) -17% Objective: (11.5) Interpret Coefficient of Determination

88) A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect drums in the future. The manufacturer collected a random sample of 35 boilers and measured the following two variables: MANHRS: PRESSURE:

y = Number of man-hours required to erect the drum x = Boiler design pressure (pounds per square inch, i.e., psi)

The simple linear model E(y) = 1 + 1 x was fit to the data. A printout for the analysis appears below: UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS PREDICTOR VARIABLES CONSTANT PRESSURE

COEFFICIENT 1.88059 0.00321

STUDENT'S T 3.22 2.17

P 0.0028 0.0300

R-SQUARED 0.4342 ADJUSTED R-SQUARED 0.4176

RESID. MEAN SQUARE (MSE) STANDARD DEVIATION

4.25460 2.06267

SOURCE REGRESSION RESIDUAL TOTAL

MS 111.008 4.25160

DF 1 34 35

SS 111.008 144.656 255.665

STD ERROR 0.58380 0.00163

F 5.19

P 0.0300

Give a practical interpretation of the coefficient of determination, r2 . A) Approximately 95% of the actual man-hours required to build a drum will fall within 43 hours of their predicted values. B) About 43% of the sample variation in number of man-hours can be explained by the simple linear model. C) About 2.06% of the sample variation in number of man-hours can be explained by the simple linear model. D) We are 43% confident that the design pressure will be a useful predictor of number of man-hours required to build a steam drum. Objective: (11.5) Interpret Coefficient of Determination

89) An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below. ^

0 = -92040

2 1 = 228 s = 3213 r = .66 r = .81 df = 23 t = 6.67

Give a practical interpretation of r2 = .66. A) We expect to predict SALARY to within 2 .66 of its true value using GMAT in a straight-line model. B) We estimate SALARY to increase $.66 for every 1-point increase in GMAT. C) 66% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. D) We can predict SALARY correctly 66% of the time using GMAT in a straight-line model. Objective: (11.5) Interpret Coefficient of Determination

90) What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Constant Size

Coefficient -2298.36 11598.9

R-Squared Adjusted R-Squared

Std Error 158.531 230.111

P -14.50 0.0000 50.41 0.0000

0.8925 Resid. Mean Square (MSE) 0.8922 Standard Deviation

1248950 1117.56

Interpret the coefficient of determination for the regression model. A) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. B) There is sufficient evidence to indicate that the size of the diamond is a useful predictor of the price of a diamond when testing at alpha = 0.05. C) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values. D) We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model. Objective: (11.5) Interpret Coefficient of Determination

91) What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Constant Size

Coefficient -2298.36 11598.9

R-Squared Adjusted R-Squared

Std Error 158.531 230.111

P -14.50 0.0000 50.41 0.0000

0.8925 Resid. Mean Square (MSE) 0.8922 Standard Deviation

1248950 1117.56

The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here: 95% confidence interval for E(Y): ($9091.60, $9509.40) 95% prediction interval for Y: ($7091.50, $11,510.00) Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all 1-carat diamonds? A) We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40. B) We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00. C) We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00. D) We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40. Objective: (11.6) Calculate and Compare Confidence Intervals for Mean of y

92) A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000’s) of graduates of the program based on the amount of tuition (in $1000’s) charged by the program. The results of a simple linear regression analysis are shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Size

Coefficient 18.1849 1.47494

Std Error 10.3336 0.14017

T 1.76 10.52

R-Squared 0.6027 Resid. Mean Square (MSE) Adjusted R-Squared 0.5972 Standard Deviation

P 0.0826 0.0000 532.986 23.0865

The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000. The results are shown here: 95% confidence interval for E(Y): ($123,390, $134,220) 95% prediction interval for Y: ($82,476, $175,130) Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all MBA programs? A) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition will fall between $123,390 and $134,220. B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition will fall between $82,476 and $175,130. C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition will fall between $82,476 and $175,130. D) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition will fall between $123,390 and $134,220. Objective: (11.6) Calculate and Compare Confidence Intervals for Mean of y

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 93) A company keeps extensive records on its new salespeople on the premise that sales should increase with experience. A random sample of seven new salespeople produced the data on experience and sales shown in the table. Months on Job

Monthly Sales y ($ thousands) 2.4 7.0 11.3 15.0 .8 3.7 12.0

2 4 8 12 1 5 9

Summary statistics yield SSxx = 94.8571, SSxy = 124.7571, SSyy = 176.5171, x = 5.8571, and y = 7.4571. Calculate a 90% confidence interval for E(y) when x = 5 months. Assume s = 1.577 and the prediction equation is ^

y = -.25 + 1.315x. Objective: (11.6) Calculate and Compare Confidence Intervals for Mean of y

94) A realtor collected the following data for a random sample of ten homes that recently sold in her area. House A B C D E F G H I J

Asking Price $114,500 $149,900 $154,700 $159,900 $160,000 $165,900 $169,700 $171,900 $175,000 $289,900

Days on Market 29 16 59 42 72 45 12 39 81 121

a. Find a 90% confidence interval for the mean number of days on the market for all houses listed at $150,000. b. Suppose a house has just been listed at $150,000. Find a 90% prediction interval for the number of days the house will be on the market before it sells. Objective: (11.6) Calculate and Compare Confidence Intervals for Mean of y

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 95) Probabilistic models are commonly used to estimate both the mean value of y and a new individual value of y for a particular value of x. A) True B) False Objective: (11.6) Find and Interpret Predication Interval for y

96) The least squares model provides very good estimates of y for values of x far outside the range of x values contained in the sample. A) True B) False Objective: (11.6) Find and Interpret Predication Interval for y

Solve the problem. 97) An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below. ^

0 = -92040

2 1 = 228 s = 3213 r = .66 r = .81 df = 23 t = 6.67

A 95% prediction interval for SALARY when GMAT = 600 is approximately ($37,915, $51,984). Interpret this interval. A) We are 95% confident that the SALARY of a top business school graduate with a GMAT of 600 will fall between $37,915 and $51,984. B) We are 95% confident that the SALARY of a top business school graduate will fall between $37,915 and $51,984. C) We are 95% confident that the mean SALARY of all top business school graduates with GMATs of 600 will fall between $37,915 and $51,984. D) We are 95% confident that the increase in SALARY for a 600-point increase in GMAT will fall between $37,915 and $51,984. Objective: (11.6) Find and Interpret Predication Interval for y

98) The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's Business School graduates are selected at random, and data on GPA (x) and starting salary (y, in $thousands) for each graduate were used to fit the model E(y) = 0 + 1 x. The results of the simple linear regression are provided below. ^

y = 4.25 + 2.75x,

SSxy = 5.15, SSxx = 1.87 SSyy = 15.17, SSE = 1.0075 Range of the x-values: 2.23 - 3.85 Range of the y-values: 9.3 - 15.6 Suppose a 95% prediction interval for y when x = 3.00 is (16, 21). Interpret the interval. A) We are 95% confident that the mean starting salary of all Business School graduates with GPAs of 3.00 will fall between $16,000 and $21,000. B) We are 95% confident that the starting salary of a Business School graduate will increase between $16,000 and $21,000 for every 3-point increase in GPA. C) We are 95% confident that the starting salary of a Business School graduate will fall between $16,000 and $21,000. D) We are 95% confident that the starting salary of a Business School graduate with a GPA of 3.00 will fall between $16,000 and $21,000. Objective: (11.6) Find and Interpret Predication Interval for y

99) What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Constant Size

Coefficient -2298.36 11598.9

R-Squared Adjusted R-Squared

Std Error 158.531 230.111

P -14.50 0.0000 50.41 0.0000

0.8925 Resid. Mean Square (MSE) 0.8922 Standard Deviation

1248950 1117.56

The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here: 95% confidence interval for E(Y): ($9091.60, $9509.40) 95% prediction interval for Y: ($7091.50, $11,510.00) Which of the following interpretations is correct if you want to use the model to determine the price of a single 1-carat diamond? A) We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40. B) We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00. C) We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00. D) We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40. Objective: (11.6) Find and Interpret Predication Interval for y

100) A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000’s) of graduates of the program based on the amount of tuition (in $1000’s) charged by the program. The results of a simple linear regression analysis are shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Size

Coefficient 18.1849 1.47494

Std Error 10.3336 0.14017

T 1.76 10.52

R-Squared 0.6027 Resid. Mean Square (MSE) Adjusted R-Squared 0.5972 Standard Deviation

P 0.0826 0.0000 532.986 23.0865

The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000. The results are shown here: 95% confidence interval for E(Y): ($123,390, $134,220) 95% prediction interval for Y: ($82,476, $175,130) Which of the following interpretations is correct if you want to use the model to predict Y for a single MBA programs? A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition will fall between $82,476 and $175,130. B) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition will fall between $82,476 and $175,130. C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition will fall between $123,390 and $134,220. D) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition will fall between $123,390 and $134,220. Objective: (11.6) Find and Interpret Predication Interval for y

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 101) A breeder of Thoroughbred horses wishes to model the relationship between the gestation period and the length of life of a horse. The breeder believes that the two variables may follow a linear trend. The information in the table was supplied to the breeder from various thoroughbred stables across the state. Horse

1 2 3 4

Gestation period x (days) 416 279 298 307

Life Length y (years) 24 25.5 20 21.5

Horse

5 6 7

Gestation period x (days) 356 403 265

Life Length y (years) 22 23.5 21

Summary statistics yield SSxx = 21,752, SSxy = 236.5, SSyy = 22, x = 332, and y = 22.5. Find a 95% prediction interval for the length of life of a horse that had a gestation period of 300 days. Use s = 2 as an estimate of ^

y = 18.89 + .01087x. Objective: (11.6) Find and Interpret Predication Interval for y

and use

102) Consider the following pairs of observations: x y a. b. c. d.

2 1

0 3

3 4

3 6

5 7

Construct a scattergram for the data. Find the least squares line, and plot it on your scattergram. Find a 99% confidence interval for the mean value of y when x = 1. Find a 99% prediction interval for a new value of y when x = 1.

Objective: (11.6) Find and Interpret Predication Interval for y

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. (Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table. For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

School Harvard Stanford Penn Northwestern MIT Chicago Duke Dartmouth Virginia Michigan Columbia Cornell CMU UNC Cal-Berkeley UCLA Texas Indiana NYU Purdue USC Pittsburgh Georgetown Maryland Rochester

GMAT 644 665 644 640 650 632 630 649 630 620 635 648 630 625 634 640 612 600 610 595 610 605 617 593 605

Acc. Rate 15.0% 10.2 19.4 22.6 21.3 30.0 18.2 13.4 23.0 32.4 37.1 14.9 31.2 15.4 24.7 20.7 28.1 29.0 35.0 26.8 31.9 33.0 31.7 28.1 35.9

Salary $ 63,000 60,000 55,000 54,000 57,000 55,269 53,300 52,000 55,269 53.300 52,000 50,700 52,050 50,800 50,000 51,494 43,985 44,119 53,161 43,500 49,080 43,500 45,156 42,925 44,499

The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using the 25 data points in the table are shown below. ----------------------------------------------------------------------^ 2 0 = -92040 1 = 228 s = 3213 r = .66 r = .81 df = 23 t = 6.67 -----------------------------------------------------------------------

103) For the situation above, write the equation of the probabilistic model of interest. A) GMAT = 0 + 1 (SALARY) + B) GMAT = 0 + 1 (SALARY) C) Salary = 0 + 1 (GMAT) +

D) Salary = 0 + 1 (GMAT)

Objective: (11.7) Apply Simple Linear Regression

104) For the situation above, write the equation of the least squares line. A) GMAT = 228 - 92040 (SALARY) B) SALARY = -92040 + 228 (GMAT) C) GMAT = -92040 + 228 (SALARY) D) SALARY = 228 + 92040 (GMAT) Objective: (11.7) Apply Simple Linear Regression

105) For the situation above, give a practical interpretation of 0 = -92040. A) We estimate the base SALARY of graduates of a top business school to be -$92,040. B) We estimate SALARY to decrease $92,040 for every 1-point increase in GMAT. C) The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data. D) We expect to predict SALARY to within 2(92040) = $184,080 of its true value using GMAT in a straight-line model. Objective: (11.7) Apply Simple Linear Regression

106) For the situation above, give a practical interpretation of 1 = 228. A) We estimate SALARY to increase $228 for every 1-point increase in GMAT. B) The value has no practical interpretation since a GMAT of 228 is nonsensical and outside the range of the sample data. C) We expect to predict SALARY to within 2(228) = $456 of its true value using GMAT in a straight-line model. D) We estimate GMAT to increase 228 points for every $1 increase in SALARY. Objective: (11.7) Apply Simple Linear Regression

107) For the situation above, give a practical interpretation of s = 3213. A) We expect the predicted SALARY to deviate from actual SALARY by at least 2(3213) = $6,426 using GMAT in a straight-line model. B) We expect to predict SALARY to within 2(3213) = $6,426 of its true value using GMAT in a straight-line model. C) Our predicted value of SALARY will equal 2(3213) = $6,426 for any value of GMAT. D) We estimate SALARY to increase $3,213 for every 1-point increase in GMAT. Objective: (11.7) Apply Simple Linear Regression

108) For the situation above, give a practical interpretation of r2 = .66. A) We estimate SALARY to increase $.66 for every 1-point increase in GMAT. B) 66% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. C) We expect to predict SALARY to within 2( .66) of its true value using GMAT in a straight-line model. D) We can predict SALARY correctly 66% of the time using GMAT in a straight-line model. Objective: (11.7) Apply Simple Linear Regression

109) For the situation above, give a practical interpretation of r = .81. A) We estimate SALARY to increase 81% for every 1-point increase in GMAT. B) There appears to be a positive correlation between SALARY and GMAT. C) We can predict SALARY correctly 81% of the time using GMAT in a straight-line model. D) 81% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. Objective: (11.7) Apply Simple Linear Regression

110) Set up the null and alternative hypotheses for testing whether a positive linear relationship exists between SALARY and GMAT in the situation above. A) H0 : 1 = 0 vs. Ha : 1 0 B) H0 : 1 > 0 vs. Ha : 1 < 0 C) H0 : 1 = 228 vs. Ha : 1 > 228

D) H0 : 1 = 0 vs. Ha : 1 > 0

Objective: (11.7) Apply Simple Linear Regression

111) For the situation above, give a practical interpretation of t = 6.67. A) Only 6.67% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. B) There is evidence (at = .05) of at least a positive linear relationship between SALARY and GMAT. C) There is evidence (at = .05) to indicate that 1 = 0. D) We estimate SALARY to increase $6.67 for every 1-point increase in GMAT. Objective: (11.7) Apply Simple Linear Regression

112) A 95% prediction interval for SALARY when GMAT = 600 is ($37,915, $51,948). Interpret this interval for the situation above. A) We are 95% confident that the SALARY of a top business school graduate will fall between $37,915 and $51,984. B) We are 95% confident that the increase in SALARY for a 600-point increase in GMAT will fall between $37,915 and $51,984. C) We are 95% confident that the mean SALARY of all top business school graduates with GMATs of 600 will fall between $37,915 and $51,984. D) We are 95% confident that the SALARY of a top business school graduate with a GMAT of 600 will fall between $37,915 and $51,984. Objective: (11.7) Apply Simple Linear Regression

113) For the situation above, which of the following is not an assumption required for the simple linear regression analysis to be valid? A) The errors of predicting SALARY have a variance that is constant for any given value of GMAT. B) The errors of predicting SALARY are normally distributed. C) The errors of predicting SALARY have a mean of 0. D) SALARY is independent of GMAT. Objective: (11.7) Apply Simple Linear Regression

Answer Key Testname: SB14ECH11TEST

1) B 2) C 3) B 4) B 5) C 6)

8) 16) SSxx =

(3.642)2 14

= .948622 = .00118171 SSxy = x

0 slope: 3; y-intercept: 0

slope: .5; y-intercept: 1.5 9) 0 = - 1, 1 = 3

10) A 11) B 12) B 13) B 14) C 15)

xy = 295.54 -

(3.642)(1,134) = .538 14

x2 -

y n x n

1,134 = 81 14

3.642 = 14

18) a.

E(y) = 0 + 1 x ^

b. y = 0 + 1 x = 172.06 - .8195x c. We would expect approximately 172 grunts after feeding a warthog that was just born. However, since the value 0 is outside the range of the original data set, this estimate is highly unreliable. d. For each additional day, we estimate the number of grunts will decrease by .8195. 19) a. xi

.26014

1 = -.08365. For every 1 mile per hour increase in the maximum speed attained, we estimate the elapsed 0-to-60 acceleration time to decrease by .08365 second.

SSxy 1 = SS = xx

.538 = 455.27 .00118171 ^

0 = y - 1 x = 81 455.27(.26014) = -37.434

Totals b.

SSxy = 28 (18)(9) = -12.5; SSxx 4

= 102 -

The least squares

equation is y = -37.434 + 455.27x. SSxy 25 = 17) 1 = SSxx 10.5

0 slope: -2; y-intercept: 4

2.3810

182 = 21; 4

-12.5 21

-.5952; x = y=

18 = 4.5; 4

9 = 2.25; 4 ^

0 = y - 1 x = 31 2.3810(2.75) = 24.4523

0 = 2.25 + .5952(4.5) = 4.9284

The least squares prediction equation

c. y = 4.9284 + .5952x

is y = 24.4523 + 2.3810x

2 5 3 8 xi = 18

Answer Key Testname: SB14ECH11TEST

20) a.

33) D 34) Assumption 1: The mean of the probability distribution of is 0.

39) a. s2 = 0.023; b. 0.303 40) B 41) D 42) a. SSE = 1650.36; s2

1.1053 d. The line appears to fit the data well. 21) C 22) D 23) C 24) C 25) C 26) B 27) D 28) C 29) C 30) A 31) A 32) The assumptions necessary are:

1. The random errors are normally distributed. 2. The random errors are independent of one another. 3. The mean of the random errors is 0. 4. The variance of the random errors, 2 , is constant for all levels of the independent variable x.

SSE = SSyy - 1 SSxy = 22 - .01087(236.5) = 19.4286 SSE 19.4286 = s2 = n- 2 7 -2 = 3.8857 s= s2 = 3.8857 =

values, y. 43) D 44) B ^

Assumption 3: The probability distribution of is normal.

45) SSE = SSyy - 1 SSxy

SSxy =

Assumption 4: The values of associated with any two observed values of y are independent. 35) A

xy -

1.971 47) D 48) a.

= 295.54 (3.642)(1,134) = .538 14

SSyy =

36) SSE = SSyy - 1 SSxy = 100 - .8(60) = 52; s2 =

= .01087

= 235.77; s = 15.35 b. We expect most of the observed y values to lie within 30.70 units of their respective least squares predicted

Assumption 2: The variance of the probability distribution of is constant for all settings of the independent variable, x. b. y increases as x increases in an approximately linear pattern. c. 1 1.7368; 0

SSxy ^ 236.5 = 46) 1 = SSxx 21,752

y2 -

= 93,110 -

SSE 52 = n - 2 30 - 2

(1,134)2 = 14

b. y = 10.6187 = .8515x

1,256

1.857

SSE = 1,256 455.27(.538) = 1,011.06

652 = 37) SSyy = 950 25 ^

781, SSE = SSyy - 1 SSxy = 781 - .2(3000)

SSE 1011.06 s2 = = n- 2 14 - 2

= 181; SSE 181 = s2 = n - 2 25 - 2

= 84.26 s = s2 = 9.179

7.87

SSE .678 = 38) a. s2 = n - 2 22 - 2 b. s = s2 .0339 .1841 c. 2s = 2(.1841) = .3682

51)

1 ± t.05 s ^ = 49 ± 1 4 = 49 ± .96 1.771 55

52)

84.26 =

We expect most of the sample number of games won, y, to fall within 2s 2(9.179) 18.358 of their least squares predicted values.

.0339

c. SSE = 1.35677, s2 = .4523, and s = .6725 d. 100% 49) C 50) C

1 ± t.025 s ^ = 49 ± 1 4 2.160 = 49 ± 55 1.17

Answer Key Testname: SB14ECH11TEST

53) a.

t = 6 > t.05 =

1.671, reject H0 ; we concluded that x and y are positively linearly related. b. (0.606, 1.074); We can be 90% confident that the true slope is between 0.606 and 1.074. 54) D 55) C 56) A 57) A 58) C 59) C 60) D 61) C 62) C 63) A

64) To determine if time spent taking telephone orders during the day is positively linearly related with the number of telephone orders received during the day, we test:

= .948622 = .00118 t=

The rejection region requires = .05 in the upper tail of the t distribution with df = n - 2 = 14 - 2 = 12. From a t table, t.05 = 1.782. The

The test statistic is given on the printout as t = 9.96. The p-value for the desired test is p = .0000/2 = .0000 (divided in half because a one-tailed test is desired.)

rejection region is t > 1.782. Since the observed value of the test statistic does not fall in the rejection region (t = 1.704 1.782), H0 cannot be rejected. There is insufficient evidence to indicate that team wins is positively linearly related with team batting average.

Since = .01 > p-value 0, H0 is rejected. There is sufficient evidence to indicate that the time spent taking telephone orders during the day is positively linearly related with the number of telephone orders received during the day. 65) We test: H0 : 1 = 0

The test statistic is t = ^

1- 0 . s/ SSxx x

66)

SSxy 236.5 1 = SS = 21,752 xx

= .01087 We test:

H0 : 1 = 0 Ha : 1 0 The test statistic is t = ^

1- 0 = s/ SSxx .01087 - 0 = .814 1.97/ 21,752 The rejection region requires /2 = .05/2 = .025 in both tails of the t distribution with n - 2 = 7 - 2 = 5 df. From a t table, t.025 = 2.571. The rejection region is t > 2.571 or t < -2.571. Since the observed value of the test statistic does not fall in the rejection region (t = .814 2.571), H0 cannot be rejected. There is insufficient evidence to indicate that the gestation period and the length of life of a horse are linearly related at = .05.

Ha : 1 > 0

x2 -

455.27 - 0 = 9.18/ .00118

1.704

H0 : 1 = 0 Ha : 1 > 0

SSxx =

(3.642)2 14

Answer Key Testname: SB14ECH11TEST

67) a.

68) a.

The scattergram does suggest that y is positively linearly related to x. b. SSxy = 45.1 -

(21)(9.9) = 3.52; SSxx 5

(21)2 = 99 = 10.8; 5 ^

3.52 1 = 10.8

.3259;

s = .1165 The test statistic .3259 is t = .1165/ 10.8 9.19. Based on 3 degrees of freedom, the rejection region is t > 2.353. Since the test statistic falls in the rejection region, we reject the null hypothesis and conclude that y is positively linearly related to x.

71) B 72) A 73) C 74) There is a weak negative correlation between years of teaching experience and success in team-teaching mathematics classes. 75) A SSxy = 76) r = SSxx · SSyy 25 = .729 (10.5)(112)

SSxy = 10,232,660; SSxx 1.833 x 1010;

77) r =.792; There is a positive linear correlation between age and number of grunts. 78) SSxy = 45.1 -

=.0005583; x = 171,140; ^

y = 51.6; 0 = 51.6 - .0005583(171,140) = -43.94

(21)(9.9) = 3.52; SSxx 5

y = 43.94 + .0005583x

= 99 -

(21)2 = 10.8; 5

SSyy = 20.79 -

c. The test statistic is t = .0005583 22.58/ 1.833 x 1010

= 1.188; r = 3.52 10.8 · 1.188

3.35. Based on 8 degrees of freedom, the rejection region is t > 1.860. Since the test statistic falls in the rejection region, we reject the null hypothesis and conclude that the number of days on the market, y, is positively linearly related to the asking price, x. 69) A 70) B

(9.9)2 5 .9827;

There is a strong linear relationship between x and y. 79) D 80) a. H0 : 1 > 0.

b. There is a weak negative correlation between years of teaching experience and success in team-teaching mathematics classes. c. No; t = -4.796 81) A

82) r2 = .627; 62.7% of the variation in number of grunts can be explained by using age in a linear model. 83) C SSyy - SSE = 84) r2 = SSyy 176.5171 - 12.435 = 176.5171 .9296 92.96% of the variation in the sample monthly sales values can be explained by using months on the job in a linear model. SSyy - SSE = 85) r2 = SSyy

112 - 52.4762 = 112 .53146 86) SSyy = 1.188; SSE = .040741; r2 = 1 .040741 .9657; 1.188

96.57% of the sample variation in y values can be attributed to the linear relationship between x and y. 87) C 88) B 89) C 90) D 91) D 92) A

Answer Key Testname: SB14ECH11TEST

93) For x = 5, y = -.25 + 1.315(5) = 6.325

101) The prediction interval is of the form:

The confidence interval is of the form:

y ± t /2s

y ± t /2s 1 (x - x)2 + n SSxx Confidence coefficient .90 = 1 = 1 - .90 = .10. /2 = .10/2 = .05. From a t table, t.05 = 2.015 with n - 2 = 7 - 2 = 5 df. The confidence interval is: 6.325 ± 2.015(1.577) 1 (5 - 5.8571)2 + 7 94.8571 6.325 ± 1.233 (5.092, 7.558) 94) a. The regression

102) a.

1 (x - x)2 + n SSxx

y = 18.89 + .01087(300) = 22.151 Confidence coefficient .95 = 1 = 1 - .95 = .05. /2 = .05/2 = .025. From a t table, t.025 = 2.571 with

b. y = 2.7273 + .8182x ^

c. For x = 1, y = 2.7273 + .8182(1) = 3.5455. For 3 degrees of freedom, t.005 =

n - 2 = 7 - 2 = 5 df. The 95% prediction interval is: 22.151 ± 2.571(2) 1+

5.841.

s = .8528; x = 1.8; SSxx = 30.8

1 (300 - 332)2 + 7 21,752

The interval is 3.5455 ± 5.841(.8528) 1 (1 - 1.8)2 + 5 30.8

22.151 ± 5.609 (16.542, 27.760)

line is y = -43.94 + .0005583x, so for x = 150,000 we have

3.5455 ± 2.3405. d. The interval is 3.5455 ± 5.841(.8528) 1 (1 - 1.8)2 + 5 30.8

y = -43.94 + .0005583(150,000) = 39.805. For df = 8, t.05 =

3.5455 ± 5.5037. 103) C 104) B 105) C 106) A 107) B 108) B 109) B 110) D 111) B 112) D 113) D

1.860.

s = 22.58236; x = 171,140; SSxx = 1.8329 x 1010

The interval is 39.805 ± 14.813. b. The interval is 39.805 ± 44.539. 95) A 96) B 97) A 98) D 99) B 100) A

McClave Statistics for Business and Economics 14e Chapter 12 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 1) Probabilistic models that include more than one dependent variable are called multiple regression models. A) True B) False Objective: (12.1) Understand Multiple Regression Models

2) A term that contains the value of a quantitative variable raised to the second power is called a higher-order term. A) True B) False Objective: (12.1) Understand Multiple Regression Models

3) A qualitative variable whose outcomes are assigned numerical values is called a coded variable. A) True B) False Objective: (12.1) Understand Multiple Regression Models

4) For a multiple regression model, we assume that the mean of the probability distribution of the random error is 0. A) True B) False Objective: (12.1) Understand Multiple Regression Models

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 5) Why is the random error term added to a multiple regression model? Objective: (12.1) Understand Multiple Regression Models

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 6) A first-order model may include terms for both quantitative and qualitative independent variables. A) True B) False Objective: (12.2) Write First-Order Model

7) A first-order model does not contain any higher-order terms. A) True B) False Objective: (12.2) Write First-Order Model

8) The method of fitting first-order models is the same as that of fitting the simple straight-line model, i.e. the method of least squares. A) True B) False Objective: (12.2) Write First-Order Model

9) In the first-order model E(y) = 0 + 1 x 1 + 2 x2 + 3 x 3 , 2 represents the slope of the line relating y to x 2 when 1 and 3 are both held fixed. A) True

B) False

Objective: (12.2) Write First-Order Model

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 10) The printout shows the results of a first-order regression analysis relating the sales price y of a product to the time in hours x 1 and the cost of raw materials x 2 needed to make the product.

a. b. c.

What is the least squares prediction equation? Identify the SSE from the printout. Find the estimator of 2 for the model.

Objective: (12.2) Write First-Order Model

11) A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.

The professor would like to use the data to find a first-order model that he might use to predict a student's grade on the first test using that student's grades on the first three quizzes. a. b. c.

Identify the dependent and independent variables for the model. What is the least squares prediction equation? Find the SSE and the estimator of 2 for the model.

Objective: (12.2) Write First-Order Model

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 12) Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y = Retail PRICE (measured in dollars) x 1 = Microprocessor SPEED (measured in megahertz) (Values in sample range from 10 to 40) x 2 = CHIP size (measured in computer processing units) (Values in sample range from 286 to 486) A first-order regression model was fit to the data. Part of the printout follows: Parameter Estimates PARAMETER STANDARD T FOR 0: VARIABLE DF ESTIMATE ERROR PARAMETER = 0 PROB > |T| INTERCEPT 1 SPEED 1 CHIP 1

-373.526392 104.838940 3.571850

1258.1243396 -0.297 22.36298195 4.688 3.89422935 0.917

0.7676 0.0001 0.3629

Identify and interpret the estimate for the SPEED -coefficient,

1 = 105; For every 1-megahertz increase in SPEED, we estimate PRICE (y) to increase $105, holding CHIP fixed.

1 = 3.57; For every $1 increase in PRICE, we estimate SPPED to increase by about 4 megahertz, holding CHIP fixed.

1 = 105; For every $1 increase in PRICE, we estimate SPEED to increase 105 megahertz, holding CHIP fixed.

1 = 3.57; For every 1-megahertz increase in SPEED, we estimate PRICE to increase $3,57, holding CHIP fixed.

Objective: (12.2) Find and Interpret Sample Estimates for

Parameters

13) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Gmat Tuition

Coefficient Std Error T P VIF -203.402 -3.94 51.6573 0.0002 0.0 0.39412 0.09039 4.36 0.0000 2.0 0.92012 0.17875 5.15 0.0000 2.0

R-Squared Adjusted R-Squared

0.6857 Resid. Mean Square (MSE) 0.6769 Standard Deviation

427.511 20.6763

Interpret the coefficient for the tuition variable shown on the printout. A) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $394.12, holding the GMAT score constant B) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $920.12, holding the GMAT score constant C) For every $1000 increase in the average starting salary, we estimate that the tuition charged by the MBA program will increase by $920.12. D) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will decrease by $203,402, holding the GMAT score constant. Objective: (12.2) Find and Interpret Sample Estimates for

Parameters

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 14) Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y = Retail PRICE (measured in dollars) x 1 = Microprocessor SPEED (measured in megahertz) (Values in sample range from 10 to 40) x 2 = CHIP size (measured in computer processing units) (Values in sample range from 286 to 486) A first-order regression model. was fit to the data. Part of the printout follows: Parameter Estimates

VARIABLE DF

PARAMETER STANDARD T FOR 0: ESTIMATE ERROR PARAMETER = 0 PROB > |T|

INTERCEPT 1 SPEED 1 CHIP 1

-373.526392 104.838940 3.571850

1258.1243396 -0.297 22.36298195 4.688 3.89422935 0.917

0.7676 0.0001 0.3629

Identify and interpret the estimate of 2 . Objective: (12.2) Find and Interpret Sample Estimates for

Parameters

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 15) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to data. A 95% confidence interval for 1 is (.06, .22). Interpret this result. A) We are 95% confident that the mean GPA of all CS freshmen after three semesters falls between .06 and .22. B) 95% of the GPAs fall within .06 to .22 of their true values. C) We are 95% confident that a CS freshman's GPA increases by an amount between .06 and .22 for every 1-point increase in average HS math grade, holding x 2 - x 5 constant.

D) We are 95% confident that a CS freshman's HS math grade increases by an amount between .06 and .22 for every 1-point increase in GPA, holding x 2 - x 5 constant. Objective: (12.2) Construct Confidence Interval for Parameter Coefficient

16) In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x 1 ) and the number of checks cashed per day (x 2 ). Data collected for n = 20 working days were used to fit the model: E(y) = 0 + 1 x 1 + 2 x 2 A partial printout for the analysis follows: Parameter Estimates

VARIABLE

PARAMETER ESTIMATE

INTERCEPT X1 X2

1 1 1

114.420972 -0.007102 0.037290

STANDARD ERROR

T FOR 0: PARAMETER = 0

PROB > |T|

18.6848744 0.00171375 0.02043937

6.124 -4.144 1.824

0.0001 0.0007 0.0857

Calculate a 95% confidence interval for 1 . A) -4.144 ± .0007 B) -.007 ± .0036

C) -.007 ± .0017

Objective: (12.2) Construct Confidence Interval for Parameter Coefficient

D) -.007 ± .0007

17) During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x 1 ), Test 2 score (x 2 ), and Test3 score (x 3 ). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y) = 1 + 1 x 1 + 2 x 2 + 3x 3 The first-order model was fit to the data for each of 12 units sampled from the production line. The results are summarized in the printout. _____________________________________________________________________ SOURCE

F VALUE

PROB > F

MODEL ERROR TOTAL

3 8 12

151417 22231 173648

50472 2779

18.16

.0075

ROOT MSE DEP MEAN

52.72 645.8

R-SQUARE ADJ R-SQ

0.872 0.824

VARIABLE

PARAMETER ESTIMATE

STANDARD ERROR

T FOR 0: PARAMETER = 0

PROB > |T|

INTERCEPT X1(TEST1) X2(TEST2) X3(TEST3)

11.98 0.2745 0.3762 0.3265

80.50 0.1111 0.0986 0.0808

0.15 2.47 3.82 4.04

0.885 0.039 0.005 0.004

Compute a 95% confidence interval for 3 . A) .33 ± .08 B) .33 ± 4.04

C) .33 ± 105

D) .33 ± .19

Objective: (12.2) Construct Confidence Interval for Parameter Coefficient

Answer the question True or False. 18) It is safe to conduct t-tests on the individual parameters in a first-order linear model in order to determine which independent variables are useful for predicting y and which are not. A) True B) False Objective: (12.2) Perform Hypothesis Test for Parameter Coefficient

Solve the problem. 19) During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x 1 ), Test 2 score (x 2 ), and Test3 score (x 3 ). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y) = 1 + 1 x1 + 2 x 2 + 3x 3 The first-order model was fit to the data for each of 12 units sampled from the production line. The results are summarized in the printout. _____________________________________________________________________ SOURCE

F VALUE

PROB > F

MODEL ERROR TOTAL

3 8 12

151417 22231 173648

50472 2779

18.16

.0075

ROOT MSE DEP MEAN

52.72 645.8

R-SQUARE ADJ R-SQ

0.872 0.824

VARIABLE

PARAMETER ESTIMATE

STANDARD ERROR

T FOR 0: PARAMETER = 0

PROB > |T|

INTERCEPT X1(TEST1) X2(TEST2) X3(TEST3)

11.98 0.2745 0.3762 0.3265

80.50 0.1111 0.0986 0.0808

0.15 2.47 3.82 4.04

0.885 0.039 0.005 0.004

Suppose the 95% confidence interval for 3 is (.15, .47). Which of the following statements is incorrect? A) We are 95% confident that the increase in Test4 score for every 1-point increase in Test3 score falls between .15 and .47, holding Test1 and Test2 fixed. B) We are 95% confident that the Test3 is a useful linear predictor of Test4 score, holding Test1 and Test2 fixed. C) We are 95% confident that the estimated slope for the Test4-Test3 line falls between .15 and .47 holding Test1 and Test2 fixed. D) At = .05, there is insufficient evidence to reject H0 : 3 = 0 in favor of Ha : 3 0. Objective: (12.2) Perform Hypothesis Test for Parameter Coefficient

20) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Gmat Tuition

Coefficient Std Error T P VIF -203.402 -3.94 51.6573 0.0002 0.0 0.39412 0.09039 4.36 0.0000 2.0 0.92012 0.17875 5.15 0.0000 2.0

R-Squared Adjusted R-Squared

0.6857 Resid. Mean Square (MSE) 0.6769 Standard Deviation

427.511 20.6763

Identify the test statistic that should be used to test to determine if the amount of tuition charged by a program is a useful predictor of the average starting salary of the graduates of the program. A) t = 5.15 B) t = -3.94 C) t = 4.36 D) t = 20.67 Objective: (12.2) Perform Hypothesis Test for Parameter Coefficient

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 21) In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x 1 ) and the number of checks cashed per day (x 2 ). Data collected for n = 20 working days were used to fit the model: E(y) = 0 + 1 x 1 + 2 x 2 A printout for the analysis follows: _____________________________________________________________________ Analysis of Variance SOURCE

F VALUE

PROB > F

MODEL ERROR C TOTAL

2 17 19

7089.06512 4541.72142 11630.78654

3544.53256 267.16008

13.267

0.0003

16.34503 93.92682 17.40188

R-SQUARE ADJ R-SQ

0.6095 0.5636

ROOT MSE DEP MEAN C.V.

Parameter Estimates

VARIABLE

PARAMETER ESTIMATE

INTERCEPT X1 X2

1 1 1

114.420972 -0.007102 0.037290

STANDARD ERROR

T FOR 0: PARAMETER = 0

PROB > |T|

18.68485744 0.00171375 0.02043937

6.124 -4.144 1.824

0.0001 0.0007 0.0857

OBS 1

Actual Value

Predict Value

Residual

Lower 95% CL Predict

Upper 95% CL Predict

7781 644

74.707

83.175

-8.468

47.224

119.126

Test to determine if there is a positive linear relationship between the number of man-hours worked, y, and the number of checks cashed per day, x 2 . Use = .05. Objective: (12.2) Perform Hypothesis Test for Parameter Coefficient

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 22) The value of R 2 is only useful when the number of data points is substantially larger than the number of parameters in the model. A) True

B) False

Objective: (12.3) Find and Interpret Multiple Coefficient of Determination

Solve the problem. 23) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to data with R 2 = 0.211. What is the correct interpretation of R2 , the coefficient of determination for the model? A) Approximately 79% of the sample variation in GPAs can be explained by the first-order model. B) We are 79% confident that the model is useful for predicting y. C) Approximately 21% of the sample variation in GPAs can be explained by the first-order model. D) We expect to predict GPA to within approximately .21 of its true value. Objective: (12.3) Find and Interpret Multiple Coefficient of Determination

24) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Gmat Tuition

Coefficient Std Error T P VIF -203.402 -3.94 51.6573 0.0002 0.0 0.39412 0.09039 4.36 0.0000 2.0 0.92012 0.17875 5.15 0.0000 2.0

R-Squared Adjusted R-Squared Source Regression Residual Total

DF 2

0.6857 Resid. Mean Square (MSE) 0.6769 Standard Deviation SS MS 67140.9 33570.5 78.53 72 30780.8 427.5 74 97921.7

F 0.0000

427.511 20.6763 P

Interpret the coefficient of determination value shown in the printout. A) At = 0.05, there is insufficient evidence to indicate that something in the regression model is useful for predicting the average starting salary of the graduates of an MBA program. B) We expect most of the average starting salaries to fall within $20,676 of their least squares predicted values. C) We can explain 68.57% of the variation in the average starting salaries around their mean using the model that includes the average GMAT score and the tuition for the MBA program. D) We expect most of the average starting salaries to fall within $41,353 of their least squares predicted values. Objective: (12.3) Find and Interpret Multiple Coefficient of Determination

Answer the question True or False. 25) The rejection of the null hypothesis in a global F-test means that the model is the best model for providing reliable estimates and predictions. A) True B) False Objective: (12.3) Test if Model is Useful for Predicting y

Solve the problem. 26) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to data. Give the null hypothesis for testing the overall adequacy of the model. A) H0 : 1 = 2 = 3 = 4 = 5 = 0 B) H0 : 1 = 0

C) H0 : 0 + 1 x 1 + 2 x 2 + 3 x 3 + 4x 4 + 5 x 5 = 0

D) H0 : 0 = 1 = 2 = 3 = 4 = 5 = 0

Objective: (12.3) Test if Model is Useful for Predicting y

27) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to data with the following results: _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL 5 28.64 5.73 11.69 .0001 ERROR 218 106.82 0.49 TOTAL 223 135.46 ROOT MSE DEP MEAN

0.700 4.635

R-SQUARE 0.211 ADJ R-SQ 0.193

VARIABLE

PARAMETER ESTIMATE

STANDARD ERROR

T FOR 0: PARAMETER = 0

PROB > |T|

INTERCEPT X1 (HSM) X2 (HSS) X3 (HSE) X4 (SATM) X5 (SATV)

2.327 0.146 0.036 0.055 0.00094 -0.00041

0.039 0.037 0.038 0.040 0.00068 0.00059

5.817 3.718 0.950 1.397 1.376 -0.689

0.0001 0.0003 0.3432 0.1637 0.1702 0.4915

Interpret the value under the column heading PROB > F. A) There is insufficient evidence (at = .01) to conclude that the first-order model is statistically useful for predicting GPA. B) There is sufficient evidence (at = .01) to conclude that the first-order model is statistically useful for predicting GPA. C) Accept H0 (at = .01); at least one of the -coefficients in the first-order model is equal to 0.

D) Over 99% of the variation in GPAs can be explained by the model. Objective: (12.3) Test if Model is Useful for Predicting y

28) During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x 1 ), Test 2 score (x 2 ), and Test3 score (x 3 ). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y) = 1 + 1 x 1 + 2 x 2 + 3x 3 The global F statistic is used to test the null hypothesis, H0 : 1 = 2 = A) The first three test scores are reliable predictors of Test4 score. B) The first three test scores are poor predictors of Test4 score. C) The model is not statistically useful for predicting Test4 score. D) The model is statistically useful for predicting Test4 score. Objective: (12.3) Test if Model is Useful for Predicting y

3 = 0. Describe this hypothesis in words.

29) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Gmat Tuition Source Regression Residual Total

Coefficient Std Error T P VIF -203.402 -3.94 51.6573 0.0002 0.0 0.39412 0.09039 4.36 0.0000 2.0 0.92012 0.17875 5.15 0.0000 2.0 DF 2

SS MS 67140.9 33570.5 78.53 72 30780.8 427.5 74 97921.7

F 0.0000

Interpret the p-value for the global f-test shown on the printout. A) At = 0.05, there is sufficient evidence to indicate that the average GMAT score of the MBA program's students is useful for predicting the average starting salary of the graduates of an MBA program. B) At = 0.05, there is insufficient evidence to indicate that the average GMAT score of the MBA program's students is useful for predicting the average starting salary of the graduates of an MBA program. C) At = 0.05, there is insufficient evidence to indicate that something in the regression model is useful for predicting the average starting salary of the graduates of an MBA program. D) At = 0.05, there is sufficient evidence to indicate that something in the regression model is useful for predicting the average starting salary of the graduates of an MBA program. Objective: (12.3) Test if Model is Useful for Predicting y

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 30) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to the data with the following results: _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL ERROR TOTAL

5 218 223

ROOT MSE DEP MEAN

28.64 106.82 135.46 0.700 4.635

5.73 0.49

11.69

R-SQUARE ADJ R-SQ

.0001

0.211 0.193

VARIABLE

PARAMETER ESTIMATE

STANDARD ERROR

T FOR 0: PARAMETER = 0

PROB > |T|

INTERCEPT X1 (HSM) X2 (HSS) X3 (HSE) X4 (SATM) X5 (SATV)

2.327 0.146 0.036 0.055 0.00094 -0.00041

0.039 0.037 0.038 0.040 0.00068 0.0059

5.817 3.718 0.950 1.397 1.376 -0.689

0.0001 0.0003 0.3432 0.1637 0.1702 0.4915

Test to determine if the model is adequate for predicting GPA. Use Objective: (12.3) Test if Model is Useful for Predicting y

= .01.

31) As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): x 1 = average high school grade in mathematics (HSM) x 2 = average high school grade in science (HSS) x 3 = average high school grade in English (HSE) x 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) 2 A first-order model was fit to data with R a = .193. 2 Interpret the value of the adjusted coefficient of determination R a . Objective: (12.3) Test if Model is Useful for Predicting y

32) In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x 1 ) and the number of checks cashed per day (x 2 ). Data collected for n = 20 working days were used to fit the model: E(y) = 0 + 1 x 1 + 2 x 2 A partial printout for the analysis follows: ___________________________________________________________________________ Analysis of Variance SOURCE

F VALUE

PROB > F

MODEL ERROR C TOTAL

2 17 19

7089.06512 4541.72142 11630.78654

3544.53256 267.16008

13.267

0.0003

16.34503 93.92682 17.40188

R-SQUARE ADJ R-SQ

0.6095 0.5636

ROOT MSE DEP MEAN C.V.

Test to determine if the model is adequate for predicting the number of man-hours worked. Use Objective: (12.3) Test if Model is Useful for Predicting y

= .025.

33) Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y = Retail PRICE (measured in dollars) x 1 = Microprocessor SPEED (measured in megahertz) (Values in sample range from 10 to 40) x 2 = CHIP size (measured in computer processing units) (Values in sample range from 286 to 486) A first-order regression model was fit to the data. Part of the printout follows: _____________________________________________________________________ Analysis of Variance SOURCE DF SS MS F VALUE PROB > F MODEL ERROR C TOTAL

2 57 59

ROOT MSE DEP MEAN C.V.

34593103.008 51840202.926 86432305.933

17296051.504 909477.24431

19.018

953.66516 3197.96667 29.82099

R-SQUARE ADJ R-SQ

0.4002 0.3792

0.0001

Test to determine if the model is adequate for predicting the price of a computer. Use Objective: (12.3) Test if Model is Useful for Predicting y

= .01.

34) The table below shows data for n = 20 observations.

a. b. c. d. e.

Use a first-order regression model to find a least squares prediction equation for the model. Find a 95% confidence interval for the coefficient of x 1 in your model. Interpret the result. Find a 95% confidence interval for the coefficient of x 2 in your model. Interpret the result. Find R2 and Ra2 and interpret these values.

Test the null hypothesis H0 : 1 = 2 = 0 against the alternative hypothesis Ha : at least one i 0. Use Interpret the result. Objective: (12.3) Test if Model is Useful for Predicting y

= .05.

35) A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.

The professor fit a first-order model to the data that he intends to use to predict a student’s grade on the first test using that student’s grades on the first three quizzes. Test the null hypothesis H0 : 1 = Interpret the result.

2 = 3 = 0 against the alternative hypothesis Ha : at least one i 0. Use

= .05.

Objective: (12.3) Test if Model is Useful for Predicting y

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 36) In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x 1 ) and the number of checks cashed per day (x 2 ). Data collected for n = 20 working days were used to fit the model: E(y) = 0 + 1 x 1 + 2 x 2 A partial printout for the analysis follows:

OBS

Actual Value

7781

644

74.707

Predict Value 83.175

Residual

Lower 95% CL Predict

Upper 95% CL Predict

-8.468

47.224

119.126

Interpret the 95% prediction interval for y shown on the printout. A) We are 95% confident that the mean number of man-hours worked per day falls between 47.224 and 119.126 for all days in which 7,781 pieces of mail are processed and 644 checks are cashed. B) We are 95% confident that between 47.224 and 119.126 man-hours will be worked during a single day in which 7,781 pieces of mail are processed and 644 checks are cashed. C) We expect to predict number of man-hours worked per day to within an amount between 47.224 and 119.126 of the true value. D) We are 95% confident that the number of man-hours worked per day falls between 47.224 and 119.126. Objective: (12.4) Find and Interpret Prediction Interval

37) During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x 1 ), Test 2 score (x 2 ), and Test3 score (x 3 ). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y) = 1 + 1 x 1 + 2 x 2 + 3x 3 The first-order model was fit to the data for each of 12 units sampled from the production line. A 95% prediction interval for Test4 score of a product with Test1 = 590, Test2 = 750, and Test3 = 710 is (583, 793). Interpret this result. A) We are 95% confident that the mean Test4 score of all manufactured products falls between 583 and 793 points. B) We are 95% confident that a product's Test4 score increases by an amount between 583 and 793 points for every 1 point increase in Test1 score, holding Test 2 and Test 3 score constant. C) We are 95% confident that a product's Test4 score will fall between 583 and 793 points when the first three scores are 590, 750, and 710, respectively. D) Since 0 is outside the interval, there is evidence of a linear relationship between Test4 score and any of the other test scores. Objective: (12.4) Find and Interpret Prediction Interval

38) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Gmat Tuition

Coefficient Std Error T P VIF -203.402 -3.94 51.6573 0.0002 0.0 0.39412 0.09039 4.36 0.0000 2.0 0.92012 0.17875 5.15 0.0000 2.0

The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate Y for a single MBA program? A) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and $173,16,30. B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30. C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640. D) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640. Objective: (12.4) Find and Interpret Prediction Interval

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 39) Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y = Retail PRICE (measured in dollars) x1 = Microprocessor SPEED (measured in megahertz) (Values in sample range from 10 to 40) x2 = CHIP size (measured in computer processing units) (Values in sample range from 286 to 486) A first-order regression model was fit to the data. Part of the printout follows:

OBS SPEED CHIP 1

386

Dep Var Predict Std Err Lower 95% Upper 95% PRICE Value Predict Predict Predict Residual 5099.0 4464.9 260.768

3942.7

4987.1

634.1

Interpret the 95% prediction interval for y when x 1 = 33 and x 2 = 386. Objective: (12.4) Find and Interpret Prediction Interval

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 40) The confidence interval for the mean E(y) is narrower that the prediction interval for y. A) True B) False Objective: (12.4) Find and Interpret Confidence Interval

Solve the problem. 41) Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y = Retail PRICE (measured in dollars) x 1 = Microprocessor SPEED (measured in megahertz) (Values in sample range from 10 to 40) x 2 = CHIP size (measured in computer processing units) (Values in sample range from 286 to 486) a first-order regression model was fit to the data. Part of the printout follows:

OBS SPEED CHIP 1

286

Dep Var Predict Std Err Lower 95% Upper 95% PRICE Value Predict Predict Predict Residual 5099.0 4464.9 260.768

3942.7

4987.1

634.1

Interpret the interval given in the printout. A) We are 95% confident that the price of a single hard drive with 33 megahertz speed and 386 CPU falls between $3,943 and $4,987. B) We are 95% confident that the average price of all hard drives falls between $3,943 and $4,987. C) We are 95% confident that the average price of all hard drives with 33 megahertz speed and 386 CPU falls between $3,943 and $4,987. D) We are 95% confident that the price of a single hard drive falls between $3,943 and $4,987. Objective: (12.4) Find and Interpret Confidence Interval

42) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Gmat Tuition

Coefficient Std Error T P VIF -203.402 -3.94 51.6573 0.0002 0.0 0.39412 0.09039 4.36 0.0000 2.0 0.92012 0.17875 5.15 0.0000 2.0

The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all MBA programs? A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640. B) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640. C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and $173,16,30. D) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30. Objective: (12.4) Find and Interpret Confidence Interval

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 43) The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below.

Fit the model E(y) = 0 + 1 x 1 + 2 x 2 to the data, letting y represent the number of bottles of water sold, x 1 the temperature, and x 2 the number of people at the park. b. Find the 95% confidence interval for the mean number of bottles of water sold when the temperature is 84°F and there are 2700 people at the park. c. Find the 95% prediction interval for the number of bottles of water sold when the temperature is 84°F and there are 2700 people at the park. Objective: (12.4) Find and Interpret Confidence Interval

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 44) Consider the interaction model E(y) = 7 + 3x 1 - 4x2 + 5x 1 x 2 . Find the slope of the line relating E(y) and x 1 when x 2 = 2.

A) 16

B) 13

C) 1

D) 10

Objective: (12.5) Write Interaction Model

45) Consider the interaction model E(y) = 3.6+ 1.2x 1 + 2.4x2 + .2x 1 x 2 . Determine the change in E(y) when x 1 is changed from 6 to 7 and x 2 is held fixed at 3.

A) 10.8

B) 4.2

C) 1.8

Objective: (12.5) Write Interaction Model

D) 11.4

46) We decide to conduct a multiple regression analysis to predict the attendance at a major league baseball game. We use the size of the stadium as a quantitative independent variable and the type of game as a qualitative variable (with two levels - day game or night game). We hypothesize the following model: E(y) = 0 + 1 x1 + 2 x2 + 3 x3 Where x1 = size of the stadium x2 = 1 if a day game, 0 if a night game A plot of the y-x1 relationship would show:

A) Two non-parallel lines C) Two non-parallel curves

B) Two parallel curves D) Two parallel lines

Objective: (12.5) Write Interaction Model

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 47) A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables: x 1 = high school GPA x 2 = SAT score The admissions officer believes the relationship between college GPA and high school GPA is linear and the relationship between SAT score and college GPA is linear. She also believes that the relationship between college GPA and high school GPA depends on the student's SAT score. Write the regression model she should fit. Objective: (12.5) Write Interaction Model

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 48) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Tuition GMAT TxG

Coefficient Std Error T 165.406 4.16 -687.851 2.19724 -11.3197 -5.15 -0.96727 -3.79 0.25535 0.01850 0.00331 5.58

R-Squared Adjusted R-Squared Source Regression Residual Total

DF 3

Cases Included 75

0.0001 0.0000 0.0003 0.0000

0.7816 Resid. Mean Square (MSE) 0.7723 Standard Deviation SS MS 76523.8 25510.9 84.68 71 21388.8 301.3 74 97921.7

F 0.0000

301.251 17.3566 P

Missing Cases 0

The global-f test statistic is shown on the printout to be the value F = 84.68. Interpret this value. A) There is sufficient evidence, at = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs. B) There is sufficient evidence, at = 0.05, to indicate that the interaction between average tuition and average GMAT score is a useful predictor of the average starting salary of graduates of MBA programs. C) There is insufficient evidence, at = 0.05, to indicate that the interaction between average tuition and average GMAT score is a useful predictor of the average starting salary of graduates of MBA programs. D) There is insufficient evidence, at = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs. Objective: (12.5) Test if Model is Useful for Predicting y

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 49) Consider the partial printout for an interaction regression analysis of the relationship between a dependent variable y and two independent variables x 1 and x 2 .

a. b. c. d.

Write the prediction equation for the interaction model. Test the overall utility of the interaction model using the global F-test at Test the hypothesis (at = .05) that x 1 and x 2 interact positively.

= .05.

Estimate the change in y for each additional 1-unit increase in x 1 when x2 = 6.

Objective: (12.5) Test if Model is Useful for Predicting y

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 50) The independent variables x 1 and x 2 interact when the effect on E(y) of a change in x 1 depends on x 2 . A) True

B) False

Objective: (12.5) Test for Interaction Between Two Variables

51) In an interaction model, the relationship between E(y) and x 1 is linear for each fixed value of x 2 but the slopes of the lines relating E(y) and x 1 may be different for two different fixed values of x 2 .

A) True

B) False

Objective: (12.5) Test for Interaction Between Two Variables

52) Once interaction has been established between x 1 and x 2 , the first-order terms for x 1 and x 2 may be deleted from the regression model leaving the higher-order term containing the product of x1 and x 2 .

A) True

B) False

Objective: (12.5) Test for Interaction Between Two Variables

Solve the problem. 53) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Tuition GMAT TxG

Coefficient Std Error T 165.406 4.16 -687.851 2.19724 -11.3197 -5.15 -0.96727 -3.79 0.25535 0.01850 0.00331 5.58

R-Squared Adjusted R-Squared Source Regression Residual Total

DF 3

Cases Included 75

0.0001 0.0000 0.0003 0.0000

0.7816 Resid. Mean Square (MSE) 0.7723 Standard Deviation SS MS 76523.8 25510.9 84.68 71 21388.8 301.3 74 97921.7

F 0.0000

301.251 17.3566 P

Missing Cases 0

One of the t-test test statistics is shown on the printout to be the value t = 5.58. Interpret this value. A) There is insufficient evidence, at = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs. B) There is sufficient evidence, at = 0.05, to indicate that the interaction between average tuition and average GMAT score is a useful predictor of the average starting salary of graduates of MBA programs. C) There is insufficient evidence, at = 0.05, to indicate that the interaction between average tuition and average GMAT score is a useful predictor of the average starting salary of graduates of MBA programs. D) There is sufficient evidence, at = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs. Objective: (12.5) Test for Interaction Between Two Variables

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 54) A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables: x 1 = high school GPA x 2 = SAT score The admissions officer believes the relationship between college GPA and high school GPA is linear and the relationship between SAT score and college GPA is linear. She also believes that the relationship between college GPA and high school GPA depends on the student's SAT score. She proposes the regression model: E(y) = 0 + 1 x 1 + 2 x 2 + 3 x 1 x 2 Explain how to determine if the relationship between college GPA and SAT score depends on the high school GPA. Objective: (12.5) Test for Interaction Between Two Variables

55) Consider the partial printout below.

Is there evidence (at

= .05) that x 1 and x 2 interact? Explain.

Objective: (12.5) Test for Interaction Between Two Variables

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False.

56) In the quadratic model E(y) = 0 + 1 x + 2 x 2 , a negative value of 1 indicates downward concavity. A) True B) False Objective: (12.6) Write and Interpret Second-Order Model

57) One of three surfaces is produced by a complete second-order model with two quantitative independent variables: a paraboloid that opens upward, a paraboloid that opens downward, or a saddle-shaped surface. A) True B) False Objective: (12.6) Write and Interpret Second-Order Model

58) The complete second-order model with two quantitative independent variables does not allow for interaction between the two independent variables. A) True B) False Objective: (12.6) Write and Interpret Second-Order Model

Solve the problem. 59) A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model E(y) = 0 + 1 x + 2 x 2 This model was fit to data collected for a sample of 32 clocks sold at auction; the resulting estimate of

1 was -.31.

Interpret this estimate of 1 . A) We estimate the auction price will decrease $.31 for each additional bidder at the auction. B) We estimate the auction price will increase $.31 for each additional bidder at the auction. C) 1 is a shift parameter that has no practical interpretation.

D) We estimate the auction price will be -$.31 when there are no bidders at the auction. Objective: (12.6) Write and Interpret Second-Order Model

60) Which equation represents a complete second-order model for two quantitative independent variables? A) E(y) = 0 + 1 x 1 x 2 + B) E(y) = 0 + 1 x 1 +

2 2 2x 1 + 3x 2

2x 2 +

3x 1 x 2 +

2 2 C) E(y) = 0 + 1 x 1 + 2 x 2 +

D) E(y) = 0 + 1 x 1 +

2x 2 +

2 2 4x 1 + 5x 2

2 3 x 1 x2 +

2 2 2 4x1 x 2 + 5 x 1 x 2

2 2 3x 1 + 4x 2

Objective: (12.6) Write and Interpret Second-Order Model

61) A graphing calculator was used to fit the model E(y) = 0 + 1 x + 2 x 2 to a set of data. The resulting screen is shown below.

Which number on the screen represents the estimator of

A) .9405

B) .9286

C) 5.5

Objective: (12.6) Write and Interpret Second-Order Model

D) 11

62) Consider the second-order model ^ 2 2 y = -3.24 + 1.12x 1 + 2.57x 2 - 3.22x 1 x 2 + 5.78 x 1 = 4.69 x 2 ^

If x 2 is held fixed at x 2 = 3, describe the relationship between y and x 1 . ^

A) The relationship between y and x 1 is quadratic with downward concavity. ^

B) The relationship between y and x 1 is linear with positive slope. ^

C) The relationship between y and x 1 is linear with negative slope. ^

D) The relationship between y and x 1 is quadratic with upward concavity. Objective: (12.6) Write and Interpret Second-Order Model

63) What relationship between x and y is suggested by the scattergram?

A) a linear relationship with negative slope B) a quadratic relationship with downward concavity C) a linear relationship with positive slope D) a quadratic relationship with upward concavity Objective: (12.6) Write and Interpret Second-Order Model

64) A study of the top MBA programs attempted to predict y = the average starting salary (in $1000's) of graduates of the program based on x = the amount of tuition (in $1000's) charged by the program. After first considering a simple linear model, it was decided that a quadratic model should be proposed. Which of the following models proposes a 2nd-order quadratic relationship between x and y? A) E(y) = 0 + 1 x1 + 2 x2 + 3 x1 x2 B) E(y) = 0 + 1 x1 + 2 x1 2 + 3 x1 3 C) E(y) = 0 + 1 x1 D) E(y) = 0 + 1 x1 + 2 x1 2 Objective: (12.6) Write and Interpret Second-Order Model

65) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Tuition TxT

Coefficient Std Error 169.910 26.5350 0.81171 -3.37373 0.03563 0.00590

R-Squared Adjusted R-Squared Source Regression Residual Total

DF 2

Cases Included 75

T 6.40 -4.16 6.03

P 0.0000 0.0001 0.0000

0.7361 Resid. Mean Square (MSE) 0.7288 Standard Deviation SS MS F 72081.8 36040.9 100.42 0.0000 72 25839.8 358.9 74 97921.7

358.887 18.9443 P

Missing Cases 0

The global-f test statistic is shown on the printout to be the value F = 100.42. Interpret this value. A) There is sufficient evidence, at = 0.05, to indicate that there is a linear relationship between average starting salary of graduates of MBA programs and the tuition of the MBA program. B) There is sufficient evidence, at = 0.05, to indicate that there is a curvilinear relationship between average starting salary of graduates of MBA programs and the tuition of the MBA program. C) There is sufficient evidence, at = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs. D) There is insufficient evidence, at = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs. Objective: (12.6) Write and Interpret Second-Order Model

66) A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary Predictor Variables Constant Tuition TxT

Coefficient Std Error 169.910 26.5350 0.81171 -3.37373 0.03563 0.00590

R-Squared Adjusted R-Squared Source Regression Residual Total

DF 2

Cases Included 75

T 6.40 -4.16 6.03

P 0.0000 0.0001 0.0000

0.7361 Resid. Mean Square (MSE) 0.7288 Standard Deviation SS MS F 72081.8 36040.9 100.42 0.0000 72 25839.8 358.9 74 97921.7

358.887 18.9443 P

Missing Cases 0

One of the t-test test statistics is shown on the printout to be the value t = 6.03. Interpret this value. A) There is sufficient evidence, at = 0.05, to indicate that there is a linear relationship between average starting salary of graduates of MBA programs and the tuition of the MBA program. B) There is insufficient evidence, at = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs. C) There is sufficient evidence, at = 0.05, to indicate that there is a curvilinear relationship between average starting salary of graduates of MBA programs and the tuition of the MBA program. D) There is sufficient evidence, at = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs. Objective: (12.6) Write and Interpret Second-Order Model

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 67) Consider the data given in the table below. X 1 2 2 3 3 4 4 4 5 5 6

Y 7 6 5 5 4 4 3 2 4 5 6

Plot the data on a scattergram. Does a second-order model seem to be a good fit for the data? Explain. Objective: (12.6) Write and Interpret Second-Order Model

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 68) A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model E(y) = 0 + 1 x + 2 x 2 This model was fit to data collected for a sample of 32 clocks sold at auction; a portion of the printout follows:

VARIABLES

PARAMETER ESTIMATE

STANDARD ERROR

T FOR 0: PARAMETER = 0

PROB > |T|

INTERCEPT X X ·X

286.42 -.31 .000067

9.66 .06 .00007

29.64 -5.14 .95

.0001 .0016 .3600

Find the p-value for testing H0 : 2 = 0 against Ha : 2 > 0. A) .05 B) .36

C) .0016

Objective: (12.6) Perform Hypothesis Test for Parameter Coefficient

D) .18

69) A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model E(y) = 0 + 1 x + 2 x 2 This model was fit to data collected for a sample of 32 clocks sold at auction. Suppose the p-value for the test of H0 : 2 = 0 vs. Ha : 2 > 0 is .02. What is the proper conclusion? A) There is no evidence (at = .05) of upward curvature in the relationship between auction price (y) and number of bidders (x). B) Reject H0 at = .05; the model is not useful for predicting auction price (y).

C) There is evidence (at = .05) of upward curvature in the relationship between auction price (y) and number of bidders (x). D) There is evidence (at = .05) of downward curvature in the relationship between auction price (y) and number of bidders (x). Objective: (12.6) Perform Hypothesis Test for Parameter Coefficient

70) A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model E(y) = 0 + 1 x + 2 x 2 This model was fit to data collected for a sample of 32 clocks sold at auction; a portion of the printout follows:

VARIABLES

PARAMETER ESTIMATE

STANDARD ERROR

T FOR 0: PARAMETER = 0

PROB > |T|

INTERCEPT X X ·X

286.42 .31 -.000067

9.66 .06 .00007

29.64 5.14 -0.95

.0001 .0016 .3600

Give the p-value for testing H0 : 2 = 0 against Ha : 2 0. A) .18 B) .0016

C) .05

Objective: (12.6) Perform Hypothesis Test for Parameter Coefficient

D) .36

71) A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model E(y) = 0 + 1 x + 2 x 2 where y = Demand (in thousands) and x = Retail price per carat (dollars). This model was fit to data collected for a sample of 12 rare gems. If the experts are correct in their assumptions about the relationship between price and demand, which of the following should be true? A) 1 > 0 B) 2 > 0 C) 2 < 0 D) 1 < 0 Objective: (12.6) Perform Hypothesis Test for Parameter Coefficient

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 72) A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model E(y) = 0 + 1 x + 2 x 2 where y = Demand (in thousands) and x = Retail price per carat (dollars). This model was fit to data collected for a sample of 12 rare gems. A portion of the printout is given below: SOURCE

PR > F

Model Error TOTAL

2 9 11

115145 1388 116533

57573 154

373

.0001

Root MSE

12.42

R-Square

.988

VARIABLES

PARAMETER ESTIMATES

STD. ERROR

T for HO: PARAMETER = 0

PR > |T|

INTERPCEP X X ·X

286.42 -.31 .000067

9.66 .06 .00007

29.64 -5.14 .95

.0001 .0006 .3647

Does the quadratic term contribute useful information for predicting the demand for the gem? Use Objective: (12.6) Perform Hypothesis Test for Parameter Coefficient

= .10.

73) The complete second-order model E(y) = 0 + 1 x 1 +

2 2 x 2 + 3 x 1 x2 + 4 x 1 +

2 5 x 2 was fit to n = 25 data

points. The printout is shown below.

a. Write the complete second-order model for the data. b. Is there sufficient evidence to indicate that at least one of the parameters 1 , 2 , 3 , 4 , and 5 is nonzero? Test using = .05. c. Test H0: 3 = 0 against Ha : 3 0. Use = .01. d. Test H0: 4 = 0 against Ha : 4 0. Use

= .01.

Objective: (12.6) Perform Hypothesis Test for Parameter Coefficient

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False.

74) When testing the utility of the quadratic model E(y) = 0 + 1 x + 2 x 2 , the most important tests involve the null hypotheses H0 : 0 = 0 and H0 : 1 = 0. A) True

B) False

Objective: (12.6) Test if Model is Useful for Predicting y

Solve the problem. 75) A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model E(y) = 0 + 1 x + 2 x 2 where y = Demand (in thousands) and x = Retail price per carat (dollars). This model was fit to data collected for a sample of 12 rare gems.

VARIABLES

PARAMETER ESTIMATES

STD. ERROR

T for HO: PARAMETER = 0

PR > |T|

INTERPCEP X X ·X

286.42 -.31 .000067

9.66 .06 .00007

29.64 -5.14 .95

.0001 .0006 .3647

Does there appear to be upward curvature in the response curve relating y (demand) to x (retail price)? A) No, since the p-value for the test is greater than .10. B) Yes, since the p-value for the test is less than .01. C) Yes, since the value of 2 is positive.

D) No, since the value of 2 is near 0. Objective: (12.6) Test if Model is Useful for Predicting y

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 76) A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model E(y) = 0 + 1 x + 2 x 2 where y = Demand (in thousands) and x = Retail price per carat (dollars). This model was fit to data collected for a sample of 12 rare gems. A portion of the printout is given below: SOURCE

PR > F

Model Error TOTAL

2 9 11

115145 1388 116533

57573 154

373

.0001

Root MSE

12.42

R-Square

VARIABLES

PARAMETER ESTIMATES

INTERPCEP X X ·X

286.42 -.31 .000067

.988

STD. ERROR

T for HO: PARAMETER = 0

PR > |T|

9.66 .06 .00007

29.64 -5.14 .95

.0001 .0006 .3647

Is there sufficient evidence to indicate the model is useful for predicting the demand for the gem? Use Objective: (12.6) Test if Model is Useful for Predicting y

= .01.

77) The table shows the profit y (in thousands of dollars) that a company made during a month when the price of its product was x dollars per unit. Profit, y 12 17 20 21 24 26 27 23 21 20 15 11 10 5 a. b. c.

Price, x 1.20 1.25 1.29 1.30 1.35 1.39 1.40 1.45 1.49 1.50 1.55 1.59 1.60 1.65

Fit the model y = 0 + 1 x + 2 x2 + to the data and give the least squares prediction equation. Plot the fitted equation on a scattergram of the data. Is there sufficient evidence of downward curvature in the relationship between profit and price? Use

= .05.

Objective: (12.6) Test if Model is Useful for Predicting y

78) Consider the data given in the table below. X 1 2 2 3 4 4 5 5 6 a. b. c.

Y 4 6 5 7 7 6 4 5 3

Plot the data on a scattergram. Does a quadratic model seem to be a good fit for the data? Explain. Use the method of least squares to find a quadratic prediction equation. Graph the prediction equation on your scattergram.

Objective: (12.6) Perform Quadratic Regression and Make Predictions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 79) When using the model E(y) = 0 + 1 x for one qualitative independent variable with a 0 1 coding convention, 1 represents the difference between the mean responses for the level assigned the value 1 and the base level. A) True B) False Objective: (12.7) Write and Interpret Model with Qualitative Variables

80) When modeling E(y) with a single qualitative independent variable, the number of 0 1 dummy variables in the model is equal to the number of levels of the qualitative variable. A) True B) False Objective: (12.7) Write and Interpret Model with Qualitative Variables

Solve the problem. 81) An elections officer wants to model voter turnout (y) in a precinct as a function of type of election, national or state. Write a model for mean voter turnout, E(y), as a function of type of election. A) E(y) = 0 + 1 x + 2 x 2 , where x = voter turnout B) E(y) = 0 + 1 x 1 + 2 x 2 , where x 1 = 1 if national, 0 if not and x 2 = 1 if state, 0 if not

C) E(y) = 0 + 1 x, where x = voter turnout D) E(y) = 0 + 1 x, where x = 1 if national, 0 if state Objective: (12.7) Write and Interpret Model with Qualitative Variables

82) It is desired to build a regression model to predict y = the sales price of a single family home, based on the neighborhood the home is located in. The goal is to compare the prices of homes that are located in four different neighborhoods. Which regression model should be built? A) E(y) = 0 + 1 x 1, where x1 is a qualitative variable that describes the four neighborhoods. B) E(y) = 0 + 1 x 1 + 2 x2 + 3 x3 , where x1 - x3 are qualitative variables that describe the four neighborhoods. C) E(y) = 0 + 1 x 1 + 2 x1 2 , where x1 is a qualitative variable that describes the four neighborhoods. D) E(y) = 0 + 1 x 1 + 2 x2 + 3 x3 + 4 x4 , where x1 - x4 are qualitative variables that describe the four neighborhoods. Objective: (12.7) Write and Interpret Model with Qualitative Variables

83) An elections officer wants to model voter turnout (y) in a precinct as a function of the type of precinct. Consider the model relating mean voter turnout, E(y), to precinct type: E(y) = 0 + 1 x 1 + 2 x 2 , where

x 1 = 1 if urban, 0 if not x 2 = 1 if suburban, 0 if not (Base level = rural)

Interpret the value of 2 . A) the rate of increase in voter turnout (y) for suburban precincts, i.e., the slope of the y-x 2 line

B) the difference between the mean voter turnout for suburban and urban precincts C) the difference between the mean voter turnout for suburban and rural precincts D) the mean voter turnout for suburban precincts Objective: (12.7) Write and Interpret Model with Qualitative Variables

84) An elections officer wants to model voter turnout (y) in a precinct as a function of the type of precinct. Consider the model relating mean voter turnout, E(y), to precinct type: E(y) = 0 + 1 x 1 + 2 x 2 , where

x 1 = 1 if urban, 0 if not x 2 = 1 if suburban, 0 if not (Base level = rural)

Interpret the value of 0 . A) the mean voter turnout for rural precincts B) the mean voter turnout for urban precincts C) the y-intercept of the line D) the difference between the mean voter turnout for urban and rural precincts Objective: (12.7) Write and Interpret Model with Qualitative Variables

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 85) In Hawaii, proceedings are under way to enable private citizens to own the property that their homes are built on. In prior years, only estates were permitted to own land, and homeowners leased the land from the estate. In order to comply with the new law, a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land. The following variables are proposed: y = Sale price of property ($ thousands) x 2 = 1 if property near Cove, 0 if not Write a regression model relating the sale price of a property to the qualitative variable x. Interpret all the s in the model. Objective: (12.7) Write and Interpret Model with Qualitative Variables

86) The model E(y) = 0 + 1 x 1 + 2 x 2 + 3 x 3 was used to relate E(y) to a single qualitative variable. How many levels does the qualitative variable have? Objective: (12.7) Write and Interpret Model with Qualitative Variables

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 87) An elections officer wants to model voter turnout (y) in a precinct as a function of the type of precinct. Consider the model relating mean voter turnout, E(y), to precinct type: E(y) = 0 + 1 x 1 + 2 x 2 , where

x 1 = 1 if urban, 0 if not x 2 = 1 if suburban, 0 if not (Base level = rural)

The p-value for the test H0 : 1 = 2 = 0 is .14. Interpret the result. A) Reject H0 at = .01; there is evidence of a difference between the mean voter turnouts for urban, suburban,

and rural precincts. B) Reject H0 at = .10; the model is useful for predicting voter turnout.

C) Reject the model since it only explains 14% of the variation. D) Do not reject H0 at = .10; there is no evidence of a difference between the mean voter turnouts for urban, suburban, and rural precincts. Objective: (12.7) Perform Hypothesis Test for Parameter Coefficient of Qualitative Variable

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 88) The model E(y) = 0 + 1 x 1 + 2 x 2 + 3 x 3 + 4x 4 was used to relate E(y) to a single qualitative variable, where x1 =

1 0

if level 2 if not

x2 =

1 0

if level 3 if not

x3 =

1 0

if level 4 if not

x4 =

1 0

if level 5 if not

This model was fit to n = 40 data points and the following result was obtained: ^

y = 14.5 + 3x 1 - 4x 2 + 10x 3 + 8x 4 a. Use the least squares prediction equation to find the estimate of E(y) for each level of the qualitative variable. b. Specify the null and alternative hypothesis you would use to test whether E(y) is the same for all levels of the independent variable. Objective: (12.7) Perform Hypothesis Test for Parameter Coefficient of Qualitative Variable

89) Twenty colleges each recommended one of its graduating seniors for a prestigious graduate fellowship. The process to determine which student will receive the fellowship includes several interviews. The gender of each student and his or her score on the first interview are shown below. Student 1 2 3 4 5 6 7 8 9 10

Gender Male Female Female Female Male Female Female Male Male Female

Score 18 17 19 16 12 15 18 16 18 20

Student 11 12 13 14 15 16 17 18 19 20

Gender Female Male Male Female Female Male Female Male Female Female

Score 17 16 16 19 16 15 12 14 16 18

a. Suppose you want to use gender to model the score on the interview y. Create the appropriate number of dummy variables for gender and write the model. b. Fit the model to the data. c. Give the null hypothesis for testing whether gender is a useful predictor of the score y. d. Conduct the test and give the appropriate conclusion. Use = .05. Objective: (12.7) Test if Model is Useful for Predicting y

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 90) If when using the model E(y) = 0 + 1 x 1 + 2 x 2 + 3 x 1 x 2 we determine that interaction between x 1 and x 2 is not significant, we can drop the x 1 x 2 term from the model and use the simpler model E(y) = 0 + 1 x 1 + 2 x 2 . A) True

B) False

Objective: (12.8) Write and Interpret Model with Quantitative and Qualitative Variables

91) One advantage to writing a single model that includes all levels of a qualitative variable rather a separate model for each level is that we obtain a pooled estimate of 2 . A) True

B) False

Objective: (12.8) Write and Interpret Model with Quantitative and Qualitative Variables

Solve the problem. 92) Consider the model y = 0 + 1 x 1 + 2 x 2 + 3 x3 + where x 1 is a quantitative variable and x 2 and x 3 are dummy variables describing a qualitative variable at three levels using the coding scheme 1 0

x2 =

if level 2 otherwise

x3 =

1 0

if level 3 otherwise ^

The resulting least squares prediction equation is y = 16.3 + 2.3x 1 + 3.5x 2 + 18x 3 . What is the response line (equation) for E(y) when x 2 = 0 and x 3 = 1? ^

A) y = 18.1 + 2.3x 1

B) y = 16.3 + 2.3x 1

C) y = 16.3 + 4.1x 1

Objective: (12.8) Write and Interpret Model with Quantitative and Qualitative Variables

D) y = 18.6 + 2.3x 1

93) Consider the model y = 0 + 1 x 1 + 2 x 2 + 3 x3 + where x 1 is a quantitative variable and x 2 and x 3 are dummy variables describing a qualitative variable at three levels using the coding scheme 1 0

x2 =

if level 2 otherwise

x3 =

1 0

if level 3 otherwise ^

The resulting least squares prediction equation is y = 36.7 + 1.3x 1 + 5.4x 2 + 3.2x 3 . What is the least squares regression equation associated with level 2? ^

A) y = 39.9 + 5.4x 2

B) y = 39.9 + 1.3x 1

C) y = 38.0 + 5.4x 2

D) y = 42.1 + 1.3x 1

Objective: (12.8) Write and Interpret Model with Quantitative and Qualitative Variables

94) Consider the model y = 0 + 1 x 1 + 2x 1 2 + 3x 2 + 4 x3 + 5 x 1x 2 + 6 x 1x 3 + 7 x1 2 x 2 +

8 x 12 x 3 +

where x 1 is a quantitative variable and x 2 and x 3 are dummy variables describing a qualitative variable at three levels using the coding scheme 1 0

x2 =

if level 2 otherwise

x3 =

1 0

if level 3 otherwise

The resulting least squares prediction equation is ^

y = 8.8 - 1.1x 1 + 3.2x1 2 + 1.6x 2 - 4.4x 3 + .02x 1 x 2 + 1.3x 1 x 3 + .01x 1 2 x 2 - .06x 1 2 x 3 What is the equation of the response curve for E(y) when x 2 = 0 and x 3 = 0? ^

B) y = 8.8 - 1.3x 1 + 3.2x 1 2

D) y = 8.8 - .22x 1 + 3.15x 1 2

A) y = 8.8 - 1.1x 1 + 3.2x 1 2

C) y = 8.8 - 1.6x 2 - 4.4x 3

Objective: (12.8) Write and Interpret Model with Quantitative and Qualitative Variables

95) It is desired to build a regression model to predict y = the sales price of a single family home, based on the x1 = size of the house and x2 = the neighborhood the home is located in. The goal is to compare the prices of homes that are located in two different neighborhoods. A complete 2nd-order model is proposed. Which regression model proposes the complete 2nd-order model? A) E(y) = 0 + 1 x 1 + 2 x2

B) E(y) = 0 + 1 x 1 + 2 x1 2 + 3 x2 + 4 x1 x2 + 3 x1 2 x2 C) E(y) = 0 + 1 x 1 + 2 x2 + 3 x1 x2 D) E(y) = 0 + 1 x 1 + 2 x1 2 + 3 x2 + 4 x2 2 Objective: (12.8) Write and Interpret Model with Quantitative and Qualitative Variables

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 96) A fast food chain test marketing a new sandwich chose 18 of its stores in one major metropolitan area. Nine of the stores were in malls and nine were free standing. The sandwich was offered at three different introductory prices. The table shows the number of new sandwiches sold at each location for each location type and price combination.

a. Write a model for the mean number of sandwiches sold, E(y), assuming that the relationship between E(y) and price, x 1 , is first-order. b. Fit the model to the data. c. Write the prediction equations for mall and free-standing stores. d. Do the data provide sufficient evidence that the change in number of sandwiches sold with respect to price is different for mall and free-standing stores? Use = .01. Objective: (12.8) Perform Hypothesis Test for Parameter Coefficient

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 97) The sum of squared errors (SSE) of a least squares regression model decreases when new terms are added to the model. A) True B) False Objective: (12.9) Conduct Test to Compare Complete and Reduced Models

98) A nested model F-test can only be used to determine whether second-order terms should be included in the model. A) True B) False Objective: (12.9) Conduct Test to Compare Complete and Reduced Models

99) In situations where two competing models have essentially the same predictive power (as determined by an F-test), it is standard procedure to use the model with the greater number of parameters. A) True B) False Objective: (12.9) Conduct Test to Compare Complete and Reduced Models

Solve the problem. 100) Operations managers often use work sampling to estimate how much time workers spend on each operation. Work sampling which involves observing workers at random points in time was applied to the staff of the catalog sales department of a clothing manufacturer. The department applied regression to the following data collected for 40 consecutive working days: TIME:

y = Time spent (in hours) taking telephone orders during the day

ORDERS:

x1 = Number of telephone orders received during the day

WEEK:

x2 = 1 weekday, 0 if Saturday or Sunday

Consider the following 2 models: Model 1: E(y) = 0 + 1 x 1 + 2 (x1 )2 + 3 x 2 + 4 x 1 x 2 + 5 (x 1 )2 x 2 Model 2: E(y) = 0 + 1 x 1 + 3 x 2 What strategy should you employ to decide which of the two models, the higher-order model or the simple linear model, is better? A) Compare R2 values; the model with the larger R2 will always be the better model.

B) Compare the two models with a t-test, i.e., test the null hypothesis, H0 : 1 = 0. C) Always choose the more parsimonious of the two models, i.e., the model with the fewest number of -coefficients. D) Compare the two models with a nested model F-test, i.e., test the null hypothesis, H0: 2 = 4 = 5 = 0.

Objective: (12.9) Conduct Test to Compare Complete and Reduced Models

101) A public health researcher wants to use regression to predict the sun safety knowledge of pre-school children. The researcher randomly sampled 35 preschoolers, assigned them to one of two groups, and then measured the following three variables: SUNSCORE: READING:

y = Score on sun-safety comprehension test x1 = Reading comprehension score

GROUP:

x2 = 1 if child received a Be Sun Safe demonstration, 0 if not

The following two models were hypothesized: Model 1: E(y) = 0 + 1 x1 + 2 x1 2 + 3 x2 + 4x1 x2 + 5 x1 2x 2 Model 2: E(y) = 0 + 1 x1 + 3 x2 + 4 x1 x2 A partial f-test was conducted to compare the two models and the resulting p-value was found to be 0.0023. Fill in the blank. The results lead us to conclude that there is (at = 0.05). A) sufficient evidence of a statistically useful model for sun-safety score. B) sufficient evidence of interaction between sun-safety score and reading score. C) insufficient evidence of quadratic relationship between sun-safety score to reading score. D) sufficient evidence of a quadratic relationship between sun-safety score to reading score. Objective: (12.9) Conduct Test to Compare Complete and Reduced Models

102) It is desired to build a regression model to predict y = the sales price of a single family home, based on the x1 = size of the house and x2 = the neighborhood the home is located in. The goal is to compare the prices of homes that are located in two different neighborhoods. The following complete 2nd-order model is proposed: E(y) = 0 + 1 x1 + 2 x1 2 + 3 x2 + 4 x1x2 + 5 x1 2 x2 . What hypothesis should be tested to determine if the quadratic terms are necessary to predict the sales price of a home? A) H0 : 1 = 3 = 4 = 0 B) H0 : 2 = 5 = 0

C) H0 : 1 = 2 = 3 = 0

D) H0 : 1 = 2 = 3 = 4 = 5 = 0

Objective: (12.9) Conduct Test to Compare Complete and Reduced Models

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 103) Operations managers often use work sampling to estimate how much time workers spend on each operation. Work sampling which involves observing workers at random points in time was applied to the staff of the catalog sales department of a clothing manufacturer. The department applied regression to the following data collected for 40 consecutive working days: TIME:

y = Time spent (in hours) taking telephone orders during the day

ORDERS:

x1 = Number of telephone orders received during the day

WEEK:

x2 = 1 weekday, 0 if Saturday or Sunday

Consider the complete 2nd-order model: E(y) = 0 + 1x 1 + 2 (x 1 )2 + 3 x 2 + 4 x 1 x 2 + 5 (x 1 )2 x 2 Explain how to conduct a test to determine if a quadratic relationship between total order time and the number of orders taken is necessary in the regression model above. Specify the null and alternative hypotheses that are to be tested. Objective: (12.9) Conduct Test to Compare Complete and Reduced Models

104) The staff of a test kitchen is attempting to determine the baking time, y, of a roast, i.e., the time it takes the internal temperature of the roast to reach 165°F, using two variables, the temperature setting of the oven, x 1 , and the weight of the roast, x 2 , in pounds. The data for 24 roasts are shown below.

a. Fit a complete second-order model to the data. b. Do the data provide sufficient evidence to indicate that the second-order terms contribute information for the prediction of y? State the null and alternative hypotheses and the test statistic. Use = .05. Objective: (12.9) Conduct Test to Compare Complete and Reduced Models

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 105) Stepwise regression is used to determine which variables, from a large group of variables, are useful in predicting the value of a dependent variable. A) True B) False Objective: (12.10) Understand and Interpret Stepwise Regression Model

106) In stepwise regression, the probability of making one or more Type I or Type II errors is quite small. A) True B) False Objective: (12.10) Understand and Interpret Stepwise Regression Model

107) The stepwise regression model should not be used as the final model for predicting y. A) True B) False Objective: (12.10) Understand and Interpret Stepwise Regression Model

108) The stepwise regression procedure may not be used when the inclusion of one or more dummy variables is under consideration. A) True B) False Objective: (12.10) Understand and Interpret Stepwise Regression Model

Solve the problem. 109) There are four independent variables, x1 , x 2 , x3 , and x 4 , that might be useful in predicting a response y. A total of

n = 40 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to useful. The computer fits all possible one-variable models of the form E(y) = 0 + 1 x i , i = 1, 2, 3, 4. The information in the table is provided from the computer printout. Variable X1 X2 X3 X4

2.4 -0.2 3.6 0.8

s 0.52 0.03 2.11 0.44

Which independent variable is declared the best one-variable predictor of y? A) x 1 B) x 2 C) x 3

D) x 4

Objective: (12.10) Understand and Interpret Stepwise Regression Model

Answer the question True or False. 110) A regression residual is the difference between an observed y value and its corresponding predicted value. A) True B) False Objective: (12.11) Understand Regression Assumptions

111) For any given model fit to a data set, the sum of the residuals is 0. A) True B) False Objective: (12.11) Understand Regression Assumptions

112) We expect all or almost all of the residuals to fall within 2 standard deviations of 0. A) True B) False Objective: (12.11) Understand Regression Assumptions

113) Residual analysis can be used to check for violations of the assumptions that the distribution of the random error component is normally distributed with mean 0. A) True B) False Objective: (12.11) Understand Regression Assumptions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 114) The first-order model below was fit to a set of data. E(y) = 0 + 1 x 1 + 2 x 2 Explain how to determine if the constant variance assumption is satisfied. Objective: (12.11) Understand Regression Assumptions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 115) Which residual plot would you examine to determine whether the assumption of constant error variance is satisfied for a model with two independent variables x 1 and x2 ? ^

A) Plot the residuals against predicted values, y. B) Plot the residuals against the independent variable x 2 . C) Plot the residuals against the independent variable x 1 .

D) Plot the residuals against observed y values. Objective: (12.11) Analyze Residual Plot

116) The model E(y) = 0 + 1 x 1 + 2 x 2 was fit to a set of data. A partial printout for the analysis follows:

OBS

Actual Value

Predict Value

Residual

Lower 95% CL Predict

Upper 95% CL Predict

7781

644

74.707

83.175

-8.468

47.224

119.126

Interpret the value of the residual when x 1 = 7,781 and x 2 = 644. ^

A) The predicted y exceeds the observed value of y by 8.468. B) Since the residual is not 0, the model is not useful for predicting y. ^

C) The predicted y is 8.468 less than the observed value of y. D) Since the residual is negative, there is evidence of a negative linear relationship between y and at least one of the two independent variables. Objective: (12.11) Analyze Residual Plot

117) A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model E(y) = 0 + 1 x + 2 x 2 This model was fit to data collected for a sample of 32 clocks sold at auction; a portion of the printout follows: _____________________________________________________________________ SOURCE DF SS MS F VALUE PROB > F MODEL ERROR TOTAL

2 29 31

4277160 514034 4791194

2138579 17725

ROOT MSE DEP MEAN

133 1327

120

.0005

R-SQUARE ADJ R-SQ

893 .885

VARIABLES

PARAMETER ESTIMATE

STANDARD ERROR

T FOR 0: PARAMETER = 0

PROB > |T|

INTERCEPT X X ·X

286.42 .31 -.000067

9.66 .06 .00007

29.64 5.14 -0.95

.0001 .0016 .3600

An outlier for the model is a clock with a residual that _____ in absolute value. (Fill in the blank.) A) exceeds 133 B) exceeds 399 C) is less than 266 D) exceeds .893 Objective: (12.11) Analyze Residual Plot

118) Suppose that the following model was fit to a set of data. E(y) = 0 + 1 x 1 + 2 x 2 ^

The corresponding plot if residuals against predicted values y is shown. Interpret the plot.

A) The residuals appear to be randomly scattered so that no model modifications are necessary. B) It appears that the variance of is not constant. C) It appears that a quadratic model would be a better fit. D) It appears that the data contain an outlier. Objective: (12.11) Analyze Residual Plot

119) A public health researcher wants to use regression to predict the sun safety knowledge of pre-school children. The researcher randomly sampled 35 preschoolers, assigned them to one of two groups, and then measured the following three variables: SUNSCORE: READING:

y = Score on sun-safety comprehension test x1 = Reading comprehension score

GROUP:

x2 = 1 if child received a Be Sun Safe demonstration, 0 if not

A regression model was fit and the following residual plot was observed.

Which of the following assumptions appears violated based on this plot? A) The errors are normally distributed B) The variance of the errors is constant C) The mean of the errors is zero D) The errors are independent Objective: (12.11) Analyze Residual Plot

120) It is desired to build a regression model to predict y = the sales price of a single family home, based on the x1 = size of the house and x2 = the neighborhood the home is located in. The goal is to compare the prices of homes that are located in two different neighborhoods. The following model is proposed: E(y) = 0 + 1 x1 + 2x2 A regression model was fit and the following residual plot was observed.

Which of the following assumptions appears violated based on this plot? A) The mean of the errors is zero B) The variance of the errors is constant C) The errors are independent D) The errors are normally distributed Objective: (12.11) Analyze Residual Plot

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 121) The model E(y) = 0 + 1 x was fit to a set of data, and the following plot of residuals against x values was obtained.

Interpret the residual plot. Objective: (12.11) Analyze Residual Plot

122) The model E(y) = 0 + 1 x was fit to a set of data, and the following plot of residuals against x values was obtained.

Interpret the residual plot. Objective: (12.11) Analyze Residual Plot

123) The model E(y) = 0 + 1 x was fit to a set of data, and the following plot of residuals against x values was obtained.

Interpret the residual plot. Objective: (12.11) Analyze Residual Plot

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question True or False. 124) The number of levels of observed x-values must be equal to the order of the polynomial in x that you want to fit. A) True B) False Objective: (12.12) Understand Problems with Multiple Regression Models

125) In the presence of multicollinearity, the predicted values of y are actually quite good for values of x far outside the range of the sampled values of x. A) True B) False Objective: (12.12) Understand Problems with Multiple Regression Models

126) In the presence of multicollinearity, you should avoid making inferences about the parameters based on the t-tests. A) True B) False Objective: (12.12) Understand Problems with Multiple Regression Models

Solve the problem. 127) It is dangerous to predict outside the range of the data collected in a regression analysis. For instance, we shouldn't predict the price of a 5000 square foot home if all our sample homes were smaller than 4500 square feet. Which of the following multiple regression pitfalls does this example describe? A) Extrapolation B) Estimability C) Stepwise Regression D) Multicollinearity Objective: (12.12) Understand Problems with Multiple Regression Models

128) In regression, it is desired to predict the dependent variable based on values of other related independent variables. Occasionally, there are relationships that exist between the independent variables. Which of the following multiple regression pitfalls does this example describe? A) Stepwise Regression B) Multicollinearity C) Extrapolation D) Estimability Objective: (12.12) Understand Problems with Multiple Regression Models

129) Which of the following is not a possible indicator of multicollinearity? A) non-significant t-tests for individual parameters when the F-test for overall model adequacy is significant B) significant correlations between pairs of independent variables C) non-random patterns in the plot of the residuals versus the fitted values D) signs opposite from what is expected in the estimated parameters Objective: (12.12) Understand Problems with Multiple Regression Models

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 130) The printout below shows part of the least squares regression analysis for the model E(y) = 0 + 1 x 1 + 2 x 2 fit to a set of data. The model attempts to predict a score on the final exam in a statistics course based on the scores on the first two tests in the class.

Is there evidence of multicollinearity in the printout? Explain. Objective: (12.12) Understand Problems with Multiple Regression Models

131) The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below.

Fit the model E(y) = 0 + 1 x 1 + 2 x 2 + 3 x 1 x 2 to the data, letting y represent the number of bottles of water sold, x 1 the temperature, and x 2 the number of people at the park. b. Identify at least two indicators of multicollinearity in the model. c. Comment on the usefulness of the model to predict the number of bottles of water sold on a Saturday when the high temperature is 103°F and there are 3500 people at the park. Objective: (12.12) Understand Problems with Multiple Regression Models

Answer Key Testname: SB14ECH12TEST

1) B 2) A 3) A 4) A 5) The random error term is added to make the mode probabilistic rather than deterministic. 6) B 7) A 8) A 9) B ^

10) a. y = -26.4843 2.1687x1 + 8.1422x 2

b. SSE = 2.8096 c. The estimator of 2 is 1.4048.

11) a. The dependent variable is “test grade.” There are three independent variables: “quiz 1,” “quiz 2,” and “quiz 3. ” ^

b. y = 15.8687 + 2.6796x 1 + 1.9780x 2 + 3.6967x 3 c.

SSE = 317.1874; The estimator of 2 is

79.2968. 12) A 13) B ^

2 = 3.57. For every one computer processing unit increase in chip size, we estimate the retail price to increase by $3.57, holding microprocessor speed constant. 15) C 16) B 17) D 18) B 19) D 20) A

14)

21) To determine if number of checks cashed per day is a positive linear predictor of number of man-hours worked, we test:

30) To determine if the model is useful for predicting y, we test:

32) To determine if the model is useful for predicting y, we test:

H0 : 1 = 2 = 3 = 4= 5=0

H0 : 1 = 2 = 0 Ha : At least one

Ha : At least one i 0

H0 : 2 = 0 Ha : 2 > 0

The test statistic is F = 11.69.

The test statistic is t = 1.824

The p-value is p = .0001.

The p-value is p = .0857/2 = .04285

At = .01, > p so H0 is rejected. There

At = .05, > p and H0 is rejected. There

is sufficient evidence to indicate the model is adequate for predicting student GPA. 31) 19.3% of the total variation of the sampled student GPAs can be explained by the least squares regression model after adjusting for sample size and number of independent variables in the model.

is sufficient evidence to indicate that the number of checks cashed per day is a positive linear predictor of the number of man-hours worked at = .05. 22) A 23) C 24) C 25) B 26) A 27) B 28) C 29) D

i 0 The test statistic is F = 13.267. The p-value is p = .0003. At = .025, > p-value, so H0 is rejected. There is sufficient evidence to indicate the model is useful for predicting the number of man-hours worked at = .025. 33) To determine if the model is useful for predicting the retail price of a computer, we test: H0 : 1 = 2 = 0 Ha : At least one i 0 The test statistic is F = 19.018. The p-value is p = .0001. At = .01, > p-value and H0 is rejected. There is sufficient evidence to indicate the model is useful for predicting the retail price of a computer at = .01.

Answer Key Testname: SB14ECH12TEST

34) a. y = 7.6253 + 2.4190x 1 + .5632x 2

b. The 95% confidence interval for 1 is (1.33, 3.51).

We are 95% confident that y increases between 1.33 and 3.51 for each 1-unit increase in x 1 , holding x 2 fixed.

c. The 95% confidence interval for 2 is (-.42, 1.54).

Since the interval includes 0, we cannot conclude that a linear relationship between y and x 2 exists, while holding x 1 fixed. d.

R2 = .8745 and 2 Ra = .8597; About

87.45% of the variation in y values can be attributed to the relationship between y and x 1

and x 2 . About 85.97% of the variation in y-values can be attributed to this relationship, after adjusting for sample size and number of independent variables. e. The p-value for the test is p = 2.18 × 108 . Since p < , we

or predicting y. 35) The p-value for the test is p = .4271. Since p > , we do not reject the null hypothesis. There is insufficient evidence to conclude that the quiz grades are a useful predictor of the test grade. 36) B 37) C 38) B 39) We are 95% confident that a 386 CPU computer with 33 megahertz speed will have a retail price between $3,942.70 and $4,987.10. 40) A 41) A 42) B

49) a. y = 16.7220 3.0373x 1 - 1.0465x 2 + 4.0717x 1 x 2

b. We test the null hypothesis H0 : 1 =

2 = 3 = 0. The F-statistic is 9394, and the associated level of significance is 2.11 × 10-11. Since

the level of significance is less than , we reject the null hypothesis and conclude the model is useful for estimating or predicting values of y. c. We test the null hypothesis H0 : 3 = 0 against Ha : 3 > 0. The t-statistic is 9.17, and two-tailed p-value is 9.48 × 10-5 . The

43) a. y = -1125.433 + 16.8969x 1 + .097421x 2

b. (499.9, 614.0) c. (369.0, 744.9) 44) B 45) C 46) A 47) E(y) = 0 + 1 x 1 + 2 x2 + 3 x 1x 2

upper-tailed p-value is 4.74 ×10-5 . Since this value is less than , we reject the null hypothesis and conclude that x 1 and

x 2 interact positively.

48) A

d. 50) A 51) A 52) B 53) B

reject the null hypothesis in favor of the alternative hypothesis. There is sufficient evidence to conclude that the model is statistically useful for estimating

31.39

54) To determine if the relationship between college GPA and SAT score depends on high school GPA, we test H0 : 3 = 0 vs Ha : 3 0. A t-test on 3 would provide the necessary information. 55) No, the p-value for the coefficient of x 1 x 2 is p = .21 which exceeds the value of . 56) B 57) A 58) B 59) C 60) B 61) B 62) D 63) B 64) D 65) C 66) C

Answer Key Testname: SB14ECH12TEST

67) A second-order (quadratic) model seems to be a good fit because as x increases the y values initially decrease and then increase.

72) To determine if the quadratic term is useful for predicting the demand for the gem, we test:

73) a. y = -.2023 + .5796x 1 + .5030x 2 + 1.9761x 1 x 2 -

.0268x 1 2 + .0129x 2 2

b. The F-value for the test of H0 : 1 = 2

H0 : 2 = 0 Ha : 2 0

= 3 = 4 = 5 = 0 is 56,487.98 and the p-value is 6.13 × 1039, which is

The test statistic is t = .95.

less than = .05. Thus, we may reject the null hypothesis and conclude that at least one of 1 , 2 , 3 ,

The p-value is p = .3647. Since = .10 < p = .3647, H0 cannot be

68) D 69) C 70) D 71) B

4 , and 5 is nonzero. c. The t-value for the test of H0 : 3 = 0

rejected. There is insufficient evidence to indicate the quadratic term is useful for predicting the demand for the gem.

is 89.78 and the p-value is 1.93 × 10-26, which is less than = .01. Thus, we may reject the null hypothesis and conclude that 3 is not zero. d. The t-value for the test of H0 : 4 = 0

is -1.06 and the p-value is .3033, which is greater than = .01. Thus, we may not reject the null hypothesis. There is insufficient evidence to conclude that 4 is not zero.

74) B 75) A

76) To determine if the model is useful for predicting the demand for the gem, we test: H0 : 1 = 2 = 0 Ha : At least one i 0 The test statistic is F = 373. The p-value is p = .0001. Since = .01 > p = .0001, H0 is rejected. There is sufficient evidence to indicate the model is useful for predicting the demand for the gem.

Answer Key Testname: SB14ECH12TEST

77) a.

y = -616.64 +

919.10x - 329.43x 2 b.

78) a. A quadratic model seems to be a good fit because as x increases the y values initially increase and then decrease.

86) The number of levels of the qualitative variable is one greater than the number of dummy variables, so there are 4 levels of the qualitative variable. 87) D 88) a. level 1: 14.5; level 2: 14.5 + 3 = 17.5; level 3: 14.5 - 4 = 10.5; level 4: 14.5 + 10 = 24.5; level 5: 14.5 + 8 = 22.5 b. H0 : 1 = 2 = 3 = 4=0 Ha : At least one

Test H0 : 2 = 0 against Ha : 2 < 0.

The t-value for the test is -15.79 and the p-value is 3.32 × 109 , which is less than = .05. Thus, we may reject the null hypothesis and conclude that 2 is

negative. There is sufficient evidence of downward curvature in the relationship between profit and price.

of the parameters 1 , 2 , 3 , and 4 differs

from 0 89) a. E(y) = 0 + 1 x, where x = {1 if male, 0 if not}

b. y = 1.0303 +

3.3968x - .5218x 2 c. See part a. 79) A 80) B 81) D 82) B 83) C 84) A

b. y = 16.9167 1.2917x c. H0 : 1 = 0

85) E(y) = 0 + 1 x, where x = 0 = mean sale price of properties not near a cove 1 = difference in mean sale prices of properties near a cove and properties not near a cove

d. The p-value is 0.1929, which is 1 if property near ,Cove greater than so we 0 if reject not the null do not hypothesis. There is not sufficient evidence to conclude that the model is useful. 90) A 91) A 92) A 93) D 94) A 95) B

96) a.

E(y) = 0 + 1 x 1 + 2 x2 + 3 x 1x 2 where x 1 = price and x 2 = {1 if free

standing, 0 if mall} ^

b. y = 491.446 95.450x 1 - 37.520x 2 + 19.189x 1 x 2 ^

c. mall: y = 491.446 - 95.450x 1 ; free ^

standing: y = 453.926 - 76.261x 1 d.

Test H0 : 3 = 0 against Ha : 3 0.

The test value is t = .5195, and the p-value is p = .6115. Since the p-value is greater than .01, there is insufficient evidence of interaction between the two variables. We cannot conclude that the change in number of sandwiches sold with respect to price is different for mall and free-standing stores. 97) A 98) B 99) B 100) D 101) D 102) B

Answer Key Testname: SB14ECH12TEST

103) To determine if the quadratic component of the model is useful, we need to conduct a nested model F-test. The test would compare the current model (i.e., the full model) to the one that does not contain the quadratic terms (i.e., the reduced model). We test the following hypotheses:

104) a. y = 14.2298 .0690x 1 + .3511x 2 +

H0 : 2 = 5 = 0 Ha : At least one of

6.49. The rejection region based on v 1 = 3 and v 2 = 18 is

2 and 5 differs from 0

114) In order to check the variance assumption,

.03334x 2 2

both y and = y - y must be calculated for each of the data values. A scatterplot

of the residuals, , versus the predicted

.001252x 1 x 2 + .000085x 1 2 b.

H0 : 3 = 4 = 5

Ha : At least one of the parameters 3 ,

sale prices, y, should be constructed. If the plot reveals a random scattering of points, then the assumption of equal variances is satisfied. 115) A 116) A 117) B 118) B 119) B 120) A 121) The curvilinear trend suggests that the model might benefit from an x 2 term.

4 , and 5 differs from 0 The test statistic is F = (.1435 - .0689)/3 = .003829

F > 3.16. Since the test statistic falls in the rejection region, we reject H0 and

conclude that at least one of the second-order terms contributes information for the prediction of y. 105) A 106) B 107) A 108) B 109) A 110) A 111) A 112) B 113) A

122) The random pattern about the 0 line indicates that the linear model is a good fit. 123) It appears that the data may contain an outlier. 124) B 125) B 126) A 127) A 128) B 129) C 130) Yes, there is evidence of multicollinearity. The F-test for overall model adequacy shows much greater significance than either of the t-tests for the individual parameters. 62

131) a. y = 3449.598 41.306x 1 - 1.627x 2 + .02183x 1 x 2

b. First indicator: The F-test for overall model adequacy shows much greater significance than any of the t-tests for the individual parameters. Second indicator: The signs of two of the parameters are negative when we expect them to be positive. c. Since the high temperature of 103°F and 3500 people at the park do not fall within the ranges of observed values for the corresponding variables, the model should not be used to make a prediction for these values.

McClave Statistics for Business and Economics 14e Chapter 13 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 1) The quality of a product is indicated by the extent to which it satisfies the needs and preferences of its manufacturer. A) True B) False Objective: (13.1) Define Quality, Processes, and Systems

2) Performance, reliability, and durability are some of the factors used to evaluate quality. A) True

B) False

Objective: (13.1) Define Quality, Processes, and Systems

3) Conformance refers to the extent to which a good or service can be adapted for use in new situations. A) True B) False Objective: (13.1) Define Quality, Processes, and Systems

4) A process adds value to the inputs of the process. A) True

B) False

Objective: (13.1) Define Quality, Processes, and Systems

5) A system receives inputs from its environment, transforms those inputs to outputs, and delivers them to its environment. A) True B) False Objective: (13.1) Define Quality, Processes, and Systems

6) With rare exceptions, all items produced by a process are identical. A) True B) False Objective: (13.1) Define Quality, Processes, and Systems

7) If quality is designed into products and process management is used in their production, mass inspection of finished products will not be necessary. A) True B) False Objective: (13.1) Define Quality, Processes, and Systems

8) People, machines, and raw materials can all contribute to the variability in the output of a system. A) True B) False Objective: (13.1) Define Quality, Processes, and Systems

9) Control charts are the tool of choice for continuously monitoring processes. A) True B) False Objective: (13.2) Understand Statistical Control

10) The centerline of a control chart is drawn at the level of the median of the sample. A) True B) False Objective: (13.2) Understand Statistical Control

11) The distribution that describes the output variable of a process may change over time. A) True B) False Objective: (13.2) Understand Statistical Control

12) The variation in the output of processes that are out of control can be entirely attributed to random behavior. A) True B) False Objective: (13.2) Understand Statistical Control

13) A business that operates out-of-control processes risks losing its customers and threatens its own survival. A) True B) False Objective: (13.2) Understand Statistical Control

14) The elimination of common causes of variation is typically the responsibility of workers, not management. A) True B) False Objective: (13.2) Understand Statistical Control

15) Special causes of variation can often be diagnosed and eliminated by workers or their immediate supervisors. A) True B) False Objective: (13.2) Understand Statistical Control

16) Most processes are naturally in a state of statistical control. A) True

B) False

Objective: (13.2) Understand Statistical Control

Solve the problem. 17) The process of monitoring and eliminating variation in order to keep a process in a state of control or to bring a process into control is called A) random behavior. B) statistical process control. C) a control chart. D) a process distribution. Objective: (13.2) Understand Statistical Control

Determine whether the statement is true or false. 18) Control charts are used to help us differentiate between process variation due to common causes and special causes. A) True B) False Objective: (13.3) Understand Control Charts

19) Control charts are useful for evaluating the past performance of a process, for monitoring its current performance, and for predicting future performance. A) True B) False Objective: (13.3) Understand Control Charts

20) Control charts may only be used for quantitative quality variables. A) True B) False Objective: (13.3) Understand Control Charts

21) The upper and lower control limits are positioned so that when the process is in control the probability of an individual value of the output variable falling outside the control limits is very large. A) True B) False Objective: (13.3) Understand Control Charts

22) If one or more values fall outside the control limits, then either a rare event has occurred or the process is out of control. A) True B) False Objective: (13.3) Understand Control Charts

23) If all points fall between the control limits, then we may safely conclude that the process is in statistical control. A) True B) False Objective: (13.3) Understand Control Charts

24) If we are unable to conclude that the process is out of control, it is better to behave as if the process were under control than to tamper with the process. A) True B) False Objective: (13.3) Understand Control Charts

25) Control limits and specification limits are essentially the same thing. A) True B) False Objective: (13.3) Understand Control Charts

Solve the problem. 26) _______ are boundary points that define the acceptable values for an output variable. A) Control bounds B) Tolerance limits C) Capability limits Objective: (13.3) Understand Control Charts

27) The primary goal of quality-improvement activities is A) to increase variation. C) to increase the mean.

B) to reduce variation. D) to change the process.

Objective: (13.3) Understand Control Charts

28) The upper and lower control limits are usually a distance of _______ from the centerline. A) 2 standard deviations B) 3 standard deviations C) 1 standard deviation D) 3.5 standard deviations Objective: (13.3) Understand Control Charts

Determine whether the statement is true or false. 29) The x-chart is typically used in conjunction with an R-chart. A) True B) False Objective: (13.4) Construct and Interpret x-bar Chart

30) When constructing an x-chart, x is used as the estimator of µ. A) True B) False Objective: (13.4) Construct and Interpret x-bar Chart

D) Specification limits

31) An unbiased estimator for A) True

can be found by dividing the mean of the ranges, R by an appropriate constant. B) False

Objective: (13.4) Construct and Interpret x-bar Chart

32) Samples should be chosen in such a way that a change in the process mean occurs within a sample rather than between samples. A) True B) False Objective: (13.4) Construct and Interpret x-bar Chart

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 33) Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Objective: (13.4) Construct and Interpret x-bar Chart

34) Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Objective: (13.4) Construct and Interpret x-bar Chart

35) Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Objective: (13.4) Construct and Interpret x-bar Chart

36) Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Objective: (13.4) Construct and Interpret x-bar Chart

37) Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Objective: (13.4) Construct and Interpret x-bar Chart

38) Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Objective: (13.4) Construct and Interpret x-bar Chart

39) Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Objective: (13.4) Construct and Interpret x-bar Chart

40) Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Objective: (13.4) Construct and Interpret x-bar Chart

(Situation C) Ten samples of n = 5 were collected to construct an x-chart. The sample means and ranges for the 10 samples are shown below. Sample Mean 1 20.2 2 22.4 3 21.2 4 18.2 5 23.2

Range 2.7 1.8 1.5 1.2 2.4

Sample Mean 6 20.4 7 15.9 8 22.3 9 20.7 10 21.1

Range 1.9 1.0 2.1 1.6 1.8

41) Calculate the centerline for constructing the x-chart. Objective: (13.4) Construct and Interpret x-bar Chart

42) Calculate the upper and lower control limits for the x-chart. Objective: (13.4) Construct and Interpret x-bar Chart

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. (Situation D) A walk-in freezer thermostat at a restaurant is set at 5°F. Because of the perishability of the food in the freezer, the restaurant manager has decided to begin monitoring the temperature inside the freezer. The managers used a precision thermometer to take sample temperature readings at five randomly chosen times per day for 10 days. The data are presented below. Day 1 2 3 4 5 6 7 8 9 10

5.22 4.40 5.11 5.65 4.68 5.01 5.20 4.30 5.45 5.06

Temperature (°F) 5.29 5.11 4.95 4.41 4.63 6.03 5.43 4.90 4.55 4.24 5.09 4.82 5.92 4.71 4.67 5.26 6.10 5.20 4.99 5.15 5.96 4.91 5.03 4.97 5.62 6.11 5.13 5.13 4.95 5.59

4.78 4.83 5.23 5.50 4.75 5.25 5.35 4.80 4.90 5.80

43) Calculate the centerline for constructing the x-chart. A) 10.245 B) 5.1224

C) 5.0700

D) 5.3062

Objective: (13.4) Construct and Interpret x-bar Chart

44) Calculate the upper and lower control limits for the x-chart. A) upper: 5.45 B) upper: 5.89 C) upper: 5.73 lower: 4.80 lower: 4.35 lower: 4.51 Objective: (13.4) Construct and Interpret x-bar Chart

D) upper: 5.63 lower: 4.61

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. (Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24 ounces. The company would like to use control charts to monitor the performance of the machine. The company decides to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty measurement times are selected and the following information is recorded. Time Mean (oz) 1 23.8 2 24.5 3 23.9 4 24.2 5 23.7 6 23.5 7 24.2 8 24.4 9 24.1 10 24.2

Range (oz) 1.05 0.85 1.12 0.95 1.22 1.42 1.02 1.10 0.75 0.60

Time Mean (oz) Range (oz) 11 24.5 1.21 12 24.7 0.65 13 24.0 0.55 14 25.5 3.21 15 24.2 1.25 16 24.4 1.35 17 24.5 0.98 18 25.0 1.30 19 24.1 0.88 20 24.2 1.01

45) Calculate the centerline for constructing the x-chart. Objective: (13.4) Construct and Interpret x-bar Chart

46) Calculate the upper and lower control limits for the x-chart. Objective: (13.4) Construct and Interpret x-bar Chart

47) Create the x-chart and interpret it. Objective: (13.4) Construct and Interpret x-bar Chart

Solve the problem. 48) The table below shows the data from samples of size n = 5 randomly chosen from the outputs of a process on 20 different days. Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a.

4.5 3.6 5.1 4.9 4.1 3.7 5.6 4.8 6.1 2.4 3.7 4.5 5.2 3.4 4.8 4.1 4.6 5.1 3.7 5.4

2.1 3.5 6.2 5.4 3.8 4.6 4.7 5.1 4.6 4.8 5.3 3.4 2.7 5.5 3.6 4.6 3.7 4.2 4.8 3.9

Data 5.4 6.1 2.4 3.5 3.8 4.8 4.1 4.3 4.7 5.6 2.9 3.4 5.1 4.6 4.8 4.9 3.5 5.6 4.9 4.2

2.7 4.9 3.7 5.4 4.6 4.2 5.1 4.6 3.8 4.1 4.7 5.2 6.2 2.4 4.4 4.9 3.7 4.1 2.3 5.4

4.5 4.2 5.1 3.7 4.9 5.2 3.1 2.7 4.2 4.8 6.3 4.5 2.9 3.4 4.6 4.3 5.2 5.7 4.5 4.3

Calculate x.

b. Calculate R. c. Find d2 and A2 . d. Construct an x-chart. e. Is the process out of control? Explain. Objective: (13.4) Construct and Interpret x-bar Chart

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 49) The R-chart is used to detect changes in process variation. A) True

B) False

Objective: (13.5) Construct and Interpret R-Chart

50) When n 6, the R-chart contains only one control limit, the lower control limit. A) True B) False Objective: (13.5) Construct and Interpret R-Chart

51) If the R-chart indicates that the process variation is in control, then it makes sense to construct and interpret the x chart. A) True B) False Objective: (13.5) Construct and Interpret R-Chart

(Situation F) Ten samples of n = 5 were collected to construct an R-chart. The sample means and ranges for the 10 samples are shown below. Sample Mean 1 20.2 2 22.4 3 21.2 4 18.2 5 23.2

Range 2.7 1.8 1.5 1.2 2.4

Sample Mean 6 20.4 7 15.9 8 22.3 9 20.7 10 21.1

Range 1.9 1.0 2.1 1.6 1.8

52) Calculate the centerline of the R-chart. A) 4.114 B) 2.057

C) 1.0386

D) 1.80

Objective: (13.5) Construct and Interpret R-Chart

53) Calculate the upper and lower control limits for the R-chart. A) Upper = 4.3485, Lower = 0 B) Upper = 3.1986, Lower = 0.4014 C) Upper = 3.6553, Lower = 0.4014 D) Upper = 3.8052, Lower = 0 Objective: (13.5) Construct and Interpret R-Chart

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. (Situation D) A walk-in freezer thermostat at a restaurant is set at 5°F. Because of the perishability of the food in the freezer, the restaurant manager has decided to begin monitoring the temperature inside the freezer. The managers used a precision thermometer to take sample temperature readings at five randomly chosen times per day for 10 days. The data are presented below. Day 1 2 3 4 5 6 7 8 9 10

5.22 4.40 5.11 5.65 4.68 5.01 5.20 4.30 5.45 5.06

Temperature (°F) 5.29 5.11 4.95 4.41 4.63 6.03 5.43 4.90 4.55 4.24 5.09 4.82 5.92 4.71 4.67 5.26 6.10 5.20 4.99 5.15 5.96 4.91 5.03 4.97 5.62 6.11 5.13 5.13 4.95 5.59

4.78 4.83 5.23 5.50 4.75 5.25 5.35 4.80 4.90 5.80

54) Calculate the centerline of the R-chart. Objective: (13.5) Construct and Interpret R-Chart

55) Calculate the upper and lower control limits for the R-chart. Objective: (13.5) Construct and Interpret R-Chart

56) Create the R-chart and interpret it. Objective: (13.5) Construct and Interpret R-Chart

(Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24 ounces. The company would like to use control charts to monitor the performance of the machine. The company decides to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty measurement times are selected and the following information is recorded. Time Mean (oz) 1 23.8 2 24.5 3 23.9 4 24.2 5 23.7 6 23.5 7 24.2 8 24.4 9 24.1 10 24.2

Range (oz) 1.05 0.85 1.12 0.95 1.22 1.42 1.02 1.10 0.75 0.60

Time Mean (oz) Range (oz) 11 24.5 1.21 12 24.7 0.65 13 24.0 0.55 14 25.5 3.21 15 24.2 1.25 16 24.4 1.35 17 24.5 0.98 18 25.0 1.30 19 24.1 0.88 20 24.2 1.01

57) Calculate the centerline of the R-chart. Objective: (13.5) Construct and Interpret R-Chart

58) Find the upper and lower control limits for the R-chart. Objective: (13.5) Construct and Interpret R-Chart

Solve the problem. 59) The table below shows the data from samples of size n = 5 randomly chosen from the outputs of a process on 20 different days. Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a.

4.5 3.6 5.1 4.9 4.1 3.7 5.6 4.8 6.1 2.4 3.7 4.5 5.2 3.4 4.8 4.1 4.6 5.1 3.7 5.4

2.1 3.5 6.2 5.4 3.8 4.6 4.7 5.1 4.6 4.8 5.3 3.4 2.7 5.5 3.6 4.6 3.7 4.2 4.8 3.9

Data 5.4 6.1 2.4 3.5 3.8 4.8 4.1 4.3 4.7 5.6 2.9 3.4 5.1 4.6 4.8 4.9 3.5 5.6 4.9 4.2

2.7 4.9 3.7 5.4 4.6 4.2 5.1 4.6 3.8 4.1 4.7 5.2 6.2 2.4 4.4 4.9 3.7 4.1 2.3 5.4

4.5 4.2 5.1 3.7 4.9 5.2 3.1 2.7 4.2 4.8 6.3 4.5 2.9 3.4 4.6 4.3 5.2 5.7 4.5 4.3

Find D3 and D4 .

b. Construct an R-chart. c. Is the process out of control? Explain. Objective: (13.5) Construct and Interpret R-Chart

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 60) The p-chart is typically used to monitor the proportion of units that conform to specification. A) True B) False Objective: (13.6) Construct and Interpret p-Chart

61) The p-chart is based on the assumption that the number of defective units in each sample is a binomial random variable. A) True B) False Objective: (13.6) Construct and Interpret p-Chart

62) In constructing a p-chart, it is advisable to use a much smaller sample size than is typically used for x- and R-charts. A) True B) False Objective: (13.6) Construct and Interpret p-Chart

63) The centerline and control limits of a p-chart should be developed using samples that were collected during a period in which the process was in control. A) True B) False Objective: (13.6) Construct and Interpret p-Chart

(Situation A) To construct a p-chart for a manufacturing process, 20 samples of size 100 were selected. The results are shown below: Sample 1 2 3 4 5 6 7 8 9 10

Sample Size 100 100 100 100 100 100 100 100 100 100

Defectives 10 8 9 6 7 3 8 6 11 10

Sample 11 12 13 14 15 16 17 18 19 20

Sample Size 100 100 100 100 100 100 100 100 100 100

64) Calculate the centerline used in constructing a p-chart. A) .0706 B) .0532

Defectives 8 8 5 9 7 9 11 4 6 8

C) .0765

D) .0266

Objective: (13.6) Construct and Interpret p-Chart

65) Calculate the upper and lower control limits for the p-chart. A) p ± .0266 B) p ± .1783 C) p ± .0532

D) p ± .0797

Objective: (13.6) Construct and Interpret p-Chart

(Situation B) A manufacturing company makes hemostats for hospital emergency rooms. The company is interested in implementing statistical process control procedures in its production operation. The production manager believes that the proportion of defective hemostats generated by the process is about 3%. The company collected one sample of 300 consecutively manufactured hemostats each day for 20 days. The data are shown below. Sample 1 2 3 4 5 6 7 8 9 10

Sample Size 300 300 300 300 300 300 300 300 300 300

Defectives 8 6 11 15 12 11 9 6 5 4

Sample 11 12 13 14 15 16 17 18 19 20

Sample Size 300 300 300 300 300 300 300 300 300 300

66) Calculate the centerline used in constructing a p-chart. A) .0297 B) .0593 Objective: (13.6) Construct and Interpret p-Chart

Defectives 12 11 14 8 7 3 9 11 10 6

C) .0317

D) .0245

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 67) Find the upper and lower control limits for the p-chart. Objective: (13.6) Construct and Interpret p-Chart

68) Construct the p-chart and interpret it. Objective: (13.6) Construct and Interpret p-Chart

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 69) Statistical process control consists of monitoring process variation, diagnosing causes of variation, and eliminating those causes. A) True B) False Objective: (13.7) Understand Causes of Variation

70) The diagnosis phase of statistical process control is concerned with tracking down causes of variation. A) True B) False Objective: (13.7) Understand Causes of Variation

71) When using a cause-and-effect diagram in process diagnosis, you begin by specifying the cause of interest and then move forward to identify potential effects of this cause. A) True B) False Objective: (13.7) Understand Causes of Variation

72) Capability analysis is used to determine when process variation is unacceptably high. A) True B) False Objective: (13.8) Understand Capability Analysis

73) A process may be in control but still not be capable of producing output that is acceptable to customers. A) True B) False Objective: (13.8) Understand Capability Analysis

74) If a capability analysis study indicates that an in-control process is not capable, it is usually off-centeredness, rather than variation, that is the culprit. A) True B) False Objective: (13.8) Understand Capability Analysis

Solve the problem. 75) The capability index for a process centered on the desired mean is (USL - LSL) 6 3 A) Cp = B) Cp = C) Cp = 6 (USL - LSL) (USL - LSL)

D) Cp =

(USL - LSL) 3

Objective: (13.8) Understand Capability Analysis

76) A process is considered capable if A) Cp 1. B) Cp 1.

C) Cp > 1.

Objective: (13.8) Understand Capability Analysis

D) Cp < 1.

77) An in-control, centered process that follows a normal distribution has a Cp of 3.0. How many standard deviations away from the process mean is the upper specification limit? A) 9 B) 18 C) 3

D) 6

Objective: (13.8) Understand Capability Analysis

78) An in-control, centered process that follows a normal distribution has a Cp = 0.6667. How many standard deviations away from the process mean is the upper specification limit? 2 A) 2 B) C) 3 3

D) 4

Objective: (13.8) Understand Capability Analysis

79) A process is in control and has a normally distributed output distribution with mean of 1000 and a standard deviation of 100. The upper and lower specification limits for the process are 1060 and 940, respectively. Assuming no changes in the behavior of the process, what percentage of the output will be unacceptable? A) 61.51% B) 54.86% C) 45.14% D) 38.49% Objective: (13.8) Understand Capability Analysis

80) A process is in control and has a normally distributed output distribution with mean of 1000 and a standard deviation of 100. The upper and lower specification limits for the process are 1060 and 940, respectively. Find the Cp value of the process. Is the system capable? A) Cp = 3.333; the system is not capable.

B) Cp = 0.2; the system is capable.

C) Cp = 3.333; the system is capable.

D) Cp = 0.2; the system is not capable.

Objective: (13.8) Understand Capability Analysis

81) Find the specification spread when USL = 9.41 and LSL = 3.79. A) 5.62 B) 6.62 C) 7

D) 5.72

Objective: (13.8) Find Specification/Process Spreads

82) Find the process spread when A) 78

= 13. B) 26

C) 156

D) 39

C) 21.6

D) 7.2

C) 642.48

D) 214.16

C) 0.0096

D) 0.0192

Objective: (13.8) Find Specification/Process Spreads

83) Find the process spread when A) 43.2

= 3.6. B) 10.8

Objective: (13.8) Find Specification/Process Spreads

84) Estimate the process spread when s = 107.08. A) 1284.96 B) 321.24 Objective: (13.8) Find Specification/Process Spreads

85) Estimate the process spread when s = 0.0032. A) 0.0384 B) 0.0064 Objective: (13.8) Find Specification/Process Spreads

86) Find the value of Cp when USL = 1.0155, LSL = 1.0065, s = 0.0015. A) 6

B) 0.1667

C) 2

Objective: (13.8) Find Specification/Process Spreads

D) 1

87) Find the value of Cp when USL = 1.0155, LSL = 1.0065, s = 0.002. A) 4.5

B) 0.375

C) 0.75

D) 1.5

Objective: (13.8) Find Specification/Process Spreads

88) Find the value of Cp when USL = 1.0155, LSL = 1.0065, s = 0.0005. A) 3

B) 0.3333

C) 0.0556

D) 18

Objective: (13.8) Find Specification/Process Spreads

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 89) The table below shows the data from samples of size n = 5 randomly chosen from the outputs of a process on 20 different days. Assume the specification limits are USL = 2.1 and LSL = 5.7. Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a. b. c.

4.5 3.6 5.1 4.9 4.1 3.7 5.6 4.8 6.1 2.4 3.7 4.5 5.2 3.4 4.8 4.1 4.6 5.1 3.7 5.4

2.1 3.5 6.2 5.4 3.8 4.6 4.7 5.1 4.6 4.8 5.3 3.4 2.7 5.5 3.6 4.6 3.7 4.2 4.8 3.9

Data 5.4 6.1 2.4 3.5 3.8 4.8 4.1 4.3 4.7 5.6 2.9 3.4 5.1 4.6 4.8 4.9 3.5 5.6 4.9 4.2

2.7 4.9 3.7 5.4 4.6 4.2 5.1 4.6 3.8 4.1 4.7 5.2 6.2 2.4 4.4 4.9 3.7 4.1 2.3 5.4

4.5 4.2 5.1 3.7 4.9 5.2 3.1 2.7 4.2 4.8 6.3 4.5 2.9 3.4 4.6 4.3 5.2 5.7 4.5 4.3

Assuming the process is under control, construct a capability analysis diagram for the process. Find the percentage of data items that fall outside the specification limits. Is the process capable? Support your answer with a numerical measure of capability.

Objective: (13.8) Construct and Interpret Capability Analysis Diagram

Answer Key Testname: SB14ECH13TEST

1) B 2) A 3) B 4) A 5) A 6) B 7) A 8) A 9) A 10) B 11) A 12) B 13) A 14) B 15) A 16) B 17) B 18) A 19) B 20) B 21) B 22) A 23) B 24) A 25) B 26) D 27) B 28) B 29) A 30) A 31) A 32) B 33) in control 34) out of control; six points in a row steadily increasing 35) in control 36) out of control; four out of five points in a row in Zone B or beyond 37) in control 38) out of control; fourteen points in a row alternating up and down 39) in control 40) out of control; nine points in a row in Zone C or beyond

48) a. b. c.

41) x = 20.56 42) upper control limit: 20.56 + 1.04 = 21.60; lower control limit: 20.56 - 1.04 = 19.52 43) B 44) C 45) 24.28 46) 24.28 ± 0.3460 x1 + x2 + ... + x20 47) x = k =

56) The R-chart is:

4.389 2.29 d2 = 2.326 and

A2 = 0.577 d.

485.6 = 24.28 20

R= R1 + R 2 + ... + R 20 k

The process appears to be in control.

57) R = R1 + R 2 + ... + R 20

22.47 = 1.1235 20

Upper Control Limit

58) Upper Control Limit

e. There are no patterns evident in the control chart to indicate that the process is out of control. 49) A 50) B 51) A 52) D 53) D

= x + A2 R = 24.28 + 0.308(1.1235) = 24.63 Lower Control Limit = x - A2 R = 24.28 0.3081(1.1235) = 23.93

54) R = R1 + R 2 + ... + R 10 k

= RD4 = 1.1235(1.777) = 1.996 Lower Control Limit = RD3 = 1.1235(0.223) = 0.251

10.53 = 1.053 10

55) Upper Control Limit = RD4 = 1.053(2.114) = 2.226 Lower Control Limit

The process is out of control.

= RD3 = 1.053(0) = 0

Answer Key Testname: SB14ECH13TEST

59) a.

D3 = 0 and D4 = 2.114 b.

77) A 67) p = 78) A Total defectives in all samples 79) B Total units sampled 80) D 178 = = .0297 81) A 6000 82) A 83) C Upper Control Limit 84) C p(1 - p) 85) D = p +3 = n 86) D 87) C .0297 + 3 88) A .0297(.9703) = 89) a. 300 .0591 Lower Control Limit =p-3

c. There are no patterns evident in the control chart to indicate that the process variation is out of control. 60) B 61) A 62) B 63) A 64) C 65) D 66) A

p(1 - p) = n

.0297 - 3 .0297(.9703) = 300

68)

.0003

b. 5% c.

5.7 - 2.1 Cp = 6(.939363)

.64; Since this value is less than 1, the process is not capable.

The process is out of control as a decreasing run of seven in a row is detected. 69) A 70) A 71) B 72) A 73) A 74) B 75) A 76) A

McClave Statistics for Business and Economics 14e Chapter 14 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 1) Price indexes measure changes in the price of a commodity or group of commodities over time. A) True B) False Objective: (14.1) Understand Index Numbers

2) A composite index number represents combinations of the prices or quantities of several commodities. A) True B) False Objective: (14.1) Understand Index Numbers

3) The Laspeyres index is a weighted index while the Paasche index is not weighted. A) True B) False Objective: (14.1) Understand Index Numbers

4) The Laspeyres index uses the purchase quantities of the period as weights. A) True B) False Objective: (14.1) Understand Index Numbers

Solve the problem. 5) A(n) _______ is a number that measures the change in a variable over time relative to the value of the variable during a base period. A) index number B) residual value C) exponential smoothing constant D) time series Objective: (14.1) Understand Index Numbers

(Situation F) The sales (in thousands of dollars) of automobiles by the three largest American automakers from 1986 through 1992 are shown in the table below. Year 1986 1987 1988 1989 1990 1991 1992

G.M. 8993 7101 6762 6244 7769 8256 9305

Ford 5810 4328 4313 4255 4934 5585 5551

Chrysler 1796 1225 1283 1182 1494 2034 2157

6) Using 1986 as the base year, and only using the Chrysler sales data, find the simple index for 1992. A) 102.49 B) 83.26 C) 120.10 D) 97.57 Objective: (14.1) Compute Index Numbers

7) Using 1986 as the base year, find the simple composite index for 1990. A) 116.92 B) 65.81 C) 151.95 Objective: (14.1) Compute Index Numbers

D) 85.53

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 8) Using 1986 as the base year, find the simple composite index for 1992. Objective: (14.1) Compute Index Numbers

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. (Situation G) The number of industrial and construction failures in the United States by the type of firm for the years 1985-1996 is given in the table.

Year 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

Commercial Manufacturing Service Construction and Mining 1637 2262 1645 1331 1770 1360 1041 1463 1122 773 1204 1013 930 1378 1165 1594 2355 1599 2366 3614 2223 3840 4872 3683 8627 5247 4433 12,787 6936 5759 16,647 7004 5662 20,911 7035 5641

Retail Trade 4799 4139 3406 2889 3183 4910 6882 9730 11,429 13,787 13,501 13,509

Wholesale Trade 1089 1028 887 740 908 1284 1709 2783 3598 4882 4835 4808

9) Using 1985 as the base period and using just construction failures, calculate the simple index for 1992. A) 215.38 B) 487.20 C) 217.88 D) 46.43 Objective: (14.1) Compute Index Numbers

10) Using 1985 as the base year and using all five types of firms, calculate the simple composite index for 1995. A) 217.88 B) 476.49 C) 416.80 D) 23.99 Objective: (14.1) Compute Index Numbers

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 11) The table below shows the price of a commodity for each of ten consecutive years. Year Price

1 $1.19

2 $1.22

3 $1.23

4 $1.45

5 $1.39

6 $1.42

7 $1.47

8 $1.55

9 $1.62

10 $1.65

a. Using Year 1 as the base period, calculate the simple index for the price of the commodity for each year. b. Plot the simple indexes for years 1-10. c. Use the simple index to interpret the trend in the price of the commodity. Objective: (14.1) Compute Index Numbers

12) The table below shows the prices and quantities of three commodities for six consecutive years.

Year 1 2 3 4 5 6

Commodity A Price Quantity 250 1200 255 1500 253 2700 255 1800 259 2100 261 2000

Commodity B Price Quantity 121 3200 115 3500 128 2400 126 2800 129 2700 135 2500

Commodity C Price Quantity 675 1800 700 1900 714 2100 721 2500 725 3100 734 3900

a. Compute the Laspeyres price index for the six-year period, using Year 1 as the base period. b. Compute the Paasche price index for the six-year period, using Year 1 as the base period. c. Plot the Laspeyres and Paasche indexes on the same graph. Comment on the differences. Objective: (14.1) Compute Index Numbers

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 13) Smoothing techniques are used to remove rapid fluctuations in a time series so the general trend can be seen. A) True B) False Objective: (14.2) Understand Exponential Smoothing

14) The exponential smoothing constant can be any number between 0 and 100. A) True B) False Objective: (14.2) Understand Exponential Smoothing

15) Smaller choices of the exponential smoothing constant w assign more weight to the current value of the series and yield a smoother series. A) True B) False Objective: (14.2) Understand Exponential Smoothing

16) One of the major weaknesses of exponential smoothing is that it is not easily adapted to forecasting. A) True B) False Objective: (14.2) Understand Exponential Smoothing

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. Year 1980 1981 1982 1983 1984 1985

Sales 1.740 1.444 0.896 1.289 1.455 4.882

17) Using a smoothing constant of w = 0.80, calculate the value of the exponentially smoothed series in 1983. A) 1.228 B) 1.289 C) 1.235 D) 1.340 Objective: (14.2) Calculate Exponentially Smoothed Series

18) Using a smoothing constant of w = 0.30, calculate the value of the exponentially smoothed series in 1982. A) 1.301 B) 1.289 C) 1.425 D) 1.150 Objective: (14.2) Calculate Exponentially Smoothed Series

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 19) Using a smoothing constant of w = 0.70, calculate the value of the exponentially smoothed series in 1985. Objective: (14.2) Calculate Exponentially Smoothed Series

Year 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

Retail Trade 4799 4139 3406 2889 3183 4910 6882 9730 11,429 13,787 13,501 13,509

Wholesale Trade 1089 1028 887 740 908 1284 1709 2783 3598 4882 4835 4808

20) Using just the wholesale trade failures and a smoothing constant w = 0.7, calculate the exponentially smoothed value for 1988. A) 845 B) 798.4 C) 932.9 D) 1015.6 Objective: (14.2) Calculate Exponentially Smoothed Series

(Situation H) The prices of coffee, gasoline, and sugar for each month of 1983 are shown below in the table.

Month January February March April May June July August September October November December

Price of Coffee (per pound) $1.47 $1.47 $1.47 $1.39 $1.36 $1.36 $1.36 $1.36 $1.36 $1.36 $1.36 $1.36

Price of Gasoline (per gallon) $1.15 $1.10 $1.06 $1.13 $1.18 $1.20 $1.21 $1.20 $1.19 $1.17 $1.16 $1.15

Price of Sugar (per pound) $0.32 $0.33 $0.32 $0.33 $0.33 $0.34 $0.34 $0.34 $0.34 $0.34 $0.33 $0.33

21) Using just the price of gasoline and a smoothing constant of w = 0.4, calculate the exponentially smoothed value for March. A) $1.076 B) $1.12 C) $1.102 D) $1.084 Objective: (14.2) Calculate Exponentially Smoothed Series

(Situation I) The average monthly retail prices (in cents per pound) of cotton and wool were recorded for each month of one year. This monthly time series appears in the table.

Month January February March April May June

Retail Prices Cotton Wool 60.2 294 61.0 287 63.9 287 65.8 284 66.2 275 64.0 257

Month July August September October November December

22) Using just the wool prices and a smoothing constant w = 0.8, find the exponentially smoothed value for May. A) 272.0 B) 275.0 C) 287.0 D) 276.9 Objective: (14.2) Calculate Exponentially Smoothed Series

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. (Situation K) Foreign Exchange rates, the values of foreign currency in U.S. dollars, are important to investors and international travelers. The table lists the monthly foreign exchange rates of the British pound (in U.S. dollars per pound) for a certain year. Month January February March April May June July August September October November December

Exchange Rate 1.13 1.10 1.13 1.23 1.25 1.28 1.38 1.39 1.36 1.42 1.44 1.44

23) Calculate the value of the exponentially smoothed series for April using a smoothing constant of w = 0.7. Objective: (14.2) Calculate Exponentially Smoothed Series

Solve the problem. 24) Consider the monthly time series shown in the table. Month January February March April May June July August September October November December a. b.

t 1 2 3 4 5 6 7 8 9 10 11 12

Y 185 192 189 201 195 199 206 203 208 209 218 216

Calculate the values in the exponentially smoothed series using w = 0.6. Graph the time series and the exponentially smoothed series on the same graph.

Objective: (14.2) Calculate Exponentially Smoothed Series

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 25) The _______ of a time series can account for fluctuations that recur during specific time periods. A) residual effect B) cyclical fluctuation C) secular trend D) seasonal effect Objective: (14.3) Understand Time Series Components

26) The tendency of a series of values to increase or decrease over a long period of time is known as the _______ of a time series. A) seasonal variation B) residual effect C) cyclical fluctuation D) secular trend Objective: (14.3) Understand Time Series Components

27) The _______ generally describes fluctuations of the time series that are attributable to business and economic conditions. A) seasonal variation B) cyclical effect C) residual effect D) secular trend Objective: (14.3) Understand Time Series Components

28) The _______ is what remains of a time series value after the secular, cyclical, and seasonal components have been removed. A) additive effect B) error effect C) residual effect D) exponential effect Objective: (14.3) Understand Time Series Components

Determine whether the statement is true or false. 29) The choice of exponential smoothing constant w has little or no effect on forecast values found using exponential smoothing. A) True B) False Objective: (14.4) Forecast Using Exponential Smoothing

30) The exponentially smoothed forecast takes into account both changes in trend and seasonality. A) True

B) False

Objective: (14.4) Forecast Using Exponential Smoothing

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. Year 1980 1981 1982 1983 1984 1985

Sales 1.740 1.444 0.896 1.289 1.455 4.882

31) Using the exponential smoothing technique to the data from 1980 to 1985, forecast the number of Chevrolet passenger cars sold to U.S. and Canadian dealers in 1986 using w = 0.3. A) 2.448 million cars B) 4.882 million cars C) 3.834 million cars D) 3.427 million cars Objective: (14.4) Forecast Using Exponential Smoothing

32) Using the exponential smoothing technique to the data from 1980 to 1985, forecast the number of Chevrolet passenger cars to be sold to U.S. and Canadian dealers in 1986 using w = 0.7. A) 3.427 million cars B) 2.448 million cars C) 4.882 million cars D) 3.834 million cars Objective: (14.4) Forecast Using Exponential Smoothing

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 33) The table below shows the price of a commodity for each of ten consecutive years. Year Price

1 $1.19

2 $1.22

3 $1.23

4 $1.45

5 $1.39

6 $1.42

7 $1.47

8 $1.55

9 $1.62

10 $1.65

Use exponential smoothing with w = 0.6 to forecast the price of the commodity in years 11 and 12. Objective: (14.4) Forecast Using Exponential Smoothing

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 34) The Holt forecasting model consists of both an exponentially smoothed component and a trend component. A) True B) False Objective: (14.5) Forecast Using Holt's Model

35) Smaller values of the trend smoothing constant v assign more weight to the most recent trend of the series and less to past trends. A) True B) False Objective: (14.5) Forecast Using Holt's Model

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. Year 1980 1981 1982 1983 1984 1985

Sales 1.740 1.444 0.896 1.289 1.455 4.882

36) Use the Holt forecasting model with trend to forecast the number of Chevrolet passenger cars sold to U.S. and Canadian dealers in 1990 using w = 0.4 and v = 0.5. A) 6.39 million cars B) 8.72 million cars C) 8.952 million cars D) 6.068 million cars Objective: (14.5) Forecast Using Holt's Model

37) Use the Holt forecasting model with trend to forecast the number of Chevrolet passenger cars sold to U.S. and Canadian dealers in 1990 using w = 0.6 and v = 0.5. A) 8.952 million cars B) 8.72 million cars C) 6.068 million cars D) 6.39 million cars Objective: (14.5) Forecast Using Holt's Model

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 38) Consider the monthly time series shown in the table. Month January February March April May June July August September October November December

t 1 2 3 4 5 6 7 8 9 10 11 12

Y 185 192 189 201 195 199 206 203 208 209 218 216

a. Use the values of Y in the table to forecast the values of Y for the next two months, using simple exponential smoothing with w = 0.7. b. Use the Holt model with w = 0.7 and v = 0.7 to forecast the values of Y for the next two months. Objective: (14.5) Forecast Using Holt's Model

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 39) Consider the actual values Y and forecast values F given in the table below. Time Period 1 2 3

Y 19.5 21.5 22.6

F 19.3 20.9 22.5

Calculate the mean absolute deviation (MAD) of the forecasts. A) 1.42 B) 0.37 C) 0.90

D) 0.30

Objective: (14.6) Calculate MAD, MAPE, and RMSE

40) Consider the actual values Y and forecast values F given in the table below. Time Period 1 2 3

Y 19.5 21.5 22.6

F 19.3 20.9 22.5

Calculate the mean absolute percentage error (MAPE) of the forecasts. A) 0.37 B) 1.42 C) 0.30 Objective: (14.6) Calculate MAD, MAPE, and RMSE

D) 0.90

41) Consider the actual values Y and forecast values F given in the table below. Time Period 1 2 3

Y 19.5 21.5 22.6

F 19.3 20.9 22.5

Calculate the root mean squared error (RMSE) of the forecasts. A) 0.90 B) 1.42 C) 0.30

D) 0.37

Objective: (14.6) Calculate MAD, MAPE, and RMSE

Determine whether the statement is true or false. 42) With N time periods in your data, a good rule of thumb is to forecast ahead no more than 2N time periods. A) True B) False Objective: (14.6) Interpret Forecast Accuracy

43) A major advantage of forecasting with smoothing techniques is that the standard deviation of the forecast errors is known prior to observing the future values. A) True B) False Objective: (14.6) Interpret Forecast Accuracy

44) Since the theoretical distributional properties of the forecast errors with smoothing methods are unknown, many analysts regard smoothing methods as descriptive procedures rather than inferential procedures. A) True B) False Objective: (14.6) Interpret Forecast Accuracy

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 45) Consider the table below which displays the price of a commodity for six consecutive years. Year 1 2 3 4 5 6

Price (dollars) 250 255 253 255 259 261

a. Calculate the values in the exponentially smoothed series using w = 0.6. b. Calculate the forecast errors for Years 7-10 if the actual values in those years are 262, 264, 263, 266 respectively. c. Calculate MAD, MAPE, and RMSE, using the forecast errors for Years 7-10. Objective: (14.6) Interpret Forecast Accuracy

46) Consider the table below which displays the price of a commodity for six consecutive years. Year 1 2 3 4 5 6

Price (dollars) 250 255 253 255 259 261

a. Use the Holt model to forecast values for Years 7-10 using w = 0.6 and v = 0.5. b. Calculate the forecast errors for Years 7-10 if the actual values in those years are 263, 267, 269, 268 respectively. c. Calculate MAD, MAPE, and RMSE, using the forecast errors for Years 7-10. Objective: (14.6) Interpret Forecast Accuracy

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 47) The least squares model is an excellent choice for forecasting time series since it works particularly well outside the region of known observations. A) True B) False Objective: (14.7) Forecast Using Simple Linear Regression

48) The straight-line regression model accounts for both the secular trend and the cyclical effect in a time series. A) True B) False Objective: (14.7) Forecast Using Simple Linear Regression

(Situation L) A farmer's marketing cooperative recorded the volume of wheat harvested by its members from 1991-2004. The cooperative is interested in detecting the long-term trend of the amount of wheat harvested. The data collected is shown in the table.

Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Wheat Harvested by Coop. Member (y, in thousands of bushels) 75 78 82 82 84 85 87 91 92 92 93 96 101 102

49) Find the least squares prediction equation for the model yt = 0 + 1 t + . ^

A) yt = 74.2 - 1.9165t

B) yt = 74.2 + 1.9165t

C) yt = -74.2 - 1.9165t

D) yt = 1.9165 - 74.2t

Objective: (14.7) Forecast Using Simple Linear Regression

50) Suppose the least squares regression equation is yt = 75 + 2t. Use the regression model to forecast the harvest in 2005. A) 110,000 bushels

B) 103,000 bushels

C) 105,000 bushels

D) 102,000 bushels

Objective: (14.7) Forecast Using Simple Linear Regression

51) Suppose the least squares regression equation is yt = 75 + 2t. Interpret the estimate of 1 in terms of the problem. A) We expect the volume of wheat harvested to increase 2000 bushels for each additional corporate member. B) We expect the volume of wheat harvested to be 2000 bushels in any given year. C) We expect the mean volume of wheat harvested to increase 2000 bushels from one year to the next. D) We expect to harvest 2000 bushels of wheat in 2005. Objective: (14.7) Forecast Using Simple Linear Regression

52) A forecast was obtained for the year 2005 and the corresponding 95% prediction interval was found to be (103, 107). Interpret this interval. A) We are 95% confident that the volume of wheat harvested in 2005 will be between 103,000 and 107,000 bushels. B) We are 95% confident that the mean volume of wheat harvested in all years will be between 103,000 and 107,000 bushels. C) We expect the volume of wheat harvested to increase between 103,000 and 107,000 bushels from one year to the next. D) We are 95% confident that the 2005 harvest will be between 103,000 and 107,000 bushels larger than the harvest in 2004. Objective: (14.7) Forecast Using Simple Linear Regression

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 53) Consider the table below which displays the price of a commodity for six consecutive years. Year 1 2 3 4 5 6

Price (dollars) 250 255 253 255 259 261

a. Use the method of least squares to fit the model E(Yt) = 0 + 1 t to the data. Write the prediction equation. b. Use the prediction equation to obtain forecasts of the prices in years 7 and 8. c. Find 95% prediction intervals for years 7 and 8. Objective: (14.7) Forecast Using Simple Linear Regression

54) Consider the monthly time series shown in the table. Month January February March April May June July August September October November December a. b. c.

t 1 2 3 4 5 6 7 8 9 10 11 12

Y 185 192 189 201 195 199 206 203 208 209 218 216

Use the method of least squares to fit the model E(Yt) = 0 + 1 t to the data. Write the prediction equation. Use the prediction equation to obtain forecasts for the next two months. Find 95% forecast intervals for the next two months.

Objective: (14.7) Forecast Using Simple Linear Regression

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 55) It is common to use dummy variables to describe seasonal differences in a time series. A) True B) False Objective: (14.8) Write and Interpret Regression Model with Trend and Seasonal Components

(Situation M) Fast food chains are closely watching what proposed legislation will do to consumption of "huge-sized meals" in the United States. Researchers have accumulated statistics on the annual consumption of "huge-sized meals" for the past 25 years. The goal of the analysis is to use the past data to predict future consumption and then compare the predicted consumption to the actual consumption in those years.

56) Propose a straight-line model for the long-term trend of the time series. Do not include a seasonal component. Let t = the year in which the data was collected (t = 1, 2, . . . , 25). A) E(Yt) = 1 t

B) E(Yt) = 0 + 1 Q1 + 3 Q2 + 4 Q3

C) E(Yt) = 0 + 1 t

D) E(Yt) = 0 + 1 t + 2 Q1 + 3 Q2 + 4 Q3

Objective: (14.8) Write and Interpret Regression Model with Trend and Seasonal Components

57) Propose a straight-line model that includes both a long-term trend and a seasonal component for the time series. Let t = the year in which the data was collected (t = 1, 2, . . . , 25) and let Q1 , Q2 , and Q3 be dummy variables used to model a seasonal effect.

A) E(Yt) = 0 + 1 t + 2 Q1 + 3 Q2 + 4 Q3

B) E(Yt) = 1 t

C) E(Yt) = 0 + 1 Q1 + 3 Q2 + 4 Q3

D) E(Yt) = 0 + 1 t

Objective: (14.8) Write and Interpret Regression Model with Trend and Seasonal Components

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 58) Retail sales for a home improvement store in quarters 1-4 over a five-year period are shown (in millions of dollars) in the table below. Quarter Year 1 2 3 4 5

1 1.2 1.3 1.4 1.4 1.6

2 1.4 1.6 1.8 1.7 2.0

3 1.5 1.5 1.8 1.9 2.1

4 1.1 1.2 1.6 1.6 1.9

a. Write a regression model that contains trend and seasonal components to describe the sales data. b. Use least squares regression to fit the model. c. Use the regression model to forecast the quarterly sales during Year 6. Give 95% prediction intervals for the forecasts. Objective: (14.8) Forecast Using Seasonal Regression Model

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 59) We plot time series residuals against observed values of Y to determine whether a cyclical component is apparent. A) True B) False Objective: (14.9) Understand Autocorrelation

60) Fourth-order autocorrelation in a quarterly time series may indicate seasonality. A) True B) False Objective: (14.9) Understand Autocorrelation

61) The value of the Durbin-Watson d-statistic always falls in the interval from 0 to 1. A) True B) False Objective: (14.9) Understand Autocorrelation

62) The d-test requires that the residuals be normally distributed. A) True B) False Objective: (14.9) Understand Autocorrelation

Solve the problem. 63) To test for first-order autocorrelation, we use the _______ test. A) Paasche B) Wilcoxon C) Laspeyres

D) Durbin-Watson

Objective: (14.9) Understand Autocorrelation

64) Which of the following statements about the Durbin-Watson d-statistic is true? A) It can assume any value between -4 and 4. B) It can assume any value between -4 and 0. C) It can assume any value between 0 and 2. D) It can assume any value between 0 and 4. Objective: (14.9) Understand Autocorrelation

(Situation N) An economist wishes to study the monthly trend in the Dow Jones Industrial Average (DJIA). Data collected over the past 40 months were used to fit the model E(Yt) = 0 + 1 t, where y = monthly close of the DJIA and t = month (1, 2, 3, . . . , 40). The regression results appear below: ^ y = 88 + 0.25t R2 = 0.37

MSE = 144

F = 4.25

Durbin-Watson d = 0.96

65) Since the data are recorded over time (months), there is a strong possibility that the residuals are positively correlated. How could you check for residual correlation using a graphical technique? ^

A) Plot the residuals against y and look for a linear trend. ^

B) Plot the residuals against y and look for outliers. ^

C) Plot the residuals against y and look for a funnel shape. D) Plot the residuals against t and look for long runs of positive and negative residuals. Objective: (14.9) Perform Durbin-Watson Test

66) What is the value of the test statistic for testing whether autocorrelation exists in the data? A) 0.37 B) 4.25 C) 0.96

D) 0.25

Objective: (14.9) Perform Durbin-Watson Test

67) Use the value of the Durbin-Watson test statistic to make a statement about autocorrelation of residuals in the regression model above. A) There is sufficient evidence (using = 0.05) to indicate that positive autocorrelation exists. B) Since the value lies in the inconclusive region (using = 0.05), we need more information before a definite conclusion can be drawn. C) There is insufficient evidence (using = 0.05) to indicate that positive autocorrelation exists. D) Approximately 98.5% of the residuals lie within 2 standard deviations of their mean 0. Objective: (14.9) Perform Durbin-Watson Test

(Situation O) Using data from the post-Korean war period, an economist modeled annual consumption, yt, as a function of total labor income, x 1t, and total property income, x 2t, with the following results. Assume data for n = 40 years were used in the analysis. ^

yt = 7.81 + 0.91x 1t + 0.57x 2t

s = 1.29

Durbin-Watson d = 2.09

68) For the situation above, set up the null and alternative hypotheses for testing for the presence of autocorrelation of residuals. A) H0 : 1 = 2 = 0 Ha : At least one

B) H0 : No first-order autocorrelation Ha : Positive or Negative first-order autocorrelation

C) H0 : No first-order autocorrelation Ha : Negative first-order autocorrelation

D) H0 : No first-order autocorrelation Ha : Positive first-order autocorrelation Objective: (14.9) Perform Durbin-Watson Test

69) For the situation above, give the rejection region for the Durbin-Watson test for autocorrelation of residuals. Use = 0.10. A) d < 1.39 B) d > 1.60 or 4 - d > 1.60 C) 1.39 < d < 1.60 D) d < 1.39 or 4 - d < 1.39 Objective: (14.9) Perform Durbin-Watson Test

70) Is there evidence of positive autocorrelation of residuals in the consumption model presented above? Test using = 0.10. A) Yes, since the Durbin-Watson statistic d = 2.09 falls in the rejection region. B) No, since the standard deviation s = 1.29 is small. C) Yes, since the standard deviation s = 1.29 is small. D) No, since the Durbin-Watson statistic d = 2.09 falls in the nonrejection region. Objective: (14.9) Perform Durbin-Watson Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 71) Consider the monthly time series shown in the table. Month January February March April May June July August September October November December

t 1 2 3 4 5 6 7 8 9 10 11 12

Y 185 192 189 201 195 199 206 203 208 209 218 216

a. Use the method of least squares to fit the model E(Yt) = 0 + 1t to the data. Write the prediction equation. b. Construct a residual plot for the model. c. Is there evidence of a cyclical component? Explain. Objective: (14.9) Perform Durbin-Watson Test

72) The printout below shows a regression analysis for a time series that included 20 observations. Regression Analysis: C2 versus C1 The regression equation is C2 = 1.20 + 0.0362 C1

Predictor Constant C1

Coef 1.19947 0.036241

S = 0.182361

SE Coef 0.08471 0.007072

R-Sq = 59.3%

T 14.16 5.12

P 0.000 0.000

R-Sq(adj) = 57.1%

Analysis of Variance Source Regression Residual Error Total

DF 1 18 19

SS 0.87340 0.59860 1.47200

MS 0.87340 0.03326

F 26.26

P 0.000

Durbin-Watson statistic = 1.87807 Locate the Durbin-Watson d-statistic and test the null hypothesis that there is no autocorrelation of residuals. Use = 0.10. Objective: (14.9) Perform Durbin-Watson Test

73) Consider the table below which displays the price of a commodity for six consecutive years. Year Price 1 250 2 255 3 253 4 255 5 259 6 261 a. Use the method of least squares to fit the model E(Yt) = 0 + 1t to the data. Write the prediction equation. b. Calculate the residuals and construct a residual plot. c. Calculate the Durbin Watson d statistic. Objective: (14.9) Perform Durbin-Watson Test

Answer Key Testname: SB14ECH14TEST

1) A 2) A 3) B 4) B 5) A 6) C 7) D 8) The simple composite index for 1992 is: I1992 = 9305 + 5551 + 2157 × 8993 + 5810 + 1796 100

= 102.49

9) A 10) C 11) a. Year

1 3 5 7 9 Index 100 103.36 116.81 123.53 136.13

2 4 6 8 10 102.52 121.85 119.33 130.25 138.66

price of the commodity is increasing with a sharp increase in Year 4 followed by a slight decrease in Year 5. During the ten-year period, the price of the commodity increased 38.66%. 12) a. Year Laspeyres Index 1 100 2 101.6717 3 105.0573 4 105.5094 5 106.6449 6 108.6321 b. Year 1 2 3 4 5 6

Paasche Index 100 101.6338 104.4819 105.5728 106.6402 108.3581

Though the values of the Laspeyres index tend to be slightly higher, there is actually very little difference between the values of the indexes. 13) A 14) B 15) B 16) B 17) C 18) C 19) The first value of the exponentially smoothed series is equal to the first value of the time series. The rest of the values are found using the following: Et = wYt + (1 - w) Et-1 , where w is the smoothing constant For w = 0.70 1980:

Et = wYt + (1 w)Et-1 , where w is the smoothing constant For w = .70: Jan: E1 = Y1 = 1.13

1981: E2 =

= 0.7(1.10) + (1 0.7)(1.13) = 1.109 March: E3 =

Y1 = 1.740

wY 3 + (1 - w)E2 = 0.7(0.896) + (1 0.7)(1.533) = 1.087 1983: E4 = wY 4 + (1 - w)E3 = 0.7(1.289) + (1 0.7)(1.087) = 1.228 1984: E5 = wY 5 + (1 - w)E4 =

0.7(4.882) + (1 0.7)(1.387) = 3.834 20) B 21) C 22) D 23) The first value of the exponentially smoothed series is equal to the first value in the time series. The rest of the values are found using the following:

Feb: E2 = wY2 + (1 - w)E1

wY 2 + (1 - w)E1 =

In general, the

wY 6 + (1 - w)E5 =

E1 =

0.7(1.444) + (1 0.7)(1.740) = 1.533 1982: E3 =

0.7(1.455) + (1 0.7)(1.228) = 1.387 1985: E6 =

wY 3 + (1 - w)E2 = 0.7(1.13) + (1 0.7)(1.109) = 1.124 April: E4 = wY 4 + (1 - w)E3 = 0.7(1.23) + (1 0.7)(1.124) = 1.198

Answer Key Testname: SB14ECH14TEST

24) a. Month January February March April May June July August September October November December

t 1 2 3 4 5 6 7 8 9 10 11 12

42) B 43) B 44) A 45) a.

Year 1 2 3 4 5 6

Smoothed Value 250 253 253 254.2 257.08 259.432

b. Year

7 8 9 10

Forecast Error 2.568 4.568 3.568 6.568

c. MAD: 4.32; MAPE: 1.63; RMSE: 4.56 46) a. Year Forecast 7 262.98 8 265.07 9 267.17 10 269.26

25) D 26) D 27) B 28) C 29) B 30) B 31) A 32) D 33) Year 11: $1.62; Year 12: $1.62 34) A 35) B 36) D 37) A 38) a. 215.72; 215.72 b. 220.31; 223.03 39) D 40) B 41) D

b. Year 7 8 9 10

Forecast Error 0.019 1.925 1.832 -1.262

c. MAD: 1.26; MAPE: 0.47; RMSE: 1.47 47) B 48) B 49) B 50) C 51) C 52) A

53) a. y = 248.6 + 1.97x b. Year 7: 262.40; Year 8: 264.37 c. Year 7: (255.97, 268.83); Year 8: (257.20, 271.54)

71) a. b.

y = 184 + 2.73t

54) a. y = 184 + 2.73t b. 219.50; 222.23 c. (211.07, 227.93); (213.50, 230.96) 55) A 56) C 57) A 58) a.

E(Yt) = 0 + 1 t + 2 Q1 + 3 Q2 + 4 Q3

1 if Quarter 1 Q1 = , 0 if not 1 if Quarter 2 Q2 = , 0 if not 1 if Quarter 3 Q3 = 0 if not ^

b. y = 1.045 + 0.0362t + 0.0088Q1 + 0.293Q2 + 0.316Q3

c. Quarter 1: 1.815, (1.5631, 2.0669); Quarter 2: 2.135, (1.8831, 2.3869); Quarter 3: 2.195, (1.9431, 2.4469); Quarter 4: 1.915, (1.6631, 2.1669) 59) B 60) A 61) B 62) A 63) D 64) D 65) D 66) C 67) A 68) B 69) D 70) D

c. No, there are no long runs of either positive or negative residuals. 72) d = 1.87807; The rejection region is d < 1.2 or 4 - d < 1.2. Since d does not fall within the rejection region, we cannot reject the null hypothesis. There is insufficient evidence of autocorrelation.

Answer Key Testname: SB14ECH14TEST

73) a. b.

y = 248.6 + 1.971t Year 1 2 3 4 5 6

Predicted Y 250.57 252.54 254.51 256.49 258.46 260.43

d = 2.53