TEST BANK for The Basic Practice of Statistics, 9th Edition Moore, Notz, Fligner by ACADEMIAMILL

Name:

Class:

Date:

Chapter 0 1. The purposes of studying statistics include: a. gaining insight and learning from data. b. seeking patterns underlying variation in data. c. describing uncertainty in data and conclusions drawn from data. d. All of the answer options are correct. ANSWER: d POINTS: 1 REFERENCES: Section: 0.1–0.4 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061064_60a80876ad0c31 2. Which of the following statements is true about learning from data? a. It does not matter where you get your data, as long as there are enough of them. b. It is important to know the context within which the problem is to be solved. c. It is possible to reach conclusions without knowing how the data were collected. d. All of the answer options are correct. ANSWER: b POINTS: 1 REFERENCES: Section: 0.1 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061065_60a80876ad0c32 3. Relationships between two variables: a. are often affected by other, lurking variables. b. do not necessarily imply cause-and-effect relationships. c. can be explored using statistical procedures. d. All of the answer options are correct. ANSWER: d POINTS: 1 REFERENCES: Section: 0.1 Chapter 0 QUESTION TYPE: Multiple Choice Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 0 HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061066_60a80876ad0c33 4. When you begin to work with a data set, you should: a. examine the context within which the data were collected. b. aim to understand the context of the problem you are trying to solve. c. look at graphs and summaries of quantitative data. d. All of the answer options are correct. ANSWER: d POINTS: 1 REFERENCES: Section: 0.1 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061067_60a80876ad0c34 5. Drawing conclusions about the greater world based on examining patterns in variation within a sample of data is called: a. data analysis. b. data production. c. statistical inference. d. None of the answer options is correct. ANSWER: c POINTS: 1 REFERENCES: Section: 0.3 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061068_60a80876ad0c35 6. Describing data using graphs and quantitative summaries is part of: a. data analysis. b. data production. c. statistical inference. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 0 d. None of the answer options is correct. ANSWER: a POINTS: 1 REFERENCES: Section: 0.2 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061069_60a80876ad0c36 7. Which four-steps, applied in the order shown, answer the question “What do the data tell me?” a. Plan your work; solve with graphs and calculations; check accuracy; and state conclusions. b. Plan your work; state a problem in context; state conclusions; and show graphs and calculations. c. State a problem in context; plan your work; solve with graphs and calculations; and state conclusions. d. State a problem in context; solve with graphs and conclusions; check accuracy; and state conclusions. ANSWER: c POINTS: 1 REFERENCES: Section: 0.4 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061070_60a80876ad0c37 8. Which of the following statements is true about variation? a. Variation indicates that there is a problem with the data. b. Variation is common in data sets. c. There is usually only one source of variation. d. All of the answer options are correct. ANSWER: b POINTS: 1 REFERENCES: Section: 0.3 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 0 DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061071_60a80876ad0c38 9. Which of the following is true? a. Because variation is everywhere, conclusions can be made with certainty. b. One of the reasons why statistics is useful is that it gives us a language that is used and understood only in university classrooms. c. Statistics allows us to say how confident we are about a finding based on a clinical trial. d. A clinical trial allows us to be certain that a vaccine reduces risk. ANSWER: c POINTS: 1 REFERENCES: Section: 0.3 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061072_60a80876ad0c39 10. It is unethical to use randomized studies to expose humans to harmful substances. Observational studies, where we compare those exposed to those not exposed, are sometimes used in such situations. Which statement describes a possibly misleading finding from such a study? a. We can safely compare those exposed to those not exposed, as long as we have enough study subjects. b. We have to be concerned about lurking variables, which might lead us to erroneously conclude that the compound is causing the disease. c. If we do not carry out a randomized study, we can be sure that lurking variables will mislead us. d. On average, an observational study will provide us with the correct conclusion. ANSWER: b POINTS: 1 REFERENCES: Section: 0.1 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061073_60a80876ad0c310 11. Suppose we want to study whether using social media causes changes in the GPAs of college first-year students. Which of the following would be an appropriate way to answer our question? a. a survey to be conducted online at the end of freshman year, in which we ask students how much Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 0 time they spent on sites such as Facebook and record their GPAs. b. an observational study that compares the GPAs of a group of freshmen who were observed to have spent at least 3 hours per day on social media to those who spent less than 30 minutes per day. c. a study that recruits volunteers who agreed to spend at least 2 hours per day on social media and another group of volunteers who agreed to spend no more than 30 minutes per day on social media. d. None of the answer options is correct. ANSWER: d POINTS: 1 REFERENCES: Section: 0.1 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061074_60a80876ad0c311 12. If we want to study the reasons why students binge drink, we should: a. randomly assign students to a group that is allowed to binge drink. b. go to a party and observe which students binge drink and which students do not, and see if we can identify differences between the two groups. c. do a survey of students, asking about binge drinking and their reasons for doing so. d. None of the answer options is correct. ANSWER: c POINTS: 1 REFERENCES: Section: 0.1 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061075_60a80876ad0c312 13. A PhD student in education wants to study the relationship between the time spent studying and the grade received for students in a specific major. The student recruits 90 students and randomly assigns them to study 0.5 hour, 1 hour, 1.5 hours, or 2 hours per day for a specific subject. These students study in their assigned time bracket for the entire semester. To explore the relationship between time spent studying and grade received, at the end of the semester the PhD student could: a. plot numerical grade received against time studied. b. calculate averages for each time group and, if they are different, declare that time studied determines grade received. c. look at variability in grades received. If students in different time groups have the same grade, the Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 0 PhD student should conclude that there is no relationship between time studied and grade received. d. None of the answer options is correct. ANSWER: a POINTS: 1 REFERENCES: Section: 0.2 Chapter 0 QUESTION TYPE: Multiple Choice HAS VARIABLES: False DATE CREATED: 5/27/2021 11:12 AM DATE MODIFIED: 5/27/2021 11:12 AM CUSTOM ID: question_1061076_60a80876ad0c313

Page 6

Name:

Class:

Date:

Chapter 1 1. Employees at a large company are surveyed about their health insurance status. Employees are coded as “1” if health insurance is obtained through the company’s benefit program, “2” if health insurance is obtained from another source (such as through a spouse’s employment benefit program), or “0” if the employee does not have health insurance. This variable is: a. numerical. b. categorical. c. quantitatively categorical. d. All of the answer options are correct. ANSWER: b 2. A company has three divisions and three conference rooms for meetings. To keep track of the use of its facilities, for each meeting the company records the name of the division holding the meeting, the conference room used, and the length of time of the meeting. Which of the variables is quantitative? a. the name of the division holding the meeting b. the conference room used c. the length of time of the meeting d. All of the answer options are correct. ANSWER: c 3. A description of different houses for sale includes the square footage of the house, whether or not the house has a finished basement, and the monthly electric bill. Which of the variables is categorical? a. the square footage of the house b. whether or not the house has a finished basement c. the monthly electric bill d. All of the answer options are correct. ANSWER: b 4. Some of the variables from a survey conducted by the U.S. Census Bureau are the number of people living in a household, the total household gross income, and the ages of household residents. Which of the variables is or are quantitative? a. the number of people living in a household b. the total household gross income c. the ages of household residents d. All of the answer options are correct. ANSWER: d 5. As part of a database of new births at a hospital, some of the variables recorded are the age of the mother, the marital status of the mother (such as single, married, or divorced), the weight of the baby, and the sex of the baby. Which of the following statements is or are true? a. The individuals in this data set are births at the hospital. b. The age of the mother and the weight of the baby are quantitative variables. c. The sex of the baby and the marital status of the mother are categorical variables. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 1 d. All of the answer options are correct. ANSWER: d 6. The difference between a frequency histogram and a relative frequency histogram is that the relative frequency histogram indicates: a. counts on the vertical (y) axis, whereas a frequency histogram indicates percents. b. counts on the horizontal (x) axis, whereas a frequency histogram indicates percents. c. percents of observations on the horizontal (x) axis, whereas a frequency histogram indicates counts. d. percents of observations on the vertical (y) axis, whereas a frequency histogram indicates counts. ANSWER: d 7. What is the difference between a histogram and a bar chart? a. There is no difference; they are exactly the same. b. A histogram is a more accurate representation of a bar chart. c. A bar chart displays a quantitative variable on the horizontal axis, whereas a histogram does not. d. A bar chart displays a categorical variable on the horizontal axis, whereas a histogram does not. ANSWER: d 8. A poll was conducted of more than 50,000 buyers of new cars, 90 days after the cars were purchased. The data on problems per 100 vehicles for cars made by Toyota and by General Motors (GM) are given in the time plot below for the years 1998–2004. The solid line is for GM, and the dashed line is for Toyota.

Page 2

Name:

Class:

Date:

Chapter 1

In 2002, the number of problems per 100 vehicles was: a. about twice as high for GM as for Toyota. b. about twice as high for Toyota as for GM. c. about 20% higher for Toyota than for GM. d. about 20% higher for GM than for Toyota. ANSWER: d 9. A poll was conducted of more than 50,000 buyers of new cars, 90 days after the cars were purchased. The data on problems per 100 vehicles for cars made by Toyota and General Motors (GM) are given in the time plot below for the years 1998–2004. The solid line is for GM and the dashed line is for Toyota.

Page 3

Name:

Class:

Date:

Chapter 1

Which of the following is a true statement? a. The quality of cars is getting poorer for both companies. b. The number of problems was higher for GM than for Toyota in each year. c. The difference in the number of problems per 100 vehicles between GM and Toyota is less than 30 for each year. d. All of the answer options are correct. ANSWER: b 10. A large university is divided into six colleges, with most students graduating from one of four of these colleges. The following bar chart gives the distribution of the percents graduating from these four most popular colleges in 2003.

Page 4

Name:

Class:

Date:

Chapter 1

The percent of students graduating from either engineering or business is: a. approximately 30%. b. approximately 40%. c. approximately 50%. d. over 60%. ANSWER: c 11. A large university is divided into six colleges, with most students graduating from one of four of these colleges. The following bar chart gives the distribution of the percents graduating from these four most popular colleges in 2003.

Page 5

Name:

Class:

Date:

Chapter 1

Which of the following is a correct statement? a. A time plot of the 2003 distribution would be more informative. b. The bar graph is skewed to the right. c. The bar graph is skewed to the left. d. None of the answer options is correct. ANSWER: d 12. The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business schools in 2004. In each class interval, the left endpoint, but not the right, is included, so the class intervals are 10 ≤ rate < 15, 15 ≤ rate < 20, etc.

Page 6

Name:

Class:

Date:

Chapter 1

What is the approximate spread of the data? a. 25 b. 30 c. 40 d. 50 ANSWER: c 13. The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business schools in 2004. In each class interval, the left endpoint, but not the right, is included, so the class intervals are 10 ≤ rate < 15, 15 ≤ rate < 20, etc.

The number of schools with an acceptance rate greater than or equal to 30% is: a. 5. b. 12. c. 10. Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 1 d. 13. ANSWER: d 14. The stemplot below displays midterm exam scores for 34 students taking a calculus course. The highest possible test score was 100. The teacher declared that an exam grade of 65 or higher was good enough for a grade of C or better. 3 6 8 4 1 4 8 5 3 3 4 4 6 2 3 3 5 5 6 7 7 0 0 1 2 3 5 6 6 8 8 9 8 1 1 3 5 9 0 3 9 This stemplot is most similar to: a. a boxplot of the data. b. a time plot of the data with the observations taken in increasing order. c. a histogram with class intervals 30 ≤ score < 40, 40 ≤ score < 50, etc. d. reporting the five-number summary for the data, with the mean. ANSWER: c 15. The stemplot below displays midterm exam scores for 34 students taking a calculus course. The highest possible test score was 100. The teacher declared that an exam grade of 65 or higher was good enough for a grade of C or better. 3 6 8 4 1 4 8 5 3 3 4 4 6 2 3 3 5 5 6 7 7 0 0 1 2 3 5 6 6 8 8 9 8 1 1 3 5 9 0 3 9 The percent of students earning a grade of C or higher (as declared by the teacher) is closest to: a. 35%. b. 50%. c. 65%. d. 80%. ANSWER: c 16. The following is a histogram showing the distribution per year of the cumulative property damage caused by tornadoes, over the period 1950 to 1999, in each of the 50 states and Puerto Rico. The data are in millions of dollars, and the class intervals are 0 to < 10, 10 to < 20, and so forth.

Page 8

Name:

Class:

Date:

Chapter 1

Which of the following statements is true? a. Approximately 25% of the tornadoes caused less than $10 million in damage. b. Approximately 25% of the annual reports of property damage were less than $10 million. c. Approximately 50% of the annual reports of property damage were less than $10 million. d. None of the answer options is correct. ANSWER: c 17. The following is a histogram showing the distribution per year of the cumulative property damage caused by tornadoes, over the period 1950 to 1999, in each of the 50 states and Puerto Rico. The data are in millions of dollars, and the class intervals are 0 to < 10, 10 to < 20, and so forth.

Page 9

Name:

Class:

Date:

Chapter 1

The percent of the data with average property damage of under $20 million dollars is about: a. 20%. b. 30%. c. 40%. d. 60%. ANSWER: d 18. The following is a histogram showing the distribution per year of the cumulative property damage caused by tornadoes over the period 1950 to 1999 in each of the 50 states and Puerto Rico. The data are in millions of dollars, and the class intervals are 0 to < 10, 10 to < 20, and so forth.

Page 10

Name:

Class:

Date:

Chapter 1

The histogram: a. is skewed to the right. b. shows some high outliers. c. has a center of about $10 million dollars. d. All of the answer options are correct. ANSWER: d 19. A sample of 40 employees from the local Honda plant was obtained, and the length of time (in months) that each employee has worked at the plant was recorded. A stemplot of these data follows. In the stemplot, 5|2 represents 52 months. 5 2 2 3 3 4 5 7 8 9 9 6 0 0 0 2 3 4 4 4 7 7 8 8 8 9 7 3 4 5 5 6 6 7 7 7 8 8 9 9 8 9 8 What would be a better way to represent this data set? a. Display the data in a time plot. b. Split the stems. Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 1 c. Use a pie chart. d. Use a bar graph with class width equal to 10. ANSWER: b 20. A sample of 40 employees from the local Honda plant is obtained, and the length of time (in months) that each employee has worked at the plant is recorded. A stemplot of these data follows. In the stemplot, 5|2 represents 52 months. 5 2 2 3 3 4 5 7 8 9 9 6 0 0 0 2 3 4 4 4 7 7 8 8 8 9 7 3 4 5 5 6 6 7 7 7 8 8 9 9 8 9 8 The percent of employees in the sample who have worked at the plant for less than five years is: a. approximately zero. b. 10%. c. 15%. d. 25%. ANSWER: d 21. Consumers’ Union measured the gas mileage per gallon of thirty-eight 1998–99 model automobiles on a special test track. The following pie chart provides information about the country of manufacture of the cars that Consumers’ Union used.

Page 12

Name:

Class:

Date:

Chapter 1

Based on this pie chart, we may conclude that: a. Japanese cars get significantly lower gas mileage than cars of other countries. We know this because their slice of the pie is at the bottom of the chart. b. More than half of the cars in the study were from the United States. c. Swedish cars get gas mileage between that of Japanese cars and that of U.S. cars. d. Mercedes Benz, Audi, Porsche, and BMW represent approximately one-quarter of the cars tested. ANSWER: b 22. Consumers’ Union measured the gas mileage per gallon of thirty-eight 1998–99 model automobiles on a special test track. The following pie chart provides information about the country of manufacture of the cars that Consumers’ Union used.

Page 13

Name:

Class:

Date:

Chapter 1

Which of the following bar graphs is equivalent to the pie chart? a.

Page 14

Name:

Class:

Date:

Chapter 1 b.

ANSWER: b Copyright Macmillan Learning. Powered by Cognero.

Page 15

Name:

Class:

Date:

Chapter 1 23. Which statement best reflects what is most important to consider when creating a pie chart? a. You should never create a pie chart, because they are inaccurate. b. The area of each of the slices must be proportional to the frequency with which the observation occurs. c. Each observation must be contained within one (and only one) slice of the pie. d. The area of each of the slices must be proportional to the frequency with which the observation occurs, and each observation must be contained within one (and only one) slice of the pie. ANSWER: d 24. Enteroliths are calcifications that form in the gut of horses. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as diet and environment) that may be related to the formation of enteroliths. Housing is a variable that is coded “1” for horses that live in a stall, “2” for horses that have access to a small paddock, “3” for horses that have a large paddock, “4” for horses that live in a pasture, and “5” for other housing. Housing is a: a. categorical variable. b. quantitative variable. c. numerical category. d. None of the answer options is correct. ANSWER: a 25. An appropriate graphical way to display housing (stall, small paddock, large paddock, pasture, or other housing) for horses is given by: a. a histogram. b. a pie chart. c. a stemplot. d. All of the answer options are correct. ANSWER: b 26. The 137 horses in a study on enteroliths, a type of stone in the gut, were housed in a small paddock, in a large paddock, in a stall, or in a grass pasture.

Page 16

Name:

Class:

Date:

Chapter 1

Based on the bar chart, the percent of horses living in paddocks, large or small, is approximately: a. 38%. b. 51%. c. 58%. d. 74%. ANSWER: c 27. Veterinary researchers wanted to know if housing might be related to whether or not a horse develops enteroliths. Attached are side-by-side pie charts of housing for horses with enteroliths (cases) and horses without (controls).

Page 17

Name:

Class:

Date:

Chapter 1

Based on these charts, it is reasonable to conclude that: a. cases and controls are equally likely to be housed in a pasture. b. cases are more likely to be housed in a pasture. c. cases are less likely to be housed in a pasture. d. the relationship cannot be determined from the pie chart. ANSWER: c 28. Enteroliths are calcifications that form in the gut of horses. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as age, diet, and environment) that may be related to the formation of enteroliths.

Page 18

Name:

Class:

Date:

Chapter 1

The histogram of age for the horses in the enteroliths study is: a. slightly left-skewed. b. symmetric. c. bimodal. d. slightly right-skewed. ANSWER: d 29. Enteroliths are calcifications that form in the gut of horses. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as age, diet, and environment) that may be related to the formation of enteroliths.

Page 19

Name:

Class:

Date:

Chapter 1

The number of horses between 10 and 20 years of age in the enterolith study is approximately: a. 28. b. 42. c. 51. d. 70. ANSWER: d 30. Enteroliths are calcifications that form in the gut of horses. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as age, diet, and environment) that may be related to the formation of enteroliths. The researchers decided to draw two histograms: one for horses with enteroliths (cases) and one for horses without (controls).

Page 20

Name:

Class:

Date:

Chapter 1

It can be deduced from the histograms that the cases are: a. slightly younger than the controls. b. slightly older than the controls. c. about the same age as the controls. d. None of the answer options is correct. ANSWER: a 31. Enteroliths are calcifications that form in the gut of horses. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as age, diet, and environment) that may be related to the formation of enteroliths. The researchers decided to draw two histograms: one for horses with enteroliths (cases) and one for horses without (controls).

Page 21

Name:

Class:

Date:

Chapter 1

The number of horses 20 years and older: a. is larger among the cases. b. is smaller among the cases. c. is about the same for both. d. cannot be determined from the histogram. ANSWER: b 32. A survey of radio stations was conducted following the attacks on the World Trade Center in 2001. One of the variables recorded was the region in which the station was located (east, center, or west). The variable “region” is: a. quantitative, because region is not a number. b. quantitative, because region is a number. c. categorical, because region is not a number. d. categorical, because region is a number. ANSWER: c 33. A survey of radio stations was conducted following the attacks on the World Trade Center in 2001. One of the variables recorded was the region in which the station was located (east, center, or west). The variable "region" can be summarized by: a. a bar graph only. Copyright Macmillan Learning. Powered by Cognero.

Page 22

Name:

Class:

Date:

Chapter 1 b. a pie chart only. c. a histogram only. d. a bar graph or a pie chart. ANSWER: d 34. A survey of radio stations was conducted following the attacks on the World Trade Center in 2001. One of the variables recorded was the region in which the station was located (east, center, or west).

The bar graph above shows that the location of the majority of radio stations: a. is in the west. b. is in the center. c. is in the east. d. cannot be determined from a bar graph. ANSWER: b 35. A survey of radio stations was conducted following the attacks on the World Trade Center in 2001.

Page 23

Name:

Class:

Date:

Chapter 1

In the pie chart above, the proportion of radio markets in the second quarter in the center of the U.S. is approximately: a. 10%. b. 20%. c. 40%. d. 60%. ANSWER: c 36. A survey of radio stations was conducted following the attacks on the World Trade Center in 2001. The station rankings were included in the survey. The histogram below has the interval limits 0 ≤ ranking < 50, 50 ≤ ranking < 100, 100 ≤ ranking < 150, 150 ≤ ranking < 200, and 200 ≤ ranking < 250.

Page 24

Name:

Class:

Date:

Chapter 1

A ranking of 100: a. will be counted in interval 2. b. will be counted in interval 3. c. can be in either interval 2 or interval 3. d. cannot be determined from the histogram. ANSWER: b 37. A survey of radio stations was conducted following the attacks on the World Trade Center in 2001. The station rankings were included in the survey. The histogram below has the interval limits 0 ≤ ranking < 50, 50 ≤ ranking < 100, 100 ≤ ranking < 150, 150 ≤ ranking < 200, and 200 ≤ ranking < 250.

Page 25

Name:

Class:

Date:

Chapter 1

A plot of the histogram, above, shows the histogram to be: a. symmetric. b. left-skewed. c. right-skewed. d. bimodal. ANSWER: c

Page 26

Name:

Class:

Date:

Chapter 2 1. A violin student records the number of hours she spends practicing during each of nine consecutive weeks: 6.2

5.0

4.3

7.4

5.8

7.2

8.4

1.2

6.3

What is the mean number of hours spent practicing per week during this period? a. 36.15 hours b. 76 hours c. 6.20 hours d. 8.40 hours ANSWER: b 2. A violin student records the number of hours she spends practicing during each of nine consecutive weeks: 6.2 5.0 4.3 7.4 5.8 7.2 8.4 1.2 6.3 What is the median number of hours spent practicing per week during this period? a. 6.15 hours b. 76 hours c. 20 hours d. 40 hours ANSWER: c 3. A violin student records the number of hours she spends practicing during each of nine consecutive weeks: 6.2 5.0 4.3 7.4 5.8 7.2 8.4 1.2 6.3 What is the first quartile for these data? a. 5.00 hours b. 5.76 hours c. 7.20 hours d. 4.65 hours ANSWER: d 4. A violin student records the number of hours she spends practicing during each of nine consecutive weeks: 6.2 5.0 4.3 7.4 5.8 7.2 8.4 1.2 6.3 What is the interquartile range (IQR) for these data? a. 3.00 hours b. 65 hours c. 20 hours d. 65 hours ANSWER: b 5. A violin student records the number of hours she spends practicing during each of nine consecutive weeks: 6.2 5.0 4.3 7.4 5.8 7.2 8.4 1.2 6.3 Considering the smallest data value (1.2) and using the 1.5

IQR rule, we would:

a. classify the value 1.2 as an outlier, because it is more than 1.5 Copyright Macmillan Learning. Powered by Cognero.

IQR below the first quartile. Page 1

Name:

Class:

Date:

Chapter 2 b. not classify the value 1.2 as an outlier, because it is not more than 1.5 IQR below the first quartile. c. classify the value 1.2 as an outlier, because it is more than 1.5 IQR below the median. d. classify the value 1.2 as an outlier, because it is more than 1.5

IQR below the mean.

ANSWER: b 6. The 18 faculty members in a college math department range in age from 32 to 68. A stemplot follows: 3 2 4 8 9 9 4 0 3 5 6 9 5 3 4 7 8 9 9 6 3 8 The median age of the faculty members is: a. 39 years. b. 45 years. c. 47.5 years. d. 49 years. ANSWER: c 7. The 18 faculty members in a college math department range in age from 32 to 68. A stemplot follows: 3 2 4 8 9 9 4 0 3 5 6 9 5 3 4 7 8 9 9 6 3 8 If the eldest faculty member retires and is replaced by a 26-year-old, the median age will: a. decrease by 2 years. b. stay the same. c. increase by 2 years. d. increase by 4 years. ANSWER: a 8. The 18 faculty members in a college math department range in age from 32 to 68. A stemplot follows: 3 2 4 8 9 9 4 0 3 5 6 9 5 3 4 7 8 9 9 6 3 8 The first and third quartiles of the ages of the faculty members are: a. 38 and 57 years. b. 39 and 57 years. c. 39 and 58 years. d. 40 and 58 years. ANSWER: c Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 2 9. The 18 faculty members in a college math department range in age from 32 to 68. A stemplot follows: 3 2 4 8 9 9 4 0 3 5 6 9 5 3 4 7 8 9 9 6 3 8 The 1.5

IQR rule would identify an age as a low outlier if it was less than:

a. 32 years. b. 28.5 years. c. 19 years. d. 10.5 years. ANSWER: d 10. The 18 faculty members in a college math department range in age from 32 to 68. A stemplot follows: 3 2 4 8 9 9 4 0 3 5 6 9 5 3 4 7 8 9 9 6 3 8 The 1.5

IQR rule would identify an age as a high outlier if it exceeded:

a. 19 years. b. 28.5 years. c. 77 years. d. 86.5 years. ANSWER: d 11. The exam scores (out of 100 points) for all students taking an introductory statistics course are used to construct the following boxplot:

Page 3

Name:

Class:

Date:

Chapter 2

Based on this boxplot, the interquartile range is closest to: a. 10. b. 25 c. 50. d. 80. ANSWER: b 12. The exam scores (out of 100 points) for all students taking an introductory statistics course are used to construct the following boxplot:

Page 4

Name:

Class:

Date:

Chapter 2

Based on this boxplot, which of the following statements is true? a. The distribution of scores is fairly symmetric. b. About half of the students scored below 63. c. Nobody scored below 25. d. All of the answer options are correct. ANSWER: d 13. The exam scores (out of 100 points) for all students taking an introductory statistics course are used to construct the following boxplot:

Page 5

Name:

Class:

Date:

Chapter 2

If each person increased his or her score by 5 points, then: a. the third quartile would increase by 5 points. b. the median score would increase by 5 points. c. the interquartile range would remain unchanged. d. All of the answer options are correct. ANSWER: d 14. The exam scores (out of 100 points) for all students taking an introductory statistics course are used to construct the following boxplot:

Page 6

Name:

Class:

Date:

Chapter 2

About 25% of the students’ scores exceeded: a. 50. b. 60. c. 75. d. 85. ANSWER: c 15. The exam scores (out of 100 points) for all students taking an introductory statistics course are used to construct the following boxplot:

Page 7

Name:

Class:

Date:

Chapter 2

If 5 points were added to each score, then standard deviation of the new scores would: a. be increased by 5. b. be increased by 25. c. be decreased by 5. d. remain unchanged. ANSWER: d 16. A sample was taken of the salaries of 20 employees of a large company. The following is a boxplot of the salaries (in thousands of dollars) for this year.

Page 8

Name:

Class:

Date:

Chapter 2

Based on this boxplot, which of the following statements is true? a. The interquartile range is about $20,000. b. The minimum salary is $20,000. c. The range of the salaries is about $75,000. d. The median salary is about $40,000. ANSWER: a 17. A sample was taken of the salaries of 20 employees of a large company. The following is a boxplot of the salaries (in thousands of dollars) for this year.

Based on this boxplot, the five-number summary (in thousands of dollars) is: a. 28, 39, 48, 60.5, 77. b. 28, 41, 48, 58, 77. c. 28, 39, 51, 58, 77. d. 28, 41, 51, 60.5, 77. ANSWER: a 18. A sample was taken of the salaries of 20 employees of a large company. The following is a boxplot of the salaries (in thousands of dollars) for this year.

Page 9

Name:

Class:

Date:

Chapter 2

Based on this boxplot, which of the following statements is true? a. The outliers are 28 and 77. b. Suspected outliers would be less than 28 or greater than 77, so there are none. c. Suspected outliers would be less than 6.75 or greater than 92.75, so there are none. d. There are outliers, but they are not shown in the boxplot. ANSWER: c 19. For each of the states and Puerto Rico, the histogram below shows the average property damage (in millions of dollars) caused by tornadoes over a 50-year period.

From the histogram, the first quartile must be: Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 2 a. in the interval 0–10. b. in the interval 10–20. c. in the interval 30–40. d. greater than 10. ANSWER: a 20. For each of the states and Puerto Rico, the histogram below shows the average property damage (in millions of dollars) caused by tornadoes over a 50-year period.

From the histogram, the median must be approximately: a. 15. b. 25. c. 30. d. 40. ANSWER: a 21. The percent of observations above the third quartile in a distribution is: a. 25%. b. 50%. Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 2 c. 75%. d. None of the answer options is correct. ANSWER: a 22. The average salary of all female workers at a large plant is $35,000. The average salary of all male workers at the plant is $41,000. If there are more female workers than male workers at the plant, then the average salary at the plant must be: a. exactly $38,000. b. larger than $38,000. c. smaller than $38,000. d. larger than $41,000. ANSWER: c 23. Which of the following is likely to have a mean that is smaller than the median? a. the salaries of all National Football League players, where a few players make much more than most players b. the scores of students (out of 100 points) on a very easy exam, in which most scores are high but a few scores are low c. the prices of homes in a large city, where there are lots of relatively inexpensive homes and a few very expensive homes d. the scores of students (out of 100 points) on a very difficult exam, in which most scores are low but a few scores are high ANSWER: b 24. Which of the following sets of four numbers has the smallest standard deviation? a. 7, 8, 9, 10 b. 5, 5, 5, 6 c. 0, 0, 10, 10 d. 0, 1, 2, 3 ANSWER: b 25. A group of four friends has a median age of 22. Three of the friends are ages 20, 18, and 24. The age of the fourth friend must be: a. 22. b. 24 or older. c. 18 or younger. d. None of these choices are correct; we can’t tell from the information provided. ANSWER: b 26. Student ages (to the nearest year) in a school are as follows: Age 18 19 20 21 22 23 24 25 32 Number of students 14 120 200 200 90 30 10 2 1 Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 2 What is true about the median age? a. It is 20. b. It would remain unchanged if the 32-year-old were replaced with an 80-year-old. c. It is between the first and third quartiles. d. All of the answer options are correct. ANSWER: d 27. Student ages (to the nearest year) in a school are as follows: Age 18 19 20 21 22 23 24 25 32 Number of students 14 120 200 200 90 30 10 2 1 What is true about the mean age? a. It is less than 20. b. It is greater than 20. c. It is exactly 20. d. It would remain unchanged if the 32-year-old were replaced with an 80-year-old. ANSWER: b 28. The following is a sample of the percent increase in five growth funds over a one-year period. 8.9% 12.2% 13.7% 14.4% 9.8% The mean percent increase in this sample is: a. 11.8%. b. 12.2%. c. 13.7%. d. 14.1%. ANSWER: a 29. There are three children in a room, ages 3, 4, and 5. If another 4-year-old enters the room: a. the mean age will stay the same, but the variance will increase. b. the mean age will stay the same, but the variance will decrease. c. the mean age and variance will stay the same. d. the mean age and variance will increase. ANSWER: b 30. In a class of 100 students, the grades on an accounting test are summarized in the following frequency table: Grade Frequency 91–100 11 81–90 31 71–80 42 61–70 16 The median grade is in which of the following intervals? a. 61–70 b. 71–80 Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 2 c. 81–90 d. 91–100 ANSWER: b 31. In a class of 100 students, the grades on an accounting test are summarized in the following frequency table: Grade Frequency 91–100 11 81–90 31 71–80 42 61–70 16 The distribution of grades is: a. symmetric. b. skewed left. c. skewed right. d. This cannot be determined from the information given. ANSWER: c 32. The median age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. The median age of the remaining four people in the room is: a. 40 years. b. 30 years. c. 25 years. d. This cannot be determined from the information given. ANSWER: d 33. The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business schools in 2004. In each class interval, the left endpoint is included but the right endpoint is not, so the class intervals are 10 ≤ rate < 15, 15 ≤ rate < 20, and so on.

What is the median acceptance rate? a. 20% b. just below 30% Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 2 c. just above 30% d. 40% ANSWER: c 34. The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business schools in 2004. In each class interval, the left endpoint is included but the right endpoint is not, so the class intervals are 10 ≤ rate < 15, 15 ≤ rate < 20, and so on.

Which of the following could be the five-number summary for these data? a. 10, 22, 31, 39, 50 b. 10, 20, 30, 40, 50 c. 10, 26, 31, 34, 50 d. 10, 22, 31, 29, 39 ANSWER: a 35. Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate the factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained seven stallions; their ages (in years) are as follows: 10 20 4 13 21 16 16 Copyright Macmillan Learning. Powered by Cognero.

Page 15

Name:

Class:

Date:

Chapter 2 The mean age for this group of stallions is: a. 16. b. 13. c. 14.3. d. 12.5. ANSWER: c 36. Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained seven stallions; their ages (in years) are as follows: 10 20 4 13 21 16 16 The median age of the stallions is: a. 16. b. 12.5. c. 14. d. None of the answer options is correct. ANSWER: a 37. Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained seven stallions; their ages (in years) are as follows: 10 20 4 13 21 16 16 The IQR of age for the stallions is: a. 17. b. 21. c. 16. d. 10. ANSWER: d 38. Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained seven stallions; their ages (in years) are as follows: 10 20 4 13 21 16 16 The youngest stallion, at 4 years old, is: a. an outlier, because it is more than 15 years below the lower quartile. b. an outlier, because it is the minimum. c. not an outlier, because it is less than 15 years below the lower quartile. d. not an outlier, because it is a positive value. ANSWER: c 39. Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained seven stallions; their ages (in years) are as follows: Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 2 10 20 4 13 21 16 16 The standard deviation of the ages for the stallions is: a. 34.9. b. 5.91. c. 10. d. 17. ANSWER: b 40. Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate the factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained 60 mares, and the frequency table below displays their ages. Age 4 5 6 7 8 10 11 12 13 14 Freq 2 2 5 5 5 4 3 5 3 5 Age 15 18 19 20 22 23 24 28 13 14 Freq 3 3 3 5 1 3 2 1 3 5 The mean age of the mares is: a. 12. b. 16. c. 13.13. d. 14.35. ANSWER: c 41. Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate the factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained 62 horses with enteroliths (cases) and 75 horses without enteroliths (controls). The graph below contains side-by-side boxplots of the ages for cases and controls.

Page 17

Name:

Class:

Date:

Chapter 2

Based on the boxplots, the mean age for the cases: a. is lower than the mean age for the controls. b. is approximately the same as the mean age for the controls. c. is higher than the mean age for the controls. d. cannot be determined from boxplots. ANSWER: a 42. Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained 62 horses with enteroliths (cases) and 75 horses without enteroliths (controls). The graph below contains side-by-side boxplots of the percent of alfalfa in the diet for cases and controls.

Page 18

Name:

Class:

Date:

Chapter 2

Based on the boxplot for cases, the distribution of the amount of alfalfa in the diet is: a. highly skewed left. b. highly skewed right. c. symmetric. d. None of the answer options is correct. ANSWER: a 43. Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained 62 horses with enteroliths (cases) and 75 horses without enteroliths (controls). The graph below contains side-by-side boxplots of the percent of alfalfa in the diet for cases and controls.

Page 19

Name:

Class:

Date:

Chapter 2

Based on the boxplot cases, the median amount of alfalfa in the diet of cases is: a. the same as for controls. b. half that for controls. c. three times that for controls. d. None of the answer options is correct. ANSWER: c 44. A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students’ total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 The mean for these data is: a. 84.3. b. 88.6. c. 92.4. Copyright Macmillan Learning. Powered by Cognero.

Page 20

Name:

Class:

Date:

Chapter 2 d. 88.0. ANSWER: b 45. A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students’ total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 The median for these data is: a. 63. b. 88. c. 92. d. 105. ANSWER: b 46. A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students’ total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 The first quartile for these data is: a. 63. b. 88. c. 92. d. 105. ANSWER: a 47. A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students’ total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 The interquartile range for these data is: a. 45. b. 63. c. 42. d. 105. ANSWER: c 48. A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students’ total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 The standard deviation for these data is: a. 29.9. b. 893.41. Copyright Macmillan Learning. Powered by Cognero.

Page 21

Name:

Class:

Date:

Chapter 2 c. 28.4. d. 804.29. ANSWER: a 49. A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students’ total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 The five-number summary for these data is: a. 63, 88.6, 105, 42, 145. b. 45, 88, 88.6, 105, 145. c. 45, 63, 92, 105, 145. d. 45, 63, 88, 105, 145. ANSWER: d 50. A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students’ total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 A student who was not included in the survey recorded a time of 240 minutes on social media. That value is: a. consistent with these data. b. inconsistent with these data. c. an outlier. d. clearly an erroneous recording. ANSWER: c 51. A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students’ total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 A high outlier is any value above: a. 105. b. 168. c. 117. d. 200. ANSWER: b 52. The table below gives exam scores for 30 students. Score 45 63 68 72 78 84 87 Freq 1 2 2 4 3 5 3 The mean for these data (rounded to the nearest integer) is: a. 85. b. 84. Copyright Macmillan Learning. Powered by Cognero.

91 3

94 3

97 2

99 1

100 1

Page 22

Name:

Class:

Date:

Chapter 2 c. 87. d. 82. ANSWER: d 53. A teacher returns an exam with possible scores ranging from 0 to 100. The students suspect that the majority of them performed poorly on the exam and request summary statistics. The teacher provides the mean, which was 72, as a summary statistic. A total of 400 students took the exam. Some of the students find the mean to be high, based on talking to other students. They take a random sample of 15 students, and they find that the mean equals 71.5 and the median equals 62. Based on this result, we conclude that: a. there are possibly some large outliers in these data. b. the exam scores are probably right-skewed. c. 50% of the students barely managed to pass the exam. d. All of the answer options are correct. ANSWER: d 54. A teacher returns an exam with possible scores ranging from 0 to 100. The students suspect that the majority of them performed poorly on the exam and request summary statistics. The teacher provides the mean, which was 72, as a summary statistic. A total of 400 students took the exam. Some of the students find the mean to be high, based on talking to other students. They take a random sample of 15 students, and they find that the mean equals 71.5 and the median equals 62. Based on this result, we conclude that: a. the boxplot is probably symmetric about the mean. b. the mean will be in the center of the boxplot. c. the mean will be off center in the boxplot and above the median. d. None of the answer options is correct. ANSWER: c 55. A teacher returns an exam with possible scores ranging from 0 to 100. The students suspect that the majority of them performed poorly on the exam and request summary statistics. The teacher provides the mean, which was 72, as a summary statistic. A total of 400 students took the exam. The teacher, after several requests, provides a boxplot of the exam scores. The students can get which of the following pieces of information from this plot? a. the median b. the IQR c. the minimum and the maximum d. All of the answer options are correct. ANSWER: d 56. A modified boxplot for a right-skewed data set uses a special character to point to: a. the median. b. the maximum. c. the third quartile. d. an outlier. Copyright Macmillan Learning. Powered by Cognero.

Page 23

Name:

Class:

Date:

Chapter 2 ANSWER: d 57. A survey of radio stations was conducted following the attacks on the World Trade Center in 2001. One of the variables recorded was the region in which the station was located (east, center, or west). In addition to the variable “region,” the following information was collected: the quartile of the media market (top, Second, third, or fourth), state, rank (a number between 1 and 205), and share (a number between 0 and 7).

The modified boxplot of station ranks above identifies how many outliers? a. none b. one c. two d. three ANSWER: a 58. A survey of radio stations was conducted following the attacks on the World Trade Center in 2001. One of the variables recorded was the region in which the station was located (east, center, or west). In addition to the variable “region,” the following information was collected: the quartile of the media market (top, second, third, or fourth), state, rank (a number between 1 and 205), and share (a number between 0 and 7). Copyright Macmillan Learning. Powered by Cognero.

Page 24

Name:

Class:

Date:

Chapter 2

The side-by-side boxplots of station rank, above, show: a. different median ranks between the regions. b. more variability in the ranks of coast stations. c. similar minimum ranks between regions. d. All of the answer options are correct. ANSWER: d

Page 25

Name:

Class:

Date:

Chapter 3 1. For this density curve, the third quartile is:

a. 0.5. b. 0.75. c. 1.5 d. 1.75. ANSWER: c 2. For this density curve, what percent of the observations lie between 1.25 and 1.75?

a. 0.25% b. 12.5% c. 25% d. 50% ANSWER: c 3. For this density curve, the median is:

Page 1

Name:

Class:

Date:

Chapter 3

a. 0.50. b. 1.50. c. 2.00. d. 3.50. ANSWER: c 4. For this density curve, the mean is:

Page 2

Name:

Class:

Date:

Chapter 3

a. greater than the median. b. equal to the median. c. less than the median. d. not possible to determine from the information given. ANSWER: b 5. A Normal distribution: a. is symmetric. b. can be completely described by a mean, , and a standard deviation, . c. has an area of exactly 1 underneath the density curve. d. All of the answer options are correct. ANSWER: d 6. Scores on a university exam are Normally distributed, with a mean of 78 and a standard deviation of 8. The professor teaching the class declares that a score of 70 or higher is required for a grade of at least C. Using the 68–95–99.7 rule, find approximately what percent of students score below 62? a. 2.5% b. 5% c. 16% d. 32% ANSWER: a 7. Scores on a university exam are Normally distributed, with a mean of 78 and a standard deviation of 8. The Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 3 professor teaching the class declares that a score of 70 or higher is required for a grade of at least C. Using the 68–95–99.7 rule, find approximately what percent of students failed to earn a grade of at least C? a. 32% b. 16% c. 5% d. 2.5% ANSWER: b 8. Scores on a university exam are Normally distributed, with a mean of 78 and a standard deviation of 8. Suppose we are told that Student A received a score of 82 on the exam. What is the standardized score (i.e,, the z-score) for this student? a. 1 b. 0.5 c. –0.5 d. 4 ANSWER: b 9. What is the area under the standard Normal curve corresponding to z > –1.62? a. 0.0044. b. 0.0526. c. 0.9474. d. 0.9956. ANSWER: c 10. What is the area under the standard Normal curve corresponding to z < 0.75? a. 0.0401 b. 0.7500 c. 0.7734 d. 0.9599 ANSWER: c 11. The area under the standard Normal curve corresponding to –0.5 < z < 1.2 is: a. 0.3085. b. 0.8849. c. 0.5764. d. 0.2815. ANSWER: c 12. Birth weights of infants at a local hospital have a Normal distribution, with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights above 125 oz is closest to: a. 0.500. b. 0.159. Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 3 c. 0.341. d. 0.841. ANSWER: b 13. Birth weights of infants at a local hospital have a Normal distribution, with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights between 125 oz and 140 oz is closest to: a. 0.819. b. 0.636. c. 0.477. d. 0.136. ANSWER: d 14. The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with = 100 and = 15. The proportion of adults with scores between 80 and 120 is closest to: a. 0.50. b. 0.66. c. 0.82. d. 0.99. ANSWER: c 15. The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with = 100 and = 15. The proportion of adults with scores above 110 is closest to: a. 0.08. b. 0.10. c. 0.25. d. 0.35. ANSWER: c 16. The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with = 100 and = 15. The score needed to be among the highest 10% of all scores is closest to: a. 81. b. 119. c. 75. d. 125. ANSWER: b 17. The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with = 100 and = 15. If you scored 130, your score would be higher than approximately what percent of adults? a. 92% b. 95% c. 97.5% Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 3 d. 99.7% ANSWER: c 18. A company produces boxes of soap powder labeled “Giant Size: 32 Ounces.” The actual weight of soap powder in such a box has a Normal distribution, with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. What proportion of boxes is underweight? a. 0.0764 b. 0.2420 c. 0.7580 d. 0.9236 ANSWER: a 19. A company produces boxes of soap powder labeled “Giant Size: 32 Ounces.” The actual weight of soap powder in such a box has a Normal distribution, with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid losing money, the company labels the top 5% (the heaviest 5%) overweight. How heavy does a box have to be for it to be labeled overweight? a. 31.60 oz b. 31.85 oz c. 34.15 oz d. 34.40 oz ANSWER: c 20. A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. What percent of successful interviewees have a GPA above 3.9? a. 2.3% b. 6.7% c. 93.3% d. 97.7% ANSWER: b 21. A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. What proportion of successful interviewees have a GPA under 3.0? a. 0.023 b. 0.227 c. 0.551 d. 0.773 Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 3 ANSWER: b 22. A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. Out of the 163 successful interviewees who made it through the interview process, only 121 can be hired. What cut-off GPA should the company use? a. 3.00 b. 3.04 c. 3.08 d. 3.12 ANSWER: b 23. Scores on the SAT math test in recent years follow approximately the N(515, 109) distribution. The proportion of students scoring at least 600 is closest to: a. 0.082. b. 0.184. c. 0.218. d. 0.782. ANSWER: c 24. Scores on the SAT math test in recent years follow approximately the N(515, 109) distribution. The proportion of students scoring between 460 and 550 is closest to: a. 0.309 b. 0.317. c. 0.626. d. 0.681. ANSWER: b 25. Scores on the SAT math test in recent years follow approximately the N(515, 109) distribution. How high must a student score in order to place in the top 5% of all students taking the SAT? a. 301 b. 336 c. 694 d. 729 ANSWER: c 26. The duration (in days) of human pregnancies follows approximately the N(266, 16) distribution. How many days would a human pregnancy need to last to be among the top 10% longest of all pregnancy durations? a. 239.7 days b. 245.5 days Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 3 c. 286.5 days d. 292.3 days ANSWER: c 27. The duration (in days) of human pregnancies follows approximately the N(266,16) distribution. What proportion of pregnancies last more than 270 days? a. 0.334 b. 0.401 c. 0.599 d. 0.621 ANSWER: b 28. The average time taken for your Internet service provider to remotely resolve a trouble ticket has a Normal distribution, with a mean of 4.3 hours and a standard deviation of 3.1 hours. What percent of the time can you expect to wait longer than a full (8-hour) business day for a resolution to a trouble ticket? a. 11.7% b. 15.7% c. 88.3% d. 100% ANSWER: a 29. The average time taken for your Internet service provider to remotely resolve a trouble ticket has a Normal distribution, with a mean of 4.3 hours and a standard deviation of 3.1 hours. What percentage of the tickets are resolved in less than half an hour? a. 11.0% b. 14.5% c. 85.5% d. 89.1% ANSWER: a 30. A cappuccino vending machine is designed to dispense an average of ounces per cup. If the ounces dispensed are Normally distributed, with a standard deviation of 0.4 oz, at what value should be set so that 6ounce cups will overflow only 2% of the time? a. 6.82 ounces b. 6.00 ounces c. 5.18 ounces d. 5.60 ounces ANSWER: c 31. The typical first year college student spends an average of = 150 minutes per day, with a standard deviation of = 50 minutes, on social media. The distribution of time on social media is known to be Normal. The proportion of students who spend at least 2 hours per day on social media equals: Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 3 a. 0.726. b. 0.964. c. 0.928. d. 0.072. ANSWER: a 32. The typical first year college student spends an average of = 150 minutes per day, with a standard deviation of = 50 minutes, on social media. The distribution of time on social media is known to be Normal. The third quartile is: a. 183.72 minutes. b. 0.25 minute. c. 116.27 minutes. d. 0.75 minute. ANSWER: a 33. The typical first year college student spends an average of = 150 minutes per day, with a standard deviation of = 50 minutes, on social media. The distribution of time on social media is known to be Normal. The median of the distribution is: a. 75 minutes. b. 150 minutes. c. 180 minutes. d. 240 minutes. ANSWER: b 34. Running times for a 400-meter race are Normally distributed for students at a certain school, with a mean of 93 seconds and a standard deviation of 16 seconds. What would a student's running time have to be to put the student in the top 1% among runners at the school? a. 130.2 seconds b. 51.8 seconds c. 134.2 seconds d. 55.8 seconds ANSWER: d 35. Running times for a 400-meter race are Normally distributed for students at a certain school, with a mean of 93 seconds and a standard deviation of 16 seconds. Thus, 99.7% of running times are approximately between: a. 45 and 141 seconds. b. 61 and 125 seconds. c. 77 and 109 seconds. d. None of the answer options is correct. ANSWER: a Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 3 36. The graph below shows a distribution that is called a chi-square distribution.

For this distribution, the median: a. is larger than the mean . b. is smaller than the mean . c. is equal to the mean . d. cannot be determined from the graph. ANSWER: b 37. Your friend took an introductory statistics class last year and learned all about density curves. Your friend draws a smooth curve with a long left tail. For such a curve, which of the following is true for the mean and median? a. mean = median b. mean > median c. mean < median d. There is not enough information to answer this question. ANSWER: c 38. Which of the following are two requirements of a density curve? a. The curve is always above the horizontal axis, and the area under the curve is one. b. The curve is always above the horizontal axis, and the curve is symmetric. c. The area above the horizontal axis must be larger than 1 if there is any area below the axis. Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 3 d. The area below the curve and above the horizontal axis must exceed 1. ANSWER: a 39. You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100) and a standard deviation of 12. The median for the exam is: a. 50. b. 72. c. 60. d. 84. ANSWER: b 40. You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100) and a standard deviation of 12. Your score was 90. Your friend took the same statistics course but with another instructor. Your friend had a score of 75 on a test, where the test had a mean of 60 and a standard deviation of 10. What can you conclude from this comparison? a. You clearly ranked better. b. You and your friend ranked equally well. c. Your friend actually ranked better. d. Nothing; the tests cannot be compared. ANSWER: b 41. Suppose you received a score of 95 out of 100 on exam 1. The mean was 79 and the standard deviation was 8. If your score on exam 2 is 90 out of 100, and the mean was 60 with a standard deviation of 15, then you did: a. worse on exam 1. b. worse on exam 2. c. better on exam 1. d. the same on both exams. ANSWER: d 42. Suppose you received a score of 91 out of 100 on Exam 1. The mean was 79 and the standard deviation was 8. What score do you need on Exam 2 to do equally well, if the mean is 60 and the standard deviation is 12? a. 78 b. 91 c. 95 d. 84 ANSWER: a

Page 11

Name:

Class:

Date:

Chapter 4 1. We have information on x, the amount of alcohol consumed according to a food diary (DR), and y, the amount of alcohol consumed according to a frequent food questionnaire (FFQ). If we make a scatter plot of x versus y, we can: a. show the relationship between the answers from the DR (x) and the FFQ (y). b. assesses whether the relationship between the answers on the DR and the answers on the FFQ is positive. c. see the answers that each study participant gave on the FFQ and on the DR. d. All of the answer options are correct. ANSWER: d 2. A scatterplot can be used to illustrate the relationship between: a. two categorical variables. b. one categorical variable and one quantitative variable. c. two quantitative variables. d. All of the answer options are correct. ANSWER: c 3. An introductory statistics class decides to investigate whether there is a relationship between performance on midterm 1 and performance on midterm 2. The instructor creates a scatterplot of midterm 2 scores (y) versus midterm 1 scores (x).

Based on the plot, which of the following statements is probably true? a. The correlation between midterm 1 scores and midterm 2 scores is positive. b. Students who did well on midterm 1 did not do so well on midterm 2, and vice versa. c. There is no relationship between midterm 1 and midterm 2 performance. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 4 d. None of the answer options is correct. ANSWER: a 4. Colleges often rely heavily on raising money for an “annual fund” to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate’s annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. In the studies described: a. annual income is an explanatory variable. b. the correlation between annual income and size of donation is positive. c. the size of the donation to the annual fund is the response variable. d. All of the answer options are correct. ANSWER: d 5. A group of students participated in an experiment to study the association between resting heart rate and exercise heart rate under various exercise conditions. Study participants stepped at a frequency of 14 steps per minute (0), 21 steps per minute (1), and 28 steps per minute (2). To investigate the relationship between resting and exercise heart rate, and to see the effects of step frequency on the relationship, a scatterplot might be created by: a. plotting resting heart rate on the y axis and exercise heart rate on the x axis. b. plotting exercise heart rate on the y axis and step frequency on the x axis. c. using separate symbols for the different step frequencies to see whether the relationship is affected by step frequency, while plotting resting heart rate on the x axis and exercise heart rate on the y axis. d. None of the answer options is correct. ANSWER: c 6. Is exposure to classical music (through instrument lessons or concert attendance) related to a child’s scholastic performance? In a study, researchers measured the amount of exposure to classical music for a group of children, along with their scores on the state’s academic proficiency exam. The explanatory variable in this study is: a. the type of instrument a child plays. b. a child’s score on the state’s proficiency exam. c. the amount of exposure a child has to classical music. d. whether a child passed the state’s proficiency exam. ANSWER: c 7. Archaeologists often find only parts of ancient human remains. For example, they may find a small finger bone, called the metacarpal bone. Because of this, researchers often ask questions like “Is it possible to predict the height of a human from the length of a metacarpal bone?” To investigate, a researcher measures the heights and metacarpal lengths of 200 adults. In making the scatterplot, the researcher should: a. plot the height of the person on the horizontal axis. b. plot the metacarpal length on the horizontal axis. c. first determine whether the heights of humans follow a Normal distribution. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 4 d. use a plotting scale that makes the overall trend roughly linear. ANSWER: b 8. Are higher than average sea surface temperatures associated with a greater than average number of hurricanes each year? In a 2010 study, the average global sea surface temperature anomaly was recorded, along with the number of Atlantic hurricanes above or below the average for that year. The response variable is: a. the number of hurricanes above or below average. b. the global sea surface temperature anomaly. c. the number of hurricanes used in the study. d. None of the answer options is correct. ANSWER: a 9. The volume of oxygen consumed (in liters per minute) while a person is at rest and the volume consumed while a person is exercising (running on a treadmill) were both measured for 50 subjects. The goal was to determine whether the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below.

In this study, the explanatory variable is: a. the volume of oxygen consumed at rest. b. the volume of oxygen consumed while running. c. the instrument used to measure the volume of oxygen consumed. d. either variable—it doesn’t matter which variable is considered the response. ANSWER: a Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 4 10. The volume of oxygen consumed (in liters per minute) while a person is at rest and the volume consumed while a person is exercising (running on a treadmill) were both measured for 50 subjects. The goal was to determine whether the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below.

The scatterplot suggests: a. only that there is a positive association between the volume of oxygen consumed at rest and the volume consumed while running. b. only that there is an outlier in the plot. c. that there is a positive association between the volume of oxygen consumed at rest and the volume consumed while running, and that there is an outlier in the plot. d. neither that there is a positive association between the volume of oxygen consumed at rest and the volume consumed while running, nor that there is an outlier in the plot. ANSWER: c 11. The volume of oxygen consumed (in liters per minute) while a person is at rest and the volume consumed while a person is exercising (running on a treadmill) were both measured for 50 subjects. The goal was to determine whether the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below.

Page 4

Name:

Class:

Date:

Chapter 4

If the outlier at x = 0.65 is removed, the correlation coefficient r will probably: a. increase. b. decrease. c. neither increase nor decrease. d. There is not enough information to determine the effect on r. ANSWER: a 12. The graph below shows a scatterplot of midterm scores plotted against homework scores. The graph contains several points that correspond to unusually low homework scores, and one of those scores is associated with the highest midterm score.

Page 5

Name:

Class:

Date:

Chapter 4

Removing this point will: a. increase the correlation. b. leave the correlation unchanged. c. decrease the correlation. d. The effect cannot be determined from the scatterplot. ANSWER: a 13. A researcher states that bone density in women is negatively associated with age. This means that: a. as women get older, bone density tends to decrease. b. as women get older, bone density tends to increase. c. below-average values of age tend to accompany below-average values of bone density. d. older women aren’t any more likely than younger women to have below-average bone density. ANSWER: a 14. When water flows across farmland, some soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (liters per second) on the amount of soil (kilograms) washed away. The data are given in the following table: Flow rate 0.31 0.85 1.26 2.47 3.75 Eroded soil 0.82 1.95 2.18 3.01 6.07 The association between flow rate and the amount of eroded soil is: a. positive. b. negative. c. neither positive nor negative. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 4 d. impossible to determine, because both variables are categorical. ANSWER: a 15. Below is a scatterplot of the number of home runs versus the number of stolen bases for major league teams in 2009. American League teams are represented by filled circles, and National League teams are represented by open circles.

We conclude that: a. there is a strong positive association for American League teams but a negative association for National League teams. b. there is a strong negative association for American League teams but a positive association for National League teams. c. there is no association for either league. d. all American League teams hit more home runs and stole more bases than did all National League teams. ANSWER: c 16. A researcher measures the correlation between two variables. This correlation indicates: a. whether there is a relationship between the two variables. b. whether a scatterplot will show an interesting pattern. c. whether a cause-and-effect relationship exists between two variables. d. the strength and direction of a linear association between two variables. ANSWER: d Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 4 17. A student wonders whether people with similar heights tend to date each other. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the pairs of data (heights in inches): Women 66 64 66 65 70 Men 72 68 70 68 74 Which of the following statements is true? a. The variables measured are all categorical. b. There is a strong positive correlation between the heights of men and women, because the women are always shorter than the men they date. c. There is a positive correlation between the heights of men and women who are dating each other. d. Correlation makes no sense here, because gender is a categorical variable. ANSWER: c 18. What can be said of the correlation between the brand of an automobile and its quality? a. The correlation is negative, because smaller cars tend to have higher quality and larger cars tend to have lower quality. b. The correlation is positive, because better brands have higher quality. c. If the correlation is negative, an arithmetic mistake was made; this correlation must be positive. d. Correlation makes no sense here, because brand is a categorical variable. ANSWER: d 19. Which of the following statements is correct? a. Changing the units of measurement of x or y does not change the value of the correlation r. b. A negative value for the correlation r indicates the data are strongly unassociated. c. The correlation always has the same units as the x variable but not the y variable. d. The correlation always has the same units as the y variable but not the x variable. ANSWER: a 20. For each menu item at a fast-food restaurant, the fat content (in grams) and the number of calories were recorded. A scatterplot of these data is given:

Page 8

Name:

Class:

Date:

Chapter 4

A plausible value for the correlation between fat content and number of calories is: a. +0.2. b. –0.9. c. +0.9. d. –1.0. ANSWER: c 21. For each menu item at a fast-food restaurant, the fat content (in grams) and the number of calories were recorded. A scatterplot of these data is given:

Page 9

Name:

Class:

Date:

Chapter 4

The restaurant decides to add six new high-calorie, low-fat pasta dishes to its menu. What is a plausible value for the new correlation coefficient describing the relationship between fat and calories? a. +0.2 b. –0.2 c. +0.7 d. –0.7 ANSWER: c 22. Consider the following scatterplot, which depicts the tread depth (measured in mils, where 1 mil = 0.001 inch) versus the number of miles driven on the tire (measured in thousands of miles).

Page 10

Name:

Class:

Date:

Chapter 4

The correlation between x and y: a. is approximately 0.97. b. is approximately –0.97. c. is approximately 0. d. cannot be computed because the trend is curved. Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 4 ANSWER: b 23. Consider the following scatterplot of two variables x and y.

We may conclude that: a. the correlation between x and y must be close to 1, because there is a nearly perfect relationship between them. b. the correlation between x and y must be close to –1, because there is a nearly perfect relationship between them but it is not a straight-line relation. c. the correlation between x and y is close to 0 because, although there is a strong relationship between these variables, it isn’t a linear relationship. d. the correlation between x and y could be any number between –1 and +1; we can say nothing more without knowing the actual values. ANSWER: c 24. Which of the following statements is false? a. Older men tend to have lower muscle density, so the correlation between age and muscle density in older men must be negative. b. Older children tend to be taller than younger children, so the correlation between age and height in children must be positive. c. A researcher finds that the correlation between two variables is close to 0, so the two variables must be unrelated. d. Taller people tend to be heavier than shorter people, so the correlation between height and weight Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 4 must be positive. ANSWER: c 25. Frequent food questionnaires (FFQ) are a simple way to obtain information on the foods that individuals consume by asking them questions about typical amounts of food consumed in a day, a week, or a month. A more accurate picture can be gained by obtaining a detailed food diary (DR) for several days that are randomly chosen over a certain time period. The data obtained from a frequent food questionnaire can be compared with the food diary to assess the validity of the questionnaire. The data below are for seven individuals who participated in such a study on alcohol consumption. DR FFQ 8.26 1.68 0.83 0 20.13 15.10 11.16 7.49 7.18 12.84 1.76 0 22.66 25.06 The correlation for these data is: a. –0.89. b. 0.89. c. 0. d. None of the answer options is correct. ANSWER: b 26. Frequent food questionnaires (FFQ) are a simple way to obtain information on the foods that individuals consume by asking them questions about typical amounts of food consumed in a day, a week, or a month. A more accurate picture can be gained by obtaining a detailed food diary (DR) for several days that are randomly chosen over a certain time period. The data obtained from a frequent food questionnaire can be compared with that obtained from the food diary to assess the validity of the questionnaire. The correlation between alcohol consumption obtained from the food questionnaire and alcohol consumption obtained from the diary was r = 0.89, based on seven individuals: DR 8.26 0.83 20.13 11.16 7.18 1.76 22.66

FFQ 1.68 0 15.10 7.49 12.84 0 25.06

Based on the seven individuals for whom data are available, which of the following statements is incorrect? a. Typical consumption, as stated on the FFQ, is positively associated with what is actually consumed. b. The FFQ is a reasonable tool to obtain information on the amount of alcohol consumed by individuals. Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 4 c. Because r > 0, the amount that is truly consumed is always larger than what is stated on the FFQ. d. All of the answer options are correct. ANSWER: c 27. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week. The response variable is: a. weekly income. b. weekly expenditure. c. gender. d. None of the answer options is correct. ANSWER: b 28. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers to spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week. The explanatory variable is: a. weekly income. b. weekly expenditure. c. gender d. All of the answer options are correct. ANSWER: a 29. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week. An appropriate graphical display of the relationship between grocery expenditure and income might be: a. a side-by-side histogram. b. a side-by-side boxplot. c. a side-by-side pie chart. d. None of the answer options is correct. ANSWER: d 30. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week.

Page 14

Name:

Class:

Date:

Chapter 4

The scatterplot of weekly grocery expenditures vs. income shows: a. a weak positive association between the two variables. b. a weak negative association between the two variables. c. a strong positive association between the two variables. d. a strong negative association between the two variables. ANSWER: a 31. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week. The gender of each shopper was also obtained. One question of interest was whether spending patterns differed much by gender.

Page 15

Name:

Class:

Date:

Chapter 4

The scatterplot above shows red dots for females and black dots for males. Based on this plot: a. males and females exhibit similar weak positive relationships between income and grocery expenditures. b. males tend to spend more as income rises, while females spend the same whether income is high or low. c. males spend more as income rises, while females spend less as income rises. d. None of the answer options is correct. ANSWER: a 32. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week. The gender of each shopper was also obtained. The relationship between grocery expenditure and income was assessed by calculating both a correlation for the females only and a correlation for the males only. For the females r = 0.45, and for the males r = 0.38. We conclude that: a. the relationship between grocery expenditures and income is stronger for males. Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 4 b. the relationship between grocery expenditures and income is the same for males and females. c. the relationship between grocery expenditures and income is stronger for females. d. there is not enough information to determine which gender has a stronger relationship between grocery expenditures and income. ANSWER: c 33. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week. The gender of each shopper was also obtained. The data below are expenditures and income for 10 selected survey participants. Income Grocery 98 52 201 78 298 108 398 121 481 80 600 99 738 162 805 81 890 105 1023 173 The correlation for these data is given by: a. 0.649. b. –0.649. c. 0.4212. d. –0.4212. ANSWER: a 34. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week. A second survey was conducted at a different supermarket, and the scatterplot was obtained for the relationship between grocery expenditures and income in that survey as well. The two scatterplots are given below:

Page 17

Name:

Class:

Date:

Chapter 4

Which of the following statements is true? a. The correlations for both surveys are similar in magnitude. b. The correlation is closer to 1 in Survey 1 than in Survey 2. c. The correlation is closer to 0 in Survey 1 than in Survey 2. d. The correlations need to be calculated to determine which is closer to 1; a scatterplot cannot provide this information. ANSWER: c 35. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week. The data below are for 10 selected survey participants: Income Grocery 98 52 201 78 Copyright Macmillan Learning. Powered by Cognero.

Page 18

Name:

Class:

Date:

Chapter 4 298 398 481 600 738 805 890 1023

108 121 80 99 162 81 105 173

The scatterplot with a linear trend line is given below:

If the expenditure for subject 7 is decreased and the expenditure for subject 8 is increased, the effect on the correlation: a. will be to decrease it. b. will be to increase it. c. will be nil; that is, there will be no effect. d. cannot be determined without knowing the new values for expenditure. Copyright Macmillan Learning. Powered by Cognero.

Page 19

Name:

Class:

Date:

Chapter 4 ANSWER: b 36. Correlation measures linear association. If the relationship between an explanatory variable x and a response y is positive and increasing but has some curvature, as shown by a trend line through the scatter, the correlation will be: a. 0. b. 0 < correlation < 1. c. –1 < correlation < 0. d. There is not enough information to determine the effect. ANSWER: b

Page 20

Name:

Class:

Date:

Chapter 5 1. The graph below shows the scores that students in an advanced statistics course received for a midterm exam and for the homework (Hw) completed before the exam. The maximum homework score a student could obtain was 500, and the maximum midterm score was 350.

Hw score Exam score

387 190

275 200

280 108

459 323

395 315

314 256

428 341

366 236

421 285

234 125

The slope for the regression line is: a. 0.84. b. 0.70. c. 0.91. d. −0.84. ANSWER: c 2. The regression equation below relates the scores students in an advanced statistics course received for homework completed and for the subsequent midterm exam. Homework scores are based on assignments that preceded the exam. The maximum homework score a student could obtain was 500, and the maximum midterm score was 350. The regression line that was obtained is given by

. If a student had a

homework score of 420, the midterm score would be predicted to be (rounded to an integer): a. 298. b. 336. c. 378. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 5 d. None of the answer options is correct. ANSWER: a 3. The data and the graph below show the scores that students in an advanced statistics course received for homework (Hw) completed and for the subsequent midterm exam. Homework scores are based on assignments that preceded the exam. The maximum homework score a student could obtain was 500, and the maximum midterm score was 350.

Hw score 387 275 280 459 395 314 428 Exam 190 200 108 323 315 256 341 score The residual for the student whose homework score was 395 is: a. negative. b. positive. c. zero. d. undetermined.

366 236

421 285

234 125

ANSWER: b 4. The graph below shows the scores that students in an advanced statistics course received for homework completed and for the subsequent midterm exam. Homework scores are based on assignments that preceded the exam. The maximum homework score a student could obtain was 500, and the maximum midterm score was 350. The mean homework score was 356 for the 10 students, and the mean exam score was 238.

Page 2

Name:

Class:

Date:

Chapter 5

If a student had scored exactly 356 on the homework and 238 on the midterm, the residual would be approximately: a. 1. b. −1. c. 0. d. The answer cannot be determined with the information given. ANSWER: c 5. The graphs below show the scores that students in an advanced statistics course received for homework completed and for the subsequent midterm exam. Homework scores are based on assignments that preceded the exam. The maximum homework score a student could obtain was 500, and the maximum midterm score was 350. The original score for student 10 was 234 (the lowest) for the homework and 125 (the lowest) for the exam. After the student reviewed the exam, the student discovered that only a third of the problems had been graded, and the student’s grade was subsequently changed to 348 (the highest). The scatterplots for the original scores and the revised scores are below. Original scores:

Page 3

Name:

Class:

Date:

Chapter 5

Revised scores:

Which of the following is true? a. The correlations for both the original and the corrected scores are the same. b. The correlation for the original scores is higher. c. The correlation for the revised scores is higher. Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 5 d. Correlation is not affected by changing some scores. ANSWER: b 6. The least-squares regression line is: a. the line that passes through the most data points. b. the line that makes the sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as small as possible. c. the line such that half of the data points fall above the line and half fall below the line. d. All of the answer options are correct. ANSWER: b 7. The following is a scatterplot of the liters of alcohol from drinking wine consumed per person and the death rates from heart disease per 100,000 people for each of 19 countries. The least-squares regression line has been drawn in on the plot.

Based on the least-squares regression line, we would predict that in a country where 7 liters of alcohol from wine were consumed per person, the death rate from heart disease per 100,000 people would be about: a. 50. b. 100. c. 260. d. 700. ANSWER: b 8. A researcher wants to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). The researcher measures the amount of soil washed away for various flow rates and, from these data, calculates the least-squares regression line to be: amount of eroded soil = 0.4 + 1.3x (where x is flow rate). The correlation between amount of eroded soil and flow rate would be: Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 5 a. 1/1.3. b. 1.3. c. positive, but we cannot say what the exact value is. d. either positive or negative, but it is impossible to say anything else about the correlation from the information given. ANSWER: c 9. In many fast-food restaurants, there is a strong correlation between a menu item’s fat content (measured in grams) and its calorie content. We want to investigate this relationship. Using all of the food menu items at a well-known fast-food restaurant, we measure the fat content and the calorie content. We decide to fit the leastsquares regression line to the data, with fat content (x) as the explanatory variable and with calorie content (y) as the response variable. A scatterplot of the data (with regression line included) and a summary of the data are provided. One of the menu items is a hamburger with 107 grams of fat and 1410 calories.

r = 0.979 (correlation between x and y) Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 5 = 40.35 grams (mean of the values of x) = 662.88 calories (mean of the values of y) = 27.99 grams (standard deviation of the values of x) = 324.90 calories (standard deviation of the values of y) The slope of the least-squares regression line is: a. −11.36. b. 11.36. c. 0.979. d. 16.08. ANSWER: b 10. In many fast-food restaurants, there is a strong correlation between a menu item’s fat content (measured in grams) and its calorie content. We want to investigate this relationship. Using all of the food menu items at a well-known fast-food restaurant, we measure the fat content and the calorie content. We decide to fit the leastsquares regression line to the data, with fat content (x) as the explanatory variable and with calorie content (y) as the response variable. A scatterplot of the data (with regression line included) and a summary of the data are provided. One of the menu items is a hamburger with 107 grams of fat and 1410 calories.

Page 7

Name:

Class:

Date:

Chapter 5

r = 0.979 (correlation between x and y) = 40.35 grams (mean of the values of x) = 662.88 calories (mean of the values of y) = 27.99 grams (standard deviation of the values of x) = 324.90 calories (standard deviation of the values of y) The intercept of the least-squares regression line is: a. 204.50. b. 662.88. c. −662.88. d. None of the answer options is correct. ANSWER: a 11. In many fast-food restaurants, there is a strong correlation between a menu item’s fat content (measured in Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 5 grams) and its calorie content. We want to investigate this relationship. Using all of the food menu items at a well-known fast-food restaurant, we measure the fat content and the calorie content. We decide to fit the leastsquares regression line to the data, with fat content (x) as the explanatory variable and with calorie content (y) as the response variable. A scatterplot of the data (with regression line included) and a summary of the data are provided. One of the menu items is a hamburger with 107 grams of fat and 1410 calories.

r = 0.979 (correlation between x and y) = 40.35 grams (mean of the values of x) = 662.88 calories (mean of the values of y) = 27.99 grams (standard deviation of the values of x) = 324.90 calories (standard deviation of the values of y) Refer to the example data point (107 grams, 1410 calories). What is the residual corresponding to this observation? a. 10 calories b. 10 grams Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 5 c. −10 grams d. −10 calories ANSWER: d 12. In many fast-food restaurants, there is a strong correlation between a menu item’s fat content (measured in grams) and its calorie content. We want to investigate this relationship. Using all of the food menu items at a well-known fast-food restaurant, we measure the fat content and the calorie content. We decide to fit the leastsquares regression line to the data, with fat content (x) as the explanatory variable and with calorie content (y) as the response variable. A scatterplot of the data (with regression line included) and a summary of the data are provided. One of the menu items is a hamburger with 107 grams of fat and 1410 calories.

r = 0.979 (correlation between x and y) = 40.35 grams (mean of the values of x) = 662.88 calories (mean of the values of y) = 27.99 grams (standard deviation of the values of x) Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 5 = 324.90 calories (standard deviation of the values of y) What is true about the regression line in this example? a. The point (40.35, 662.88) lies on the regression line. b. 97.9% of the variation is explained by the regression model. c. When there are 0 grams of fat, there will be approximately 200 calories. d. 95.8% of the response variables can be explained by the predictors. ANSWER: a 13. The proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is: a. the correlation coefficient. b. the slope of the least-squares regression line. c. the square of the correlation coefficient. d. the intercept of the least-squares regression line. ANSWER: c 14. Which of the following is correct? a. If a straight line is a good summary of the data, the mean of the residuals from least-squares regression should be zero. b. The square of the correlation is the slope of the least-squares regression line. c. The square of the correlation is the proportion of the data lying on the least-squares regression line. d. The correlation r is the slope of the least-squares regression line. ANSWER: a 15. Suppose we fit the least-squares regression line to a set of data. The plot of the residuals is given below.

This plot suggests that: a. a straight line is not a good summary for the data. b. the correlation must be zero. c. the correlation must be positive. Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 5 d. outliers must be present. ANSWER: a 16. The correlation between the height and weight of children aged 6 to 9 is found to be about r = 0.8. Suppose we use the height x of a child to predict the weight y of the child. We conclude that: a. the least-squares regression line of y on x would have a slope of 0.8. b. about 80% of the time, age will accurately predict weight. c. height is generally 80% of a child’s weight. d. the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64. ANSWER: d 17. Suppose the least-squares regression line for a set of data has slope 72.4. Now suppose we remove a point from the data, compute the least-squares regression line, and find that the new slope is 8.7. The point removed would be considered: a. robust. b. influential. c. a residual. d. a response. ANSWER: b 18. The following is a scatterplot for profits versus sales (in tens of thousands of dollars) for a sample of 14 large companies. The correlation between sales and profits is 0.949.

Page 12

Name:

Class:

Date:

Chapter 5

From this information we see that: a. there is one very influential observation in the data. b. there is a clear error because profits cannot be negative. c. profits can be accurately predicted from sales. d. All of the answer options are correct. ANSWER: a 19. The following is a scatterplot for profits versus sales (in tens of thousands of dollars) for a sample of 14 large companies. The correlation between sales and profits is 0.949.

Page 13

Name:

Class:

Date:

Chapter 5

If we omitted the observation in the upper right corner of the scatterplot, the slope of the regression line would: a. increase. b. decrease. c. change very little. d. There is not enough information to determine the answer. ANSWER: b 20. John’s parents recorded his height at various ages up to 66 months. Below is a record of the results. Age (months) 36 48 54 60 66 Height (inches) 35 38 41 43 45 John’s parents decide to use the least-squares regression line of John’s height on age to predict his height at age 21 years (252 months). We conclude that: Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 5 a. John’s height (in inches) should be about half his age (in months). b. John’s parents will get a fairly accurate estimate of his height at age 21 years, because the data are clearly correlated. c. such a prediction could be misleading, because it involves extrapolation. d. All of the answer options are correct. ANSWER: c 21. For which of the following scatterplots would the correlation be close to 1?. a.

Page 15

Name:

Class:

Date:

Chapter 5 d. . All of the answer options are correct because, in each plot, the points lie on a well-defined curve. ANSWER: b 22. The following is a scatterplot of the percent of children under age 18 who are not in school or in the labor force versus the number of juvenile violent crime arrests for each of the 50 states. The least-squares regression line has been drawn in on the plot.

Predicting the number of juvenile violent crime arrests if 25% of the children are not in school or in the labor force is called: a. association. b. extrapolation. c. causation. d. correlation. ANSWER: b 23. A researcher obtained students' average SAT scores in each of the 50 states and the average teacher salaries in each of the 50 states and found a negative correlation between these variables. The researcher concluded that a lurking variable must be present. By “lurking variable,” the researcher means: a. a variable that is not among the variables studied but that affects the response variable. b. the true cause of a response. c. any variable that produces a large residual. d. the true variable, which is explained by the explanatory variable. ANSWER: a 24. A study of elementary school children, ages 6 to 11, finds a high positive correlation between shoe size x and score y on a test of reading comprehension. The observed correlation is most likely to be due to: a. the effect of a lurking variable, such as age or years of reading experience. Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 5 b. a mistake, because the correlation must be negative. c. cause and effect (larger shoe size causes higher reading comprehension). d. reverse cause and effect (higher reading comprehension causes larger shoe size). ANSWER: a 25. Curiously, during months when sales of beer are above average, sales of ice cream also tend to be above average; and during months when sales of beer are below average, sales of ice cream also tend to be below average. Which of the following can we conclude from these facts? a. The correlation between beer sales and ice cream sales is negative. b. For a lot of people, drinking beer causes a desire for ice cream, or vice versa. c. A scatterplot of monthly ice cream sales versus monthly beer sales would show that a straight line describes the pattern in the plot, but it would have to be a horizontal line. d. None of the answer options is correct. ANSWER: d 26. The owner of a chain of supermarkets notices that there was a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. The owner is curious whether the observed association is due to a cause-and-effect relationship between eating ice cream and desiring beer. To investigate this, the owner should use: a. the least-squares regression line. b. the correlation coefficient. c. the square of the correlation coefficient. d. a well-designed experiment. ANSWER: d 27. According to the 2010 census, those states with an above-average number of people who fail to complete high school (x) tend to have an above-average number of infant deaths (x). In other words, there is a positive association between x and x. The most plausible explanation for this association is that: a. x causes x. Thus, programs to keep teens in school will help reduce the number of infant deaths. b. x causes x. Thus, programs that reduce infant deaths will ultimately reduce the number of high school dropouts. c. lurking variables are probably present. For example, states with large populations will have both a larger number of people who fail to complete high school and a larger number of infant deaths. d. the association between x and x is purely coincidental. It is implausible to believe that the observed association could be anything other than accidental. ANSWER: c 28. A newspaper article is summarized as follows: According to a new study, teachers may be more inclined to give higher grades to students, hoping to gain favor with the university administrators who grant tenure. The study examined the average grade and teaching evaluation in a large number of courses given in 1997 in order to investigate the effects of grade inflation on evaluations. “I am concerned with student evaluations because Copyright Macmillan Learning. Powered by Cognero.

Page 17

Name:

Class:

Date:

Chapter 5 instruction has become a popularity contest for some teachers,” said Professor Smith, who recently completed the study. Results showed that a higher average grade directly corresponded to a more positive evaluation. The statement underlined above means the study found that: a. higher course grades are positively associated with a more positive teaching evaluation. b. teaching evaluation is negatively associated with course grade. c. there is a perfect positive correlation between course grade and teaching evaluation. d. All of the answer options are correct. ANSWER: a 29. A newspaper article is summarized as follows: According to a new study, teachers may be more inclined to give higher grades to students, hoping to gain favor with the university administrators who grant tenure. The study examined the average grade and teaching evaluation in a large number of courses given in 1997 in order to investigate the effects of grade inflation on evaluations. “I am concerned with student evaluations because instruction has become a popularity contest for some teachers,” said Professor Smith, who recently completed the study. Results showed that a higher average grade directly corresponded to a more positive evaluation. Which of the following would be a valid conclusion to draw from the study? a. Teachers can improve their teaching evaluations by giving higher grades. b. A good teacher, as measured by teaching evaluations, helps students learn better, which results in higher grades. c. Higher grades result in above-average teaching evaluations. d. None of the answer options is correct. ANSWER: d 30. Intrigued by a 2013 study at the University of Nebraska that suggested marijuana smokers may be thinner than other adults, a group of students did a project to explore the relationship between body mass index (BMI) and amount of time spent under the influence of marijuana (measured in hours per week). Based on a random sample of 33 students at their university, they used BMI as the response variable. The equation of the leastsquares regression line is: hours per month under influence = 49.2 − 1.15 BMI. Also, r2 = 0.134.

Page 18

Name:

Class:

Date:

Chapter 5

The correlation coefficient for these data is: a. 0.134. b. 0.366. c. −0.134. d. −0.366. ANSWER: d 31. Intrigued by a 2013 study at the University of Nebraska that suggested marijuana smokers may be thinner than other adults, a group of students did a project to explore the relationship between body mass index (BMI) and amount of time spent under the influence of marijuana (measured in hours per week). Based on a random sample of 33 students at their university, they used BMI as the response variable. The equation of the leastsquares regression line is: hours per month under influence = 49.2 − 1.15 BMI. Also, r2 = 0.134. Copyright Macmillan Learning. Powered by Cognero.

Page 19

Name:

Class:

Date:

Chapter 5

How effective is the regression model for these data? a. extremely effective, because 13.4% of the variation in the data is explained by the model b. not effective, because only 13.4% of the variation in the data is explained by the model c. extremely effective, because 36.6% of the variation in the data is explained by the model d. not effective, because only 36.6% of the variation in the data is explained by the model ANSWER: b 32. Intrigued by a 2013 study at the University of Nebraska that suggested marijuana smokers may be thinner than other adults, a group of students did a project to explore the relationship between body mass index (BMI) and amount of time spent under the influence of marijuana (measured in hours per week). Based on a random sample of 33 students at their university, they used BMI as the response variable. The equation of the leastsquares regression line is: hours per month under influence = 49.2 − 1.15 BMI. Also, = 0.134. Copyright Macmillan Learning. Powered by Cognero.

Page 20

Name:

Class:

Date:

Chapter 5

Which of the following would be a valid conclusion to draw from the study? a. Smoking more frequently can lead to a decrease in BMI. b. There is a weak negative relationship between hours per month under the influence and BMI. c. There is a strong association, but the pattern is nonlinear. d. None of the answer options is correct. ANSWER: b 33. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper’s family and the grocery bill for that week. The gender of the shopper was also obtained. The data below are expenditures and income for 10 selected survey participants. Copyright Macmillan Learning. Powered by Cognero.

Page 21

Name:

Class:

Date:

Chapter 5 Income Grocery 98 52 201 78 298 108 398 121 481 80 600 99 738 162 805 81 890 105 1023 173 The slope of the regression line for these data is given by: a. 0.07951. b. –0.07951. c. 0.649. d. –0.649. ANSWER: a 34. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper’s family and the grocery bill for that week. The gender of the shopper was also obtained. The data below are expenditures and income for 10 selected survey participants. Income Grocery 98 52 201 78 298 108 398 121 481 80 600 99 738 162 805 81 890 105 1023 173 The intercept of the regression line for these data is given by: a. 105.9. b. 0.079. c. 61.91. d. 43.82. ANSWER: c 35. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was Copyright Macmillan Learning. Powered by Cognero.

Page 22

Name:

Class:

Date:

Chapter 5 administered asking about the weekly income of the shopper’s family and the grocery bill for that week. The gender of the shopper was also obtained. The graph below contains a scatterplot with a least-squares line.

The intercept can be estimated as approximately: a. 51. b. 61. c. 71. d. 81. ANSWER: b 36. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper’s family and the grocery bill for that week. The gender of the shopper was also obtained. The graph below contains a scatterplot with a least-squares line.

Page 23

Name:

Class:

Date:

Chapter 5

The average income in the sample was $553. Based on the least-squares line, the average grocery bill for this sample was approximately: a. $90. b. $95. c. $100. d. $105. ANSWER: d 37. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income was related to shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper’s family and the grocery bill for that week. A least-squares line was obtained for the data, and the residual sum of squares was obtained. The residual sum of squares measures the: sum of squared distances of the response variable values to the mean of the response variable. a. sum of squared distances of the explanatory variable to the mean of the explanatory variable. b. sum of the squared distance between the observed response and the corresponding predicted Copyright Macmillan Learning. Powered by Cognero.

Page 24

Name:

Class:

Date:

Chapter 5 c. value on the least-squares line for each point. d. None of the answer options is correct. ANSWER: c 38. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper’s family and the grocery bill for that week. The least-squares line had a slope of 0.079. The average amount by which the grocery bill increases for an increase of $100 per week is: a. $7.9. b. $10.0. c. $0.079. d. The answer cannot be determined from the information provided. ANSWER: a 39. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper’s family and the grocery bill for that week. The correlation was found to be r = 0.649. The percent of variation in the response explained by the regression line is: a. 64.9%. b. 0.649%. c. 42.1%. d. 0.421%. ANSWER: c 40. An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper’s family and the grocery bill for that week. The correlation was found to be r = 0.649. The standard deviation for the grocery bills was 37.87, and for income it was 309.04. Therefore, the slope of the least-squares line is: a. 0.649. b. 0.0795. c. 0.0021. d. 5.296. ANSWER: b 41. Given the least-squares regression line y = –3 + 3x, which of the following is true? a. The relationship between x and y is positive. b. The relationship between x and y is negative. Copyright Macmillan Learning. Powered by Cognero.

Page 25

Name:

Class:

Date:

Chapter 5 c. As x decreases, y increases. d. None of the answer options is correct. ANSWER: a 42. A frequent flyer was interested in the relationship between dollars spent on flying and the distance flown. She randomly sampled 20 frequent flyers of a certain airline. She collected the number of miles flown in the previous year and the total amount of money the flyer spent. A regression line of distance flown on money spent was fit to the data, and the intercept and slope were calculated to be a = 24,000 and b = 10. A person who spent $2000 is predicted to have flown: a. 24,000 miles. b. 34,000 miles. c. 44,000 miles. d. 54,000 miles. ANSWER: c 43. A frequent flyer was interested in the relationship between dollars spent on flying and the distance flown. She randomly sampled 20 frequent flyers of a certain airline. She collected the number of miles flown in the previous year and the total amount of money the flyer spent. A regression line of distance flown on money spent was fit to the data, and the intercept and slope were calculated to be a = 24,000 and b = 10. One of the randomly sampled frequent flyers was found to have spent $2500 and to have flown 41,000 miles. The residual for this observation is: a. 4000. b. –8000. c. 12,000. d. –16,000. ANSWER: b 44. A frequent flyer was interested in the relationship between dollars spent on flying and the distance flown. She randomly sampled 20 frequent flyers of a certain airline. She collected the number of miles flown in the previous year and the total amount of money the flyer spent. A regression line of distance flown on money spent was fit to the data, and the intercept and slope were calculated to be a = 24,000 and b = 10. The amounts spent ranged from a low of $1200 to a high of $9000. If all the frequent flyers spend similar amounts in the coming year and fly similar distances, except for the flyer who spent $9000 but will spend $20,000 next year, that observation is best described as: a. an outlier, because the explanatory value is very large. b. an outlier, because the response variable is likely to be very large. c. an influential observation, because the explanatory variable is large and deleting it could change the slope coefficient. d. None of the answer options is correct. ANSWER: c 45. A frequent flyer was interested in the relationship between dollars spent on flying and the distance flown. She randomly sampled 20 frequent flyers of a certain airline. She collected the number of miles flown in the Copyright Macmillan Learning. Powered by Cognero.

Page 26

Name:

Class:

Date:

Chapter 5 previous year and the total amount of money the flyer spent. A regression line of distance flown on money spent was fit to the data, and the intercept and slope were calculated to be a = 24,000 and b = 10. A least-squares line is: a. called resistant, because an outlier in the response value does not always change the slope value. b. called resistant, because an outlier in the explanatory value can potentially greatly affect the value of the slope. c. not resistant, because an outlier in the response may not change the value of the slope. d. not resistant, because an outlier in the explanatory value can greatly change the slope. ANSWER: d 46. A frequent flyer was interested in the relationship between dollars spent on flying and the distance flown. She randomly sampled 20 frequent flyers of a certain airline. She collected the number of miles flown in the previous year and the total amount of money the flyer spent. A regression line of distance flown on money spent was fit to the data, and the intercept and slope were calculated to be a = 24,000 and b = 10. Based on the regression line, we can conclude that: a. if a frequent flyer has more money to spend, that person will fly more. b. if a frequent flyer has less money to spend, that person will fly less or shop for cheaper flights. c. if a frequent flyer has more money to spend, that person will shop for more expensive flights. d. there is a positive association between distance flown and amount of money spent on flying. ANSWER: d

Page 27

Name:

Class:

Date:

Chapter 6 1. A study was conducted on horses to identify factors that might contribute to the formation of enteroliths— stones that form in the colon of the horse and eventually lead to blockage and death. The table below summarizes disease status by sex (gelding, mare, and stallion). Horses that have enteroliths are listed as case, and horses that do not are listed as control. Sex Disease Status: Case Disease Status: Control Total Gelding 29 41 Mare 28 32 Stallion 5 2 Total 62 75 What percent of geldings had enteroliths? a. 41% b. 47% c. 21% d. 56% ANSWER: a

70 60 7 137

2. A study was conducted on horses to identify factors that might contribute to the formation of enteroliths— stones that form in the colon of the horse and eventually lead to blockage and death. The table below summarizes disease status by sex (gelding, mare, and stallion). Horses that have enteroliths are listed as case, and horses that do not are listed as control. Sex Disease Status: Case Disease Status: Control Total Gelding 29 41 70 Mare 28 32 60 Stallion 5 2 7 Total 62 75 137 Which of the following statements is not supported by the data? a. Mares are more likely than geldings to develop enteroliths. b. Less than half of geldings develop enteroliths. c. Stallions are the least likely to develop enteroliths. d. Mares are slightly more likely than stallions to develop enteroliths. ANSWER: c 3. An administrator in charge of residential life services recently conducted a survey of undergraduate college students at a small university. A random sample of 300 students was selected from each class level (first year, sophomore, junior, or senior). Each student was asked to complete and return a short questionnaire on the quality of campus residences. Some students returned the questionnaire; some did not. This is summarized in the table below. Class Returned No response Total First year 110 190 300 Sophomore 130 170 300 Junior 170 130 300 Senior 160 140 300 What percent of first years returned the questionnaire? Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 6 a. 50% b. 47.5% c. 36.7% d. 63.3% ANSWER: c 4. An administrator in charge of residential life services recently conducted a survey of undergraduate college students at a small university. A random sample of 300 students was selected from each class level (first year, sophomore, junior, or senior). Each student was asked to complete and return a short questionnaire on the quality of campus residences. Some students returned the questionnaire; some did not. This is summarized in the table below. Class Returned No response Total First year 110 190 300 Sophomore 130 170 300 Junior 170 130 300 Senior 160 140 300 Which of the following conclusions seems to be supported by the data? a. Juniors and seniors appear to be more likely to return the survey than first years and sophomores. b. Juniors and seniors are happier with the quality of campus residences than first years and sophomores. c. Students who did not return the questionnaire are unhappy with the quality of campus residences. d. The percent of students returning the questionnaire is the same for each class. ANSWER: a 5. An administrator in charge of residential life services recently conducted a survey of undergraduate college students at a small university. A random sample of 300 students was selected from each class level (first year, sophomore, junior, or senior). Each student was asked to complete and return a short questionnaire on the quality of campus residences. Some students returned the questionnaire; some did not. This is summarized in the table below. Class Returned No response Total First year 110 190 300 Sophomore 130 170 300 Junior 170 130 300 Senior 160 140 300 What percent of all students surveyed returned the questionnaire? a. 50% b. 52.5% c. 47.5% d. None of the answer options is correct. ANSWER: c 6. An administrator in charge of residential life services recently conducted a survey of undergraduate college students at a small university. A random sample of 300 students was selected from each class level (first year, sophomore, junior, or senior). Each student was asked to complete and return a short questionnaire on the Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 6 quality of campus residences. Some students returned the questionnaire; some did not. This is summarized in the table below. Class Returned No response Total First year 110 190 300 Sophomore 130 170 300 Junior 170 130 300 Senior 160 140 300 How many different marginal distributions could be plotted from these data? a. 0 b. 1 c. 2 d. None of the answer options is correct. ANSWER: c 7. A study was conducted on horses to identify factors that might contribute to the formation of enteroliths— stones that form in the colon of the horse and eventually lead to blockage and death. The table below summarizes disease status by sex (gelding, mare, and stallion). Horses that have enteroliths are listed as case, and horses that do not are listed as control. Sex Disease Status: Case Disease Status: Control Total Gelding 29 41 70 Mare 28 32 60 Stallion 5 2 7 Total 62 75 137 The proportion calculated as p = (62/137) = 0.4526 is: a. the inverse proportion. b. the marginal proportion of cases. c. the restricted proportion of cases that are geldings. d. None of the answer options is correct. ANSWER: b 8. An administrator in charge of residential life services recently conducted a survey of undergraduate college students at a small university. A random sample of 300 students was selected from each class level (first year, sophomore, junior, or senior). Each student was asked to complete and return a short questionnaire on the quality of campus residences. Some students returned the questionnaire; some did not. This is summarized in the table below: Class Returned No response Total First year 110 190 300 Sophomore 130 170 300 Junior 170 130 300 Senior 160 140 300 How many different conditional distributions could be plotted from these data? a. 2 b. 4 c. 6 Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 6 d. None of the answer options is correct. ANSWER: c 9. A study was conducted on horses to identify factors that might contribute to the formation of enteroliths— stones that form in the colon of the horse and eventually lead to blockage and death. The table below summarizes disease status by sex (gelding, mare, and stallion). Horses that have enteroliths are listed as case, and horses that do not are listed as control. Sex Disease Status: Case Disease Status: Control Total Gelding 29 41 70 Mare 28 32 60 Stallion 5 2 7 Total 62 75 137 How many conditional distributions for disease status p (being a case, given sex) can be calculated for these data? a. 1 b. 2 c. 3 d. 4 ANSWER: c 10. A study was conducted on horses to identify factors that might contribute to the formation of enteroliths— stones that form in the colon of the horse and eventually lead to blockage and death. The table below summarizes disease status by sex (gelding, mare, and stallion). Horses that have enteroliths are listed as case, and horses that do not are listed as control. Sex Disease Status: Case Disease Status: Control Total Gelding 29 41 70 Mare 28 32 60 Stallion 5 2 7 Total 62 75 137 How many conditional distributions for gender p (being a mare, given disease status) can be calculated for these data? a. 1 b. 2 c. 3 d. 4 ANSWER: b 11. The following table describes the opinions of the 570 people who returned a residential life services questionnaire to researchers at a small university. Students were classified by class (first year, sophomore, junior, or senior) and by their opinion of campus residence quality (high quality, medium quality, or low quality). Class High Medium Low Total First year 65 25 20 110 Sophomore 55 30 45 130 Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 6 Junior 60 40 70 170 Senior 30 60 70 160 Total 210 155 205 570 What percent of seniors feel that the quality of campus residences is not high? a. 37.5% b. 43.8% c. 81.3% d. 63.2% ANSWER: c 12. The following table describes the opinions of the 570 people who returned a residential life services questionnaire to researchers at a small university. Students were classified by class (first year, sophomore, junior, or senior) and by their opinion of campus residence quality (high quality, medium quality, or low quality). Class High Medium Low Total First year 65 25 20 110 Sophomore 55 30 45 130 Junior 60 40 70 170 Senior 30 60 70 160 Total 210 155 205 570 What percent of all students who responded are sophomores? a. 25% b. 19.3% c. 22.8% d. 29.8% ANSWER: c 13. The following table describes the opinions of the 570 people who returned a residential life services questionnaire to researchers at a small university. Students were classified by class (first year, sophomore, junior, or senior) and by their opinion of campus residence quality (high quality, medium quality, or low quality). Class High Medium Low Total First year 65 25 20 110 Sophomore 55 30 45 130 Junior 60 40 70 170 Senior 30 60 70 160 Total 210 155 205 570 Of the students who feel campus residences are of high quality, what percent are seniors? a. 14.3% b. 18.8% c. 28.1% d. 33.3% ANSWER: a Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 6 14. The following table describes the opinions of the 570 people who returned a residential life services questionnaire to researchers at a small university. Students were classified by class (first year, sophomore, junior, or senior) and by their opinion of campus residence quality (high quality, medium quality, or low quality). Class High Medium Low Total First year 65 25 20 110 Sophomore 55 30 45 130 Junior 60 40 70 170 Senior 30 60 70 160 Total 210 155 205 570 Which marginal or conditional distribution would you use to determine what percent of all students who responded are sophomores? a. the marginal distribution of class b. the marginal distribution of opinion of residence quality c. the conditional distribution of opinion of residence quality, given that class is “sophomore” d. None of the answer options is correct. ANSWER: a 15. The following table describes the opinions of the 570 people who returned a residential life services questionnaire to researchers at a small university. Students were classified by class (first year, sophomore, junior, or senior) and by their opinion of campus residence quality (high quality, medium quality, or low quality). Class High Medium Low Total First year 65 25 20 110 Sophomore 55 30 45 130 Junior 60 40 70 170 Senior 30 60 70 160 Total 210 155 205 570 Which marginal or conditional distribution would you use to determine what percent of the students who feel campus residences are of high quality are seniors? a. the marginal distribution of class b. the marginal distribution of opinion of residence quality c. the conditional distribution of class, given that opinion of residence quality is high d. None of the answer options is correct. ANSWER: c 16. If X and Y are categorical variables, one way to identify whether there is a relationship between them is to: a. calculate the correlation between X and Y. b. draw a scatterplot of the X- and Y-values. c. make a two-way table of the X- and Y-values. d. All of the answer options are correct. ANSWER: c 17. In a study of the link between high blood pressure and cardiovascular disease, a group of white men aged 35 Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 6 to 64 was followed for five years. At the beginning of the study, each man had his blood pressure measured, and it was classified as either low systolic blood pressure (less than 140 mm Hg) or high blood pressure (140 mm Hg or higher). The following table gives the number of men in each blood pressure category at the beginning of the study and the number of deaths from cardiovascular disease during the five-year period. Blood Pressure Deaths Total Low 10 2000 High 50 3500 Based on these data, which of the following statements is correct? a. These data are consistent with the idea that there is a link between high blood pressure and death from cardiovascular disease. b. The mortality rate (proportion of deaths) for men with high blood pressure is five times that for men with low blood pressure. c. These data probably understate the link between high blood pressure and death from cardiovascular disease, because men tend to understate their true blood pressure. d. All of the answer options are correct. ANSWER: a 18. Since 2000, the median wage in the United States has risen by 1%, while the median wage for every educational subgroup (high school dropouts, high school graduates, college graduates, and people with advanced degrees) has decreased. This apparent contradiction is an example of: a. extrapolation. b. Simpson’s paradox. c. causation. d. correlation. ANSWER: b 19. A study was conducted on horses to identify factors that might contribute to the formation of enteroliths— stones that form in the colon of the horse and eventually lead to blockage and death. The table below summarizes disease status by sex (gelding, mare, and stallion). Horses that have enteroliths are listed as case, and horses that do not are listed as control. Sex Disease Status: Case Disease Status: Control Total Gelding 29 41 70 Mare 28 32 60 Stallion 5 2 7 Total 62 75 137 If you want to check whether there is an association between sex and case status, you should: a. compare the conditional probabilities of being a case, given sex. b. make a scatterplot of case status versus sex. c. compare the marginal probabilities for case status and sex. d. All of the answer options are correct. ANSWER: a 20. In a recent round of layoffs at a company, the percent of employees 50 and older who were laid off was much higher than the percent of employees younger than 50 who were laid off. However, when the data were Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 6 analyzed separately in each job category, the percent of employees 50 and older who were laid off was lower than the percent of employees younger than 50 who were laid off in each job category. This reversal of direction of the association between age and being laid off, when job category is taken into account, is called: a. Simpson’s paradox. b. least-squares regression. c. negative association. d. a residual plot. ANSWER: a 21. Applicants looking for a job at a restaurant chain may apply to be a server or a kitchen worker. The table below summarizes the numbers of male and female applicants hired for the jobs for which they applied. Male Server

Female Server

Male Female Kitchen Kitchen Worker Worker Not hired 80 120 Not hired 30 15 Hired 20 50 Hired 80 25 The proportion of male applicants for a job as server who were hired is: a. 0.067. b. 0.133. c. 0.2. d. 0.4. ANSWER: c 22. Applicants looking for a job at a restaurant chain may apply to be a server or a kitchen worker. The table below summarizes the numbers of high school student (H) and undergraduate (U) applicants hired for the jobs for which they applied. Server Kitchen Worker H U H U Not hired 80 120 Not hired 30 15 Hired 20 50 Hired 80 25 The proportion of undergraduate (U) applicants for a job as kitchen worker who were hired is: a. 0.1. b. 0.375. c. 0.4. d. 0.625. ANSWER: d 23. Applicants looking for a job at a restaurant chain may apply to be a server or a kitchen worker. The table below summarizes the number of high school student (H) and undergraduate (U) applicants hired for the jobs for which they applied. Server Kitchen Worker H U H U Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 6 Not hired 80 120 Not hired 30 15 Hired 20 50 Hired 80 25 The proportion of all high school (H) applicants hired is: a. 0.091. b. 0.476. c. 0.523. d. 0.909. ANSWER: b 24. Applicants looking for a job at a restaurant chain may apply to be a server or a kitchen worker. The table below summarizes the number of high school student (H) and undergraduate (U) applicants hired for the jobs for which they applied. Server Kitchen Worker H U H U Not hired 80 120 Not hired 30 15 Hired 20 50 Hired 80 25 The proportion of undergraduate (U) hires who are servers is: a. 0.2. b. 0.333. c. 0.667. d. 0.8. ANSWER: c 25. Applicants looking for a job at a restaurant chain may apply to be a server or a kitchen worker. The table below summarizes the number of high school student (H) and undergraduate (U) applicants hired for the jobs for which they applied. Server Kitchen Worker H U H U Not hired 80 120 Not hired 30 15 Hired 20 50 Hired 80 25 From these data, we may conclude that: a. high school students are advantaged in applying for kitchen jobs, whereas undergraduates are advantaged in applying to be servers. b. overall, the proportion of high school applicants hired is greater than the proportion of undergraduates hired. c. the restaurant hires more servers than kitchen workers. d. All of the answer options are correct. ANSWER: a 26. A company exploring ways to help its employees improve work/life balance conducted a survey of 360 of its workers that asked (among other things) about the number of hours they typically spent on social media each day and about their stress level. Hours/day on social Stress Level:

Stress Level:

Total Page 9

Name:

Class:

Date:

Chapter 6 media

High

Medium

Low

Less than 2 2 to 6 More than 6 Total

12 45 19 76

40 101 8 149

56 43 36 135

108 189 63 360

What percent of all employees who responded had a high stress level? a. 15.7% b. 21.1% c. 22.8% d. 25.0% ANSWER: b 27. A company exploring ways to help its employees improve work/life balance conducted a survey of 360 of its workers that asked (among other things) about the number of hours they typically spent on social media each day and about their stress level. Hours/day on social Stress Level: media High Less than 2 12 2 to 6 45 More than 6 19 Total 76

Stress Level: Medium 40 101 8 149

Stress Level: Low 56 43 36 135

Total 108 189 63 360

Of the employees who spent the most time on social media, what percent had a high stress level? a. 21.1% b. 23.8% c. 30.2% d. 59.2% ANSWER: c 28. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The table below provides the answers on the time slept and the time spent studying. Hours/day Less than 6 6 to 8 hours More than 8 Total studied hours slept slept hours slept Less than 2 20 40 20 80 2 to 3 10 30 10 50 3 to 4 20 20 20 60 More than 4 20 20 10 50 Total 70 110 60 240 What proportion of the students slept less than 6 hours at night? a. 0.286 Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 6 b. 0.292 c. 0.25 d. 0.333 ANSWER: b 29. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The table below provides the answers on the time slept and the time spent studying. Hours/day Less than 6 6 to 8 hours More than 8 Total studied hours slept slept hours slept Less than 2 20 40 20 80 2 to 3 10 30 10 50 3 to 4 20 20 20 60 More than 4 20 20 10 50 Total 70 110 60 240 What proportion of the students studied 3 or more hours per day? a. 0.25 b. 0.46 c. 0.21 d. 0.67 ANSWER: b 30. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The table below provides the answers on the time slept and the time spent studying. Hours/day Less than 6 6 to 8 hours More than 8 Total studied hours slept slept hours slept Less than 2 20 40 20 80 2 to 3 10 30 10 50 3 to 4 20 20 20 60 More than 4 20 20 10 50 Total 70 110 60 240 What proportion of the first year undergraduates slept at least 6 hours at night? a. 1 b. 0.46 c. 0.71 d. 0.25 ANSWER: c 31. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The table below provides the answers on the time slept and the time spent studying. Hours/day Less than 6 6 to 8 hours More than 8 Total Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 6 studied hours slept slept hours slept Less than 2 20 40 20 80 2 to 3 10 30 10 50 3 to 4 20 20 20 60 More than 4 20 20 10 50 Total 70 110 60 240 What proportion of the students slept at least 6 hours at night and studied more than 4 hours per day? a. 0.6 b. 0.4 c. 0.78 d. 0.125 ANSWER: d 32. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The table below provides the answers on the time slept and the time spent studying. Hours/day Less than 6 6 to 8 hours More than 8 Total studied hours slept slept hours slept Less than 2 20 40 20 80 2 to 3 10 30 10 50 3 to 4 20 20 20 60 More than 4 20 20 10 50 Total 70 110 60 240 What proportion, among the students who slept more than 8 hours, studied more than 4 hours? a. 0.2 b. 0.1 c. 0.17 d. 0.25 ANSWER: c 33. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The table below provides the answers on the time slept and the time spent studying. Hours/day Less than 6 6 to 8 hours More than 8 Total studied hours slept slept hours slept Less than 2 20 40 20 80 2 to 3 10 30 10 50 3 to 4 20 20 20 60 More than 4 20 20 10 50 Total 70 110 60 240 Among the students who studied more than 4 hours, what proportion slept less than 6 hours at night? a. 0.29 b. 0.08 Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 6 c. 0.4 d. 0.2 ANSWER: c 34. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The table below provides the answers on the time slept and the time spent studying. Hours/day Less than 6 6 to 8 hours More than 8 Total studied hours slept slept hours slept Less than 2 20 40 20 80 2 to 3 10 30 10 50 3 to 4 20 20 20 60 More than 4 20 20 10 50 Total 70 110 60 240 Among the students who slept at most 8 hours, what proportion studied at least 3 hours? a. 0.67 b. 0.36 c. 0.73 d. 0.44 ANSWER: d 35. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The table below provides the answers on the time slept and the time spent studying. Hours/day Less than 6 6 to 8 hours More than 8 Total studied hours slept slept hours slept Less than 2 20 40 20 80 2 to 3 10 30 10 50 3 to 4 20 20 20 60 More than 4 20 20 10 50 Total 70 110 60 240 Did the students who studied 3 or more hours sleep less than the other students? a. Yes, because anyone who studies more has less time to sleep. b. No, because students who study more party less. c. Yes, because the proportion of students who slept at most 8 hours among those studying 3 hours or more is 0.73, while the proportion who slept at most 8 hours among those studying less than 3 hours is 0.769. d. There is not enough information to answer this question. ANSWER: c 36. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The table below provides the answers on the time slept and the time spent studying. Hours/day studied Less than 6 6 to 8 hours More than 8 Total Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 6 hours slept slept hours slept Less than 2 20 40 20 80 2 to <4 10 30 10 50 3 or more 4 20 20 20 60 Total 70 110 60 240 Is there an association between the number of hours studied and the number of hours slept? a. Yes, because the proportion sleeping less than 6 hours increases as the number of hours studied increases. b. No, because a student who studies more has no reason to sleep less. c. No, because a sleep-deprived student cannot study many hours. d. Yes, because the more a student studies, the less time there is for sleeping. ANSWER: a 37. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The tables below provide the answers on the time slept and the time spent studying by whether or not the students went out. Hours Stayed in Hours Went out: Hours Hours slept: dorm: slept: Hours/day slept: 6 Total slept: 6 Total less Hours/day less studied or more or more than 6 studied than 6 Less than 2 3 9 12 Less than 2 40 120 160 2 or more 14 14 28 2 or more 20 20 40 Total 17 23 40 Total 60 140 200 For both groups of students, those who went out and those who stayed in the dorm, the students who studied more: a. slept less. b. slept more. c. slept the same. d. Sleeping and studying were unrelated. ANSWER: a 38. A sociologist studying first year undergraduates carried out a survey, asking (among other questions) how often the students went out per week, how many hours they studied per day, and how many hours they slept at night. The tables below provide the answers on the time slept and the time spent studying by whether or not the students went out. Hours Stayed in Hours Went out: Hours Hours slept: dorm: slept: Hours/day slept: 6 Total slept: 6 Total less Hours/day less studied or more or more than 6 studied than 6 Less than 2 3 9 12 Less than 2 40 120 160 2 or more 14 14 28 2 or more 20 20 40 Total 17 23 40 Total 60 140 200 When we examine the data, we find that students who studied more slept less, both among those who went out Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 6 and among those who stayed in the dorm. When we combine both groups of students, we find that those who studied more also slept more. This is an example of: a. the Probability paradox. b. Andersen’s paradox. c. the Gaussian paradox. d. Simpson’s paradox. ANSWER: d

Page 15

Name:

Class:

Date:

Chapter 8 1. Each month, the census bureau mails survey forms to 250,000 households asking questions about the people living in the household and about such things as motor vehicles and housing costs. Telephone calls are made to households that don’t return the form. In one month, responses were obtained from 240,000 of the households contacted. The sample is: a. the 250,000 households initially contacted. b. the 240,000 households that responded. c. the 10,000 households that did not respond. d. all U.S. households. ANSWER: b 2. Each month, the census bureau mails survey forms to 250,000 households asking questions about the people living in the household and about such things as motor vehicles and housing costs. Telephone calls are made to households that don’t return the form. In one month, responses were obtained from 240,000 of the households contacted. The population of interest is: a. the residents of a suburb who support a new recreation center. b. the 250,000 households contacted. c. U.S. households with phones. d. all U.S. households. ANSWER: d 3. Each month, the census bureau mails survey forms to 250,000 households asking questions about the people living in the household and about such things as motor vehicles and housing costs. Telephone calls are made to households that don’t return the form. In one month, responses were obtained from 240,000 of the households contacted. A household that does not return the form and cannot be contacted by telephone is an example of: a. simple random sampling. b. under-coverage. c. nonresponse. d. volunteer bias. ANSWER: c 4. Veterinarians often use nonsteroidal anti-inflammatory drugs (NSAIDs) to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice is in the United States. They obtained a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. What is the population of interest? a. all veterinarians b. all veterinarians treating large animals c. all veterinarians in the United States treating large animals, including horses d. All of the answer options are correct. ANSWER: c 5. Veterinarians often use nonsteroidal anti-inflammatory drugs (NSAIDs) to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice is in the United States. They obtained Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 8 a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. Which of the following statements is correct? a. The sample consisted of all veterinarians on the list and, therefore, equaled the target population. b. The sample consisted of all veterinarians who returned the questionnaire. c. The sample consisted of all veterinarians who treat horses with NSAIDs. d. None of the answer options is correct. ANSWER: b 6. A student organization wanted to study voting preferences in its student body during the 2020 presidential election. They selected 120 students at random from each class, first years through seniors. The sampling technique used is: a. simple random sampling. b. stratified random sampling. c. volunteer sampling. d. multistage sampling. ANSWER: b 7. A political party sends a mail survey to 1500 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current president. Of the 1500 surveys sent out, 480 are returned, and of these, 120 show that the respondent is satisfied with the president’s job performance. The population is: a. the 1500 registered voters in the community selected to receive the survey. b. the 480 respondents who answered the survey. c. the 120 respondents who are satisfied with the president’s job performance. d. all registered voters in the community. ANSWER: d 8. A group of veterinarians at a major veterinary hospital were interested in investigating a possible link between enteroliths (stones that form in the colon of horses) and diet. They decided to conduct a survey of the feeding practices for horses in the hospital’s state. They created a survey questionnaire and administered it to the owners of every fifth horse being treated at the hospital. The population of interest is: a. all horses brought to the clinic. b. all horses in the state. c. all horses that are diagnosed with enteroliths. d. None of the answer options is correct. ANSWER: b 9. A group of veterinarians at a major veterinary hospital were interested in investigating a possible link between enteroliths (stones that form in the colon of horses) and diet. They decided to conduct a survey of the feeding practices for horses in the hospital’s state. They created a survey questionnaire and administered it to the owners of every fifth horse being treated at the hospital. The sample is: a. a volunteer sample. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 8 b. a simple random sample. c. a convenience sample. d. a stratified random sample. ANSWER: c 10. A political party sends a mail survey to 1500 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current president. Of the 1500 surveys sent out, 480 are returned, and of these, 120 show that the respondent is satisfied with the president’s job performance. The sample is: a. the 1500 randomly selected voters who received the questionnaire. b. the 480 voters who returned the surveys. c. the 120 voters surveyed who are satisfied with the president’s job performance. d. the voters in the president’s district. ANSWER: b 11. A political party sends a mail survey to 1500 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current president. Of the 1500 surveys sent out, 480 are returned, and of these, 120 show that the respondent is satisfied with the president’s job performance. This is an example of: a. a survey with little bias, because an individual will know for certain whether he or she approves of the president’s job performance. b. a survey with little bias, because 1500 voters represent an important part of the president’s district. c. a survey with no bias. d. None of the answer options is correct. ANSWER: d 12. Veterinarians often use nonsteroidal anti-inflammatory drugs (NSAIDs) to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice is in the United States. They obtained a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. Which of the following statements is not correct? a. Such a low response rate has the potential for response bias. b. The intended sample consisted of the target population. c. The chance to be selected into the sample was the same for all veterinarians. d. The sample was a volunteer sample. ANSWER: d 13. Surveys, if not done correctly, can lead to seriously biased samples. Which of the following is not a bias due to the sampling plan? a. bias due to selecting a volunteer sample b. bias due to selecting a convenience sample c. bias due to nonresponse Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 8 d. bias due to selecting a stratified random sample ANSWER: c 14. To assess the opinion of students at The Ohio State University about campus safety, a reporter for the student newspaper interviews 15 students that she meets walking on the campus late at night who are willing to give their opinion. The sample is: a. all those students walking on campus late at night. b. all students at universities with safety issues. c. the 15 students interviewed. d. all students approached by the reporter. ANSWER: c 15. To assess the opinion of students at The Ohio State University about campus safety, a reporter for the student newspaper interviews 15 students that she meets walking on the campus late at night who are willing to give their opinion. The method of sampling used is: a. simple random sampling. b. a Gallup Poll. c. voluntary response. d. a census. ANSWER: c 16. To assess the opinion of students at The Ohio State University about campus safety, a reporter for the student newspaper interviews 15 students that she meets walking on the campus late at night who are willing to give their opinion. The sample obtained is: a. a simple random sample of students who feel safe. b. a stratified random sample of students who feel safe. c. a probability sample of students with night classes. d. probably biased. ANSWER: d 17. A group of veterinarians at a major veterinary hospital were interested in investigating a possible link between enteroliths (stones that form in the colon of horses) and diet. They decided to conduct a survey of the feeding practices for horses admitted to the veterinary hospital. To obtain a simple random sample, they used a computer to generate 4-digit ID numbers for all horses. They used random digit tables to select the horses. Which of the following is a step in selecting a random sample by this procedure? a. Pick a random starting point in the table and read 4 digits. b. Read 4 digits across a line, and if the 4 digits correspond to a horse ID, select the animal. c. Discard any sequence that does not correspond to a horse ID, and move to the next 4 digits. d. All of the answer options are correct. ANSWER: d 18. A group of veterinarians at a major veterinary hospital were interested in investigating a possible link between enteroliths (stones that form in the colon of horses) and diet. They decided to conduct a survey of the Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 8 feeding practices for horses admitted to the veterinary hospital. To obtain a random sample of the 5000 horses that had been admitted to the hospital over the last 10 years, the veterinarians sequentially assigned numbers (starting with 0001) to the horses, in order of admittance. They then picked a random starting point and sampled every 100th horse to get a random sample of 50 horses. This procedure corresponds to: a. simple random sample, because all horses have the same chance of being picked. b. a stratified random sample, because the procedure is obviously not a simple random sample. c. a type of random sample, but not a simple random sample, because not all samples are possible. d. None of the answer options is correct. ANSWER: c 19. A group of veterinarians at a major veterinary hospital were interested in investigating a possible link between enteroliths (stones that form in the colon of horses) and diet. They decided to conduct a survey of the feeding practices for horses admitted to the veterinary hospital. To obtain a simple random sample of the 5000 horses that had been admitted to the hospital over the last 10 years, the veterinarians sequentially assigned numbers (starting with 0001) to the horses, in order of admittance, and they used random digit tables to select 100 horses. After the veterinarians obtained the sample, they were able to find information on the diet of 53 horses. Which of the following could create bias due to nonresponse? a. Owners who feed poor diets are less likely to participate in a survey on their horse’s diet. b. Owners who are very diligent on getting information about their horse’s nutritional needs and harmful diets are too busy to answer questions about diet. c. Owners who are extremely busy and do not feed their horses personally do not respond, because they would not know the answer to all the questions. d. All of the answer options are correct. ANSWER: d 20. Import customs officials sometimes randomly select crates of cargo for close, but time-consuming, inspection. Suppose there are nine crates of cargo from the following companies, each containing several hundred items. Customs officials will randomly select four for close inspection. 1. Ravenburg 4. Dallhoise 7. Cherryport 2. Corsair 5. Baggate 8. Foxwood 1. Ravenburg 4. Dallhoise 7. Cherryport To do this, officials will use the numerical labels attached to the foregoing names and the following list of random digits, which they will read from left to right, starting at the beginning of the list. 748803 12009 45287 71753 98236 66419 84533 11793 20495 05907 11384 The simple random sample is: a. 7488. b. 7483. c. Cherryport, Dallhoise, Foxwood, and Sapphire. d. Cherryport, Foxwood, Bamboro, and Strommond. ANSWER: c 21. A small math department has six faculty members and 30 students. The department can send six people to a national convention, and it would like to send four students and two faculty members. Of the 30 students, four are selected randomly. Two faculty members are randomly selected from the six. This is an example of: Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 8 a. simple random sampling. b. stratified random sampling. c. voluntary response sampling. d. a census. ANSWER: b 22. The Excite Poll is an online poll at poll.excite.com. You click on an answer to become part of the sample. One poll question was “Do you prefer watching first-run movies at a movie theater or waiting until they are available on home video or pay-per-view?” A total of 8896 people responded, with 1118 saying they preferred theaters. From this survey, you should conclude that: a. Americans prefer watching movies at home. b. a larger sample is necessary. c. the poll uses voluntary response, so the results tell us little about the population of all adults. d. movie theaters should lower their prices. ANSWER: c 23. The magazine High Times has a website that once asked visitors whether recreational marijuana use should be legal. This is an example of: a. voluntary response sampling. b. a survey with little bias, because a large simple random sample was used. c. a survey with little bias, because someone who responded would know his or her opinion. d. All of the answer options are correct. ANSWER: a 24. A student asks each person in one of his classes how many hours, on average, they spend studying each week. This is an example of: a. convenience sampling. b. a double-blind experiment. c. a simple random sample. d. voluntary response sampling. ANSWER: a 25. At a large university, a simple random sample of five tenured professors is selected, and a simple random sample of 10 tenure track professors is selected. The two samples are combined to give an overall sample of 15 professors. The overall sample is: a. a simple random sample. b. biased due to imbalance. c. a stratified sample. d. All of the answer options are correct. ANSWER: c 26. During the 1936 presidential election between Franklin D. Roosevelt and Alf Landon, the Literary Digest Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 8 received 2.3 million mail-in ballots that it used to predict the results: a landslide in favor of Landon. Clearly, there has never been a President Landon, so the prediction was incorrect. Why? a. A sample taken only from Literary Digest readers would not necessarily represent the views of the American public in general. b. The survey relied on voluntary responses, which would introduce a bias. c. The survey was subject to nonresponse bias. d. All of the answer options are correct. ANSWER: d 27. Advice columnist Ann Landers once asked her readers with children to answer the following question: “If you had it to do over again, would you have children?” Readers were invited to send a response to this question by mail. Of the approximately 10,000 responses that Landers received, approximately 70% said “no.” The sample is: a. the approximately 10,000 readers who sent a response. b. the approximately 70% of women who answered “no.” c. the respondents who regretted having children. d. all readers. ANSWER: a 28. Advice columnist Ann Landers once asked her readers with children to answer the following question: “If you had it to do over again, would you have children?” Readers were invited to send a response to this question by mail. Of the approximately 10,000 responses that Landers received, approximately 70% said “no.” The sample: a. is probably representative of all parents. b. is probably not representative of all parents, because people who feel very strongly about this issue are more likely to respond than people who do not. c. has little bias, because more than 10,000 people responded, yielding a very large sample. d. is probably not representative, because only 10,000 people responded. ANSWER: b 29. Advice columnist Ann Landers once asked her readers with children to answer the following question: “If you had it to do over again, would you have children?” Readers were invited to send a response to this question by mail. Of the approximately 10,000 responses that Landers received, approximately 70% said “no.” The population of interest is: a. the more than 10,000 people who responded. b. all readers who are parents. c. the readers with children who regret having children. d. the children who were unwanted. ANSWER: b 30. A public opinion poll in Ohio was set up to determine whether registered voters in the state approved of a measure to ban smoking in all public areas. The researchers selected a simple random sample of 50 registered voters from each county in the state and asked whether the voters approved or disapproved of the measure. This Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 8 is an example of: a. a systematic county sample. b. a stratified sample. c. a multistage sample. d. a simple random sample. ANSWER: b 31. To select a sample of undergraduate students in the United States, I first select a simple random sample of four states. From each of these states, I select a simple random sample of two colleges or universities. Finally, from each of these eight colleges or universities, I select a simple random sample of 20 undergraduates. My final sample consists of 160 undergraduates. This is an example of: a. simple random sampling. b. stratified random sampling. c. multistage sampling. d. convenience sampling. ANSWER: c 32. A news release for a diet product company reports: “There’s good news for the 65 million Americans currently on a diet.” Its own study showed that people who lose weight can keep it off. The sample was 20 graduates of the company’s program who endorsed the program in commercials. The results of the sample are probably: a. biased, overstating the effectiveness of the diet. b. biased, understating the effectiveness of the diet. c. unbiased, because the people in the sample are nationally recognized individuals. d. unbiased, but they could be more accurate if a larger sample size were used. ANSWER: a 33. Researchers must be cautious when designing web-based surveys, because these surveys are particularly sensitive to: a. voluntary response bias. b. under-coverage. c. nonresponse. d. All of the answer options are correct. ANSWER: d 34. A sociologist studying first year undergraduates at a major university carried out a survey, asking (among other questions) how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist used an introductory sociology class to carry out the survey. The population of interest is: a. the students at the university. b. the students in the sociology class. c. the first year undergraduates at the university. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 8 d. the first year undergraduates in the sociology class. ANSWER: c 35. A sociologist studying first year undergraduates at a major university carried out a survey, asking (among other questions) how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist used an introductory sociology class to carry out the survey, instructing the students to participate only if they were first year undergraduates. The sample consists of: a. the students enrolled in the class. b. the students who were in class for the survey and answered the survey questions. c. the first year undergraduates at the university. d. the first year undergraduates in the class who answered the survey questions. ANSWER: d 36. A sociologist studying first year undergraduates at a major university carried out a survey, asking (among other questions) how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist used an introductory sociology class to carry out the survey and asked only the first year undergraduates to answer the questions. The sample is called: a. a convenience sample. b. a volunteer sample. c. a random sample. d. a targeted sample. ANSWER: a 37. A sociologist studying first year undergraduates at a major university carried out a survey, asking (among other questions) how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist, who knows about proper sampling, should select which type of a sample? a. a volunteer sample b. a random sample c. a two-step sample d. a hierarchical sample ANSWER: b 38. A sociologist studying first year undergraduates at a major university carried out a survey, asking (among other questions) how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist used an introductory sociology class to carry out the survey. The sociologist knew from previous studies that pre-med majors and non-pre-med majors often behave differently regarding study and sleep patterns. She decided that she needed to ensure adequate numbers of pre-med and non-pre-med majors. Therefore, she knew she should take: a. a multistage sample. b. two convenience samples, one of pre-med students and one of students who are not pre-med. c. a stratified random sample. d. a multigroup sample. Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 8 ANSWER: c 39. A sociologist studying first year undergraduates at a major university carried out a survey, asking (among other questions) how often students went out per week, how many hours they studied per day, and how many hours they slept at night. Which of the following strategies will provide a simple random sample? a. Contacting the registrar and obtaining a list of all first year undergraduates, from which a random sample will then be selected. b. Using the enrollment list of the introductory class and selecting all the first year undergraduates. c. Using the class list of the introductory class and randomly selecting a fraction of the students enrolled. d. Using all the students in the class because, after all, they resemble typical students at the university. ANSWER: a 40. A sociologist studying first year undergraduates at a major university carried out a survey, asking (among other questions) how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist decided to use his introductory sociology class to conduct the survey. If the survey is not representative of the first year undergraduates at the university, the conclusions from the study are likely to be: a. on target. b. biased. c. overly efficient. d. None of the answer options is correct. ANSWER: b 41. A sociologist studying first year undergraduates at a major university carried out a survey, asking (among other questions) how often students went out per week, how many hours they studied per day, and how many hours they slept at night. Students will often overstate the number of hours studied, because they do not want to admit to not studying enough. This type of distortion is called: a. false answer. b. nonresponse bias. c. under-coverage bias. d. response bias. ANSWER: d 42. A sociologist studying first year undergraduates at a major university carried out a survey, asking (among other questions) how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist, who would like a simple random sample but found it too timeconsuming to obtain such a sample, decided to use all students enrolled in his own class. This type of sample: a. is a convenience sample. b. is likely to result in under-coverage of certain types of first year students. c. could lead to biased conclusions. d. All of the answer options are correct. ANSWER: d Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 8 43. A properly designed survey should have which of the following? a. a random sample b. a carefully defined objective c. a clearly defined population of interest d. All of the answer options are correct. ANSWER: d 44. Which of the following might cause under-coverage of older people in surveys of the general population? a. online surveys b. surveys that employ randomly dialed cell phone numbers c. surveys conducted at shopping malls d. All of the answer options are correct. ANSWER: d

Page 11

Name:

Class:

Date:

Chapter 9 1. Some researchers have noted that adolescents who spend a lot of time playing video or computer games are at greater risk for depression and violence. This is an example of: a. a valid conclusion, because “more time yields more aggression” is a positive association. b. an observational study with lurking variables that may explain the association. c. a single-blind experiment, because the subjects knew they were playing games. d. a paired data experiment, because we are studying both aggression and game playing. ANSWER: b 2. A veterinarian interested in studying the causes of enteroliths (stones that form in the gut of horses) decided to compare the diets of horses with enteroliths, and horses without enteroliths, that were admitted to the veterinary hospital. This study is an example of: a. an experimental study. b. a survey. c. an observational study. d. None of the answer options is correct. ANSWER: c 3. A veterinarian is interested in studying the causes of enteroliths (stones that form in the gut of horses). An observational study comparing the diet of horses admitted to the veterinary hospital with enteroliths, and the diet of horses admitted for other reasons, does not allow causal conclusions to be drawn because: a. an observational study can only establish correlations, unless the investigation is double-blind. b. associations in observational studies can be confounded by lurking variables. c. the study does not match horses. d. All of the answer options are correct. ANSWER: b 4. Sickle-cell disease is a painful disorder of the red blood cells that, in the United States, affects mostly African Americans. To investigate whether the drug hydroxyurea can reduce the pain associated with sickle-cell disease, a study by the National Institutes of Health gave the drug to 150 sickle-cell sufferers and a placebo to another 150. Neither doctors nor patients were told who received the drug. The number of episodes of pain reported by each subject was recorded. This is an example of: a. an observational study. b. an experiment, but not a double-blind experiment. c. a double-blind experiment. d. a paired data experiment. ANSWER: c 5. A veterinarian is interested in studying the causes of enteroliths (stones that form in the gut of horses). In order to establish a causal relationship between diet and enteroliths, the veterinarian needs to: a. use a double-blind observational study. b. use a non-randomized experimental design in which the examining veterinarian is blind to the diet the horse is fed. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 9 c. use a comparative randomized experiment. d. administer a survey questionnaire to all horse owners entering the veterinary hospital. ANSWER: c 6. A placebo is an important element of many clinical trials because: a. it serves as a control for the experiment. b. it allows the researcher to adjust for the psychological effects of receiving medical attention. c. the use of the placebo can help avoid confounding. d. All of the answer options are correct. ANSWER: d 7. Apparently, according to some studies, men who drive expensive sports cars have lower blood pressure and fewer cardiovascular health problems. We can’t conclude that driving expensive sports cars lowers blood pressure or improves cardiovascular health, because the studies described are clearly: a. experiments. b. observational studies, not experiments—lurking variables may explain the association. c. paired data experiments. d. stratified experiments. ANSWER: b 8. At a local health club, a researcher samples 75 people whose primary exercise is cardiovascular and 75 people whose primary exercise is strength training. The researcher’s objective is to assess the effect of type of exercise on cholesterol. Each subject reported to a clinic to have his or her cholesterol measured. The subjects were unaware of the purpose of the study, and the technician measuring the cholesterol was not aware of the subject’s type of exercise. This approach is: a. an observational study. b. an experiment, but not a double-blind experiment. c. a double-blind experiment. d. fundamentally flawed, because only a well-designed experiment with randomized assignment to treatments can be used to determine a cause-and-effect relationship. ANSWER: d 9. A veterinarian interested in studying the causes of enteroliths in horses suspects that a diet high in alfalfa may be a cause. The veterinarian decides to use the following design: Identify 30 horses at high risk for enteroliths, and divide them into 10 groups of 3 horses. Some groups consist of horses in barn stalls, some groups consist of horses in outdoor paddocks, and some groups consist of horses in pastures. Within each group, one horse is randomly assigned to an alfalfa diet, one is assigned to a grass hay diet, and one horse is fed oat hay. When a horse is in a pasture, all the other horses in that pasture receive the same diet as the study horse. Therefore, only one horse could be selected from a given pasture. The study is: a. a randomized block design. b. a matched pairs design. c. a completely randomized design. d. a comparative observational design. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 9 ANSWER: a 10. To investigate whether college students are more likely than senior citizens to prefer Democratic candidates, a political scientist selects a large sample of registered voters, both college students and senior citizens. She asks every voter whether she or he voted for the Republican or the Democratic candidate in the last election. This is: a. an observational study. b. a multistage sample. c. a double-blind experiment. d. a block design. ANSWER: a 11. In order to investigate treatments for morbid obesity, obese subjects satisfying fairly strict requirements were randomly assigned to one of three treatment groups: (1) gastric bypass surgery, (2) participation in a diet and exercise program, or (3) both gastric bypass surgery and participation in a diet and exercise program. Researchers observed the amount of weight lost five years after the study began. The response is: a. the kind of program to which a subject was assigned. b. the amount of weight lost five years after the study began. c. gastric bypass surgery. d. random assignment. ANSWER: b 12. A veterinarian interested in studying the causes of enteroliths in horses suspects that a diet high in alfalfa may be a cause. The veterinarian decides to use the following design: Identify 30 horses at high risk for enteroliths, and divide them into 10 groups of 3 horses. Some groups consist of horses in barn stalls, some groups consist of horses in outdoor paddocks, and some groups consist of horses in pastures. Within each group, one horse is randomly assigned to an alfalfa diet, one is assigned to a grass hay diet, and one horse is fed oat hay. When a horse is in a pasture, all the other horses in that pasture will receive the same diet as the study horse. Therefore, only one horse can be selected from a given pasture. After one year, the horses are given radiographs to determine whether enteroliths are present in the gut. The response is: a. the diet a horse is given. b. the amount of feed a horse is given. c. the number of enteroliths. d. the presence or absence of enteroliths. ANSWER: d 13. In order to investigate treatments for morbid obesity, obese subjects satisfying fairly strict requirements were randomly assigned to one of three treatment groups: (1) gastric bypass surgery, (2) participation in a diet and exercise program, or (3) both gastric bypass surgery and participation in a diet and exercise program. Researchers observed the amount of weight lost five years after the study began. This study has: a. four factors. b. three treatments. c. two treatments. Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 9 d. None of the answer options is correct. ANSWER: b 14. A veterinarian interested in studying the causes of enteroliths in horses suspects that a diet high in alfalfa may be a cause. The veterinarian decides to use the following design: Identify 30 horses at high risk for enteroliths, and divide them into 10 groups of 3 horses. Some groups consist of horses in barn stalls, some groups consist of horses in outdoor paddocks, and some groups consist of horses in pastures. Within each group, one horse is randomly assigned to an alfalfa diet, one is assigned to a grass hay diet, and one horse is fed oat hay. When a horse is in a pasture, all the other horses in that pasture will receive the same diet as the study horse. Therefore, only one horse could be selected from a given pasture. This study has: a. one factor and three treatments. b. one treatment and three factors. c. three treatments and three factors. d. one factor and one treatment. ANSWER: a 15. In order to investigate treatments for morbid obesity, obese subjects satisfying fairly strict requirements were randomly assigned to one of three treatment groups: (1) gastric bypass surgery, (2) participation in a diet and exercise program, or (3) both gastric bypass surgery and participation in a diet and exercise program. Researchers observed the amount of weight lost five years after the study began. This study uses the principles of: a. randomization. b. confounding. c. blocking. d. All of the answer options are correct. ANSWER: a 16. The purpose of blocking is: a. to arrange experimental units according to similarity. b. to ensure that the results from an experiment are accurate. c. to control the effects of an outside variable that is not of interest to the researchers. d. All of the answer options are correct. ANSWER: c 17. A veterinarian interested in studying the causes of enteroliths in horses suspects that a diet high in alfalfa may be a cause. The veterinarian decides to use the following design: identify 30 horses at high risk for enteroliths, and divide them into 10 groups of 3 horses. Some groups consist of horses in barn stalls, some groups consist of horses in outdoor paddocks, and some groups consist of horses in pastures. Within each group, one horse is randomly assigned to an alfalfa diet, one is assigned to a grass hay diet, and one horse is fed oat hay. When a horse is in a pasture, all the other horses in that pasture will receive the same diet as the study horse. Therefore, only one horse could be selected from a given pasture. The blocking is done: a. to reduce the potentially confounding effect of comparing more than two treatments. b. to reduce the potentially confounding effect of the type of housing. Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 9 c. to increase the treatment effects. d. All of the answer options are correct. ANSWER: b 18. A researcher studying the effect of price cuts on consumers’ expectations makes up two different histories of the store price of a hypothetical brand of laundry detergent for the past year. Eight students in a business class view one or the other price history on a computer. Some students see a steady price, whereas others see regular sales that temporarily cut the price. Students are asked what price they would expect to pay. The names of the eight subjects follow. 1. Franklin 2. James 3. Wright 4. Edwards 5. Rust 6. Walsh 7. Gofberg 8. Williams Use the following list of random digits: 41842 81868 71035 09001 43367 49497. Starting at the beginning of this list and using single-digit labels, assign the first four subjects selected to the steady price group and the remaining four to the fluctuating price group. The subjects assigned to the fluctuating price group are: a. Franklin, James, Wright, and Edwards. b. Edwards, Franklin, Williams, and James. c. Rust, Walsh, Gofberg, and Williams. d. Wright, Rust, Walsh, and Gofberg. ANSWER: d 19. A researcher studying the effect of price cuts on consumers’ expectations makes up two different histories of the store price of a hypothetical brand of laundry detergent for the past year. Eight students in a business class view one or the other price history on a computer. Some students see a steady price, whereas others see regular sales that temporarily cut the price. Students are asked what price they would expect to pay. The response is: a. the laundry detergent. b. the eight business students. c. the price the students would expect to pay. d. the sale prices. ANSWER: c 20. A researcher studying the effect of price cuts on consumers’ expectations makes up two different histories of the store price of a hypothetical brand of laundry detergent for the past year. Eight students in a business class view one or the other price history on a computer. Some students see a steady price, whereas others see regular sales that temporarily cut the price. Students are asked what price they would expect to pay. The experimental units are: a. all business students at the college. Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 9 b. the eight business students who participated. c. the business students who were in the fluctuating price group. d. the price the students would expect to pay. ANSWER: b 21. A researcher studying the effect of price cuts on consumers’ expectations makes up two different histories of the store price of a hypothetical brand of laundry detergent for the past year. Eight students in a business class are randomly assigned to view one or the other price history on a computer. Some students see a steady price, whereas others see regular sales that temporarily cut the price. Students are asked what price they would expect to pay. This is an example of: a. a matched pairs experiment. b. a two-factor design. c. a randomized comparative experiment. d. a randomized observational study. ANSWER: c 22. A nutritionist has designed an intervention to motivate parents of preschool children to provide more fruits and vegetables to their children. To study the effectiveness of this intervention, the nutritionist will conduct an experiment in which half of the selected study participants will receive the intervention and the other half will not. Study subjects will be recruited from families with children who receive medical care for their children through the university health center. One factor that must be accounted for is whether the family receives aid through the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC), which provides funds for fruits and vegetables to the mothers. Which of the following experiments should the nutritionist use? a. a completely randomized design b. a matched design where children are matched on age and gender, and the WIC child does not get the intervention c. a randomized matched pairs design where parents are matched on age, gender, and WIC program participation d. a matched pairs observational study ANSWER: c 23. A study is conducted to investigate the effects of a new exercise program on lameness in race horses. A group of horses at a local race track is selected for the study. The horses are randomly assigned to two groups. Group 1 horses will train according to the new program for one month, rest for two weeks, and then train according to the old program for one month. Group 2 horses will have the order of the old and new programs reversed. Here, each horse serves as its own control. The two groups are necessary to avoid: a. a carryover effect, since the order of treatment may influence the subject’s response. b. a placebo effect. c. a double-blind effect. d. a confounded effect. ANSWER: a 24. A nutritionist has designed an intervention to motivate parents of preschool children to provide more fruits Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 9 and vegetables to their children. To study the effectiveness of this intervention, the nutritionist will conduct an experiment in which half of the selected study participants will receive the intervention and the other half will not. Study subjects will be recruited from families with children who receive medical care for their children through the university health center. The nutritionist will compare the amount of fruit consumed per day by the children in families who received the intervention and the amount consumed by those who did not. Which of the following is true? a. The amount of fruit consumed is the treatment. b. The amount of fruit consumed is the factor. c. The amount of fruit consumed is the response. d. The amount consumed is the carryover effect from before and after the intervention. ANSWER: c 25. A study is done to assess the effects of a new medication on the resting heart rate of dogs. Two breeds will be used in the study because of the availability of experimental subjects, even though the researcher is not interested in the differences in the medication’s effectiveness between breeds. What type of experimental design should be used? a. no blinding; no blocking b. no blinding; blocking on dog breed c. double-blind; no blocking d. double-blind; blocking on dog breed ANSWER: b 26. In a study of human development, investigators showed two different types of movies to groups of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by children watching one type of movie with the number eaten by children watching the other type. One type of movie was shown at 8 a.m. (right after the children had breakfast), and the other type of movie was shown at 11 a.m. (right before the children were to have lunch). It was found that more crackers were eaten during the movie shown at 11 a.m. than during the movie shown at 8 a.m. The investigators concluded that the different types of movies had different effects on appetite. The results cannot be trusted because: a. the study was not double-blind—neither the investigators nor the children should have been aware of which type of movie was being shown. b. the investigators were biased—they knew beforehand what the study would show. c. the investigators should have used several bowls, with crackers randomly placed in each. d. the time at which each movie was shown is a confounding variable. ANSWER: d 27. In a study of human development, investigators showed two different types of movies to groups of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by children watching one type of movie with the number eaten by children watching the other type. One type of movie was shown at 8 a.m. (right after the children had breakfast), and the other type of movie was shown at 11 a.m. (right before the children were to have lunch). It was found that more crackers were eaten during the movie shown at 11 a.m. than during the movie shown at 8 a.m. The investigators concluded that the different types of movies had different effects on appetite. The response variable in this experiment is: a. the number of crackers eaten. Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 9 b. the different types of movies. c. the time at which each movie was shown. d. the bowls. ANSWER: a 28. In a study of human development, investigators showed two different types of movies to groups of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by children watching one type of movie with the number eaten by children watching the other type. One type of movie was shown at 8 a.m. (right after the children had breakfast), and the other type of movie was shown at 11 a.m. (right before the children were to have lunch). It was found that more crackers were eaten during the movie shown at 11 a.m. than during the movie shown at 8 a.m. The investigators concluded that the different types of movies had different effects on appetite. The treatment in this experiment is: a. the number of crackers eaten. b. the different kinds of movies. c. the time at which each movie was shown. d. the bowls. ANSWER: b 29. A researcher finds 1000 mildly overweight women who exercise regularly, have not had a heart attack, and are willing to participate in the study. This researcher randomly assigns 500 of the women to take an appetite suppressant. The other 500 women are given a placebo. Both groups are followed for five years, and the amount of weight lost after this time is recorded. The factor in the experiment is: a. the weight lost by women in the study. b. the use of a control group taking a placebo. c. the treatment taken by women in the study—appetite suppressant or placebo. d. the length of the study. ANSWER: c 30. A researcher finds 1000 mildly overweight women who exercise regularly, have not had a heart attack, and are willing to participate in the study. The researcher randomly assigns 500 of the women to take an appetite suppressant. The other 500 women are given a placebo. Both groups are followed for five years, and the amount of weight lost after this time is recorded. The response variable in this experiment is: a. the amount of weight lost. b. the proportion of women in each group who stayed in the study. c. whether the women exercised. d. the age of the women. ANSWER: a 31. A study attempts to compare two sunscreens. Each of 50 subjects with varying skin complexions will use both sunscreens—Screen A on one side of the body and Screen B on the other side. For each subject, a coin is tossed to determine which side receives Screen A and which receives Screen B. Researchers measure the amount of ultraviolet light exposure over both treated areas for each subject. This is an example of: a. a matched pairs experiment. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 9 b. a double-blind observational study. c. a stratified analysis. d. the placebo effect. ANSWER: a 32. One hundred sixty people who suffer from painful diabetic neuropathy have volunteered to participate in a study. Eighty are selected at random and are given the drug gabapentin, which, although it was originally intended to prevent epileptic seizures, has properties that may make it useful to alleviate neuropathy. The remaining participants are given a placebo. A neurologist evaluates the symptoms of all volunteers after two months to determine whether there has been substantial improvement in the severity of the symptoms. This study would be double-blind if: a. neither drug had any identifying marks on it. b. neither the volunteers nor the neurologist were allowed to see each other during the session in which the neurologist evaluated the severity of the symptoms. c. neither the volunteers nor the neurologist knew which subjects had received the drug and which had received the placebo. d. All of the answer options are correct. ANSWER: c 33. One hundred sixty people who suffer from painful diabetic neuropathy have volunteered to participate in a study. Eighty are selected at random and are given the drug gabapentin, which, although it was originally intended to prevent epileptic seizures, has properties that may make it useful to alleviate neuropathy. The remaining participants are given a placebo. A neurologist evaluates the symptoms of all volunteers after two months to determine whether there has been substantial improvement in the severity of the symptoms. Suppose the volunteers were first divided into men and women, and then half of the men were randomly assigned to the new drug and half of the women were assigned to the new drug. The remaining volunteers received the placebo. This would be an example of: a. replication. b. confounding—the effects of gender will be mixed up with the effects of the drug. c. a block design. d. a matched pairs design. ANSWER: c 34. One hundred sixty people who suffer from painful diabetic neuropathy have volunteered to participate in a study. Eighty are selected at random and are given the drug gabapentin, which, although it was originally intended to prevent epileptic seizures, has properties that may make it useful to alleviate neuropathy. The remaining participants are given a placebo. A neurologist evaluates the symptoms of all volunteers after two months to determine whether there has been substantial improvement in the severity of the symptoms. Does the use of volunteers make this study invalid? a. Yes, because of volunteer bias. b. Yes, because there is no way to determine the effect of the drug on people who do not have symptoms of neuropathy. c. No, because the subjects are randomly assigned to treatment groups. Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 9 d. No, because blocking was used. ANSWER: c 35. Will a fluoride mouthwash used after brushing reduce cavities? Twenty sets of twins were used to investigate this question. One member of each set of twins used the mouthwash after brushing, and the other did not. After six months, the number of cavities for those using the mouthwash was compared with the number of cavities for those who did not use the mouthwash. This experiment uses: a. random placebos. b. double blinding. c. double replication. d. a matched pairs design. ANSWER: d 36. Medical researchers are excited about a new cancer treatment that destroys tumors by cutting off their blood supply. To date, the treatment has been used only on mice, but in mice it has been nearly 100% effective in eradicating tumors and appears to have no side effects. As evidence of the effectiveness of the new treatment in treating cancer in humans, these studies: a. display a high degree of statistical significance, so the treatment will work in humans with nearly 100% certainty. b. are convincing, assuming the results have been replicated in a large number of mice. c. are convincing, assuming that proper randomization and control were used. d. suffer from lack of realism. ANSWER: d 37. Randomly assigning all subjects to treatment groups is called: a. a completely randomized design. b. a randomized complete block design. c. a randomized comparative experiment. d. None of the answer options is correct. ANSWER: a 38. Researchers have noted that children who learn to play a musical instrument through taking lessons have higher average SAT scores, higher average GPAs, and higher average class ranks. This is an example of: a. an experiment. b. an observational study. c. the establishing of a causal relationship through correlation. d. a block design, with music and no-music groups as blocks. ANSWER: b 39. Researchers have noted that children who learn to play a musical instrument through taking lessons have higher average SAT scores, higher average GPAs, and higher average class ranks. The various measures of academic success described are examples of: Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 9 a. explanatory variables. b. response variables. c. confounding variables. d. None of the answer options is correct. ANSWER: b 40. An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. Before the start of the class, each student is asked about the number of hours slept the previous night. Each student’s eye movement is then tracked throughout the lecture. The amount of time when the student is not either focused on the instructor or taking notes is recorded. This is an example of: a. an observational study. b. a sample survey. c. a randomized experiment. d. a matched pairs study. ANSWER: a 41. An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. Before the start of the class, each student is asked about the number of hours slept the previous night. Each student’s eye movement is then tracked throughout the lecture. The amount of time when the student is not either focused on the instructor or taking notes is recorded. The class is offered at 11 a.m. A potential confounder is given by the number of classes a student has prior to calculus, because: a. the greater the number of classes earlier in the day, the earlier the student has to get up, so he or she sleeps less. b. the greater the number of classes earlier in the day, the more a student has to prepare, so she or he probably stays up late. c. many classes earlier in the day will leave a student tired just from having to stay focused for several hours. d. All of the answer options are correct. ANSWER: d 42. An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. Before the start of the class, each student is asked about the number of hours slept the previous night. Each student’s eye movement is then tracked throughout the lecture. The amount of time when the student is not either focused on the instructor or taking notes is recorded. The class is held at 11 a.m., and the instructor also asks questions about prior classes that day. The response variable is: a. the number of hours slept the night before. b. the amount of time neither focused nor taking notes. c. the time of day the class is given. d. the number of prior classes that day. ANSWER: b 43. An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 9 study the students in a calculus class. The educator has contacted a statistician to help plan a proper study for the assessment of cause and effect. The type of study required is called: a. a replicated observational study. b. a quasi-experiment. c. a completely randomized design. d. a blocked study. ANSWER: c 44. An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. After consultation with a statistician, the educator decides to randomly allocate students to a group that will sleep for 8 hours the night before class or a group that will sleep 6 hours. The educator does not know which group a student belongs to when she or he comes to class. The study subjects are: a. the groups assigned to sleeping either 6 or 8 hours. b. the students participating in the experiment. c. the students who do not fall asleep in class. d. the students who are enrolled in any of the calculus classes. ANSWER: b 45. An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. Each student enrolled in the class is randomly assigned to sleep either 6 or 8 hours the night before class. Each student’s eye movement is then tracked throughout the lecture. The amount of time when the student is not either focused on the instructor or taking notes is recorded. This study has: a. one factor and one treatment. b. two factors and one treatment. c. one factor and two treatments. d. two factors and two treatments. ANSWER: c 46. An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. After consultation with a statistician, the educator decides to randomly allocate students to a group that will sleep for 8 hours the night before class or a group that will sleep 6 hours. The educator does not know which group a student belongs to when she or he comes to class. The educator, after talking to some students and before the experiment, decides that the number of classes students have on the same day before calculus could potentially confound the study and wishes to make an adjustment. The design that allows for such an adjustment is called: a. a randomized block design. b. a placebo-controlled completely randomized design. c. a double-blind design. d. a matched block design. ANSWER: a 47. An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 9 study the students in a calculus class. After consultation with a statistician, the educator decides to randomly allocate students to a group that will sleep for 8 hours the night before class or a group that will sleep 6 hours. The educator does not know which group a student belongs to when she or he comes to class. This study is: a. Double-blind, because the educator does not know who belongs to the 6-hour group or to the 8-hour group. b. double blind, because the students have been told not to inform the educator which treatment group they belong to. c. a placebo-controlled study, because 8 hours is normal sleeping time. d. a single-blind randomized study, because the educator does not know the treatment groups that the students belong to, but the students know. ANSWER: d 48. An insurance underwriter wonders whether sports cars “cause” people to drive too fast or those with a propensity for speeding are drawn to sports cars. She secures some research funds and recruits 100 car buyers to her study. She randomly assigns 25 drivers to each of four groups: (1) sports car white, (2) sports car red, (3) non-sports car white, or (4) non-sports car red. The primary research questions are: (1) Do sports cars make people drive faster? and (2) Does color make a difference? This study has: a. four treatments. b. two treatments. c. four treatments and a placebo. d. two treatments and a placebo. ANSWER: a 49. An insurance underwriter wonders whether sports cars “cause” people to drive too fast or those with a propensity for speeding are drawn to sports cars. She secures some research funds and recruits 100 car buyers to her study. She randomly assigns 25 drivers to each of four groups: (1) sports car white, (2) non-sports car red, (3) non-sports car white, and (4) non-sports car red. The primary research questions are: (1) Do sports cars make people drive faster? and (2) Does color make a difference? The underwriter worries that gender affects driving behavior and thinks it may actually be a confounder. She decides to randomize males and females separately. This is a. a randomized block design with one factor and two blocks. b. a randomized block design with two factors and two blocks. c. a completely randomized design. d. an observational study with stratification. ANSWER: b 50. An insurance underwriter wonders whether sports cars “cause” people to drive too fast or those with a propensity for speeding are drawn to sports cars. She secures some research funds and recruits 100 car buyers to her study. She randomly assigns 25 drivers to each of four groups: (1) sports car white, (2) sports car red, (3) non-sports car white, and (4) non-sports car red. The primary research questions are: (1) Do sports cars make people drive faster? and (2) Does color make a difference? The underwriter finds that drivers of red sports cars are the fastest, followed by drivers of red non-sports car. The conclusion is that: a. driving a sports car makes people drive fast. Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 9 b. driving a red sports car makes people drive fast. c. driving a red car makes people drive fast. d. All of the answer options are correct. ANSWER: c 51. An insurance underwriter wonders whether sports cars “cause” people to drive too fast or those with a propensity for speeding are drawn to sports cars. She secures some research funds and recruits 100 car buyers to her study. She randomly assigns 25 drivers to each of four groups: (1) sports car white, (2) sports car red, (3) non-sports car white, and (4) non-sports car red. The primary research questions are: (1) Do sports cars make people drive faster? and (2) Does color make a difference? The result shows that people driving red cars drive faster than those driving white cars. There is no statistically significant difference by type. This conclusion is: a. wrong, because the stated purpose was to study type, not color. b. valid, because this was a randomized study and drivers were randomized on color and type. c. wrong, because you cannot study two different things, such as type and color, at once. d. valid, because sports cars obviously make people drive fast. ANSWER: b

Page 14

Name:

Class:

Date:

Chapter 10 1. When a felony convict is released from prison, the person is often placed on parole for some time. During parole, the person can be returned to prison by the supervising parole agent without a trial or conviction. A criminologist plans a randomized study comparing an intervention with a regular release from prison to study the effectiveness of the intervention in preventing re-incarceration. The criminologist prepares an informedconsent form and plans to enroll parolees during the first meeting with the parole agent, who will introduce the study to the parolee. This procedure is appropriate because: a. parolees are adults and are free to participate or not. b. there are no risks to the parolee, only potential benefits. c. the parole agent has the best interest of the parolee in mind and will advise accordingly. d. None of the answer options is correct. ANSWER: d 2. A veterinarian is studying surgery to repair damaged colons in horses. The veterinarian intends to experiment with a specific drug, in an effort to determine whether the use of the drug improves the chances that a horse will not have a blood clot during the surgery. Does the veterinarian, who works for a major research university, need to obtain approval from the Institutional Review Board before beginning any procedures? a. No, because the study does not involve humans. b. Yes, because the study involves live animals. c. No, because only informed consent from the owners of the horses needs to be obtained. d. None of the answer options is correct. ANSWER: b 3. A new surgical procedure is to be tested for effectiveness in saving limbs. The procedure is at a fairly early stage of development, and little is known about it. The investigators wish to conduct a study to improve their surgical technique and to compare the new procedure with the established procedure, which has a 50% success rate. The study will assign 20 patients to either the established procedure or the new procedure in a systematic way. This study should: a. be approved, because future patients will benefit from it. b. not be approved, because it is not an experiment. c. be approved, because comparing experimental and control subjects will yield valid conclusions. d. not be approved, because there is no benefit to current patients. ANSWER: d 4. A randomized clinical trial is a type of study that: a. studies the effectiveness of medical treatments on actual patients. b. compares two or more treatments by surveying subjects who were prescribed these treatments. c. is always a double-blind experiment. d. is always a block design. ANSWER: a 5. A randomized placebo-controlled clinical trial may be conducted: a. if medical science will benefit and there is minimal harm to humans, even though there is no benefit to current patients. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 10 b. if there is reason to hope that the treatment will help patients who are subjects in the trial. c. if there is strong evidence that the treatment works and the clinical trial will confirm it. d. All of the answer options are correct. ANSWER: b 6. In order to investigate treatments for morbid obesity, obese subjects satisfying fairly strict requirements were randomly assigned to one of three treatment groups: (1) gastric bypass surgery, (2) participation in a diet and exercise program, or (3) both gastric bypass surgery and participation in a diet and exercise program. This clinical trial is ethical because: a. all subjects are likely to receive benefits. b. randomization is ethical if no treatment seems to work better than the others. c. the interests of the study subjects prevail. d. All of the answer options are correct. ANSWER: d 7. Which of the following groups are subject to coercion to participate in a clinical trial by other persons with the power to impose punishment for refusal to participate? a. adults with a serious illness b. parents of a child, if the parents are against participation but the child is not c. prisoners d. All of the answer options are correct. ANSWER: c 8. Informed consent refers to: a. asking the patient to sign a form stating that the patient agrees to participate in a clinical trial. b. outlining to the patient how the study will be conducted. c. providing the patient with a detailed description of the study, including all benefits and risks, and asking for written consent. d. None of the answer options is correct. ANSWER: c 9. Anonymity in a study means that: a. the identity of participants is not revealed, and identifiers are inaccessible to others. b. the individual patients do not know what treatment they receive. c. the investigators do not know what treatment any individual patient receives. d. neither the patients nor the investigators know what treatment any individual patient receives. ANSWER: a 10. Confidentiality in a randomized clinical trial of a new drug means that: a. a patient can be confident that the treating physician is knowledgeable about the new drug. b. the patient will be provided with all confidential information related to the trial. c. all data about the patient will be kept confidential, even when study results are published. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 10 d. All of the answer options are correct. ANSWER: c 11. A criminologist wishes to evaluate a new parolee release program that provides job skills. A person convicted of a felony is often referred to parole when first released from prison. While on parole, a parolee must meet with a parole agent at regular and frequent intervals, must undergo random drug tests and searches of his or her the residence, and can be returned to prison for parole violations at the request of a parole agent. A parolee is not a free person. With respect to participation in this research study: a. a parolee can provide informed consent and does not fall under the rules for prisoners because the person is no longer physically confined to a prison. b. a parolee can provide informed consent and does not fall under the rules for prisoners, because the project provides job skills that are good to have. c. a parolee is not a free person and is subject to return to prison, so the same rules that apply to prisoners apply to parolees. d. None of the answer options is correct. ANSWER: c 12. A nutritionist and a psychologist plan a study to evaluate the effects of a healthy, low-fat, and low-sugar diet on the ability to concentrate and perform complicated tasks. The researchers plan first to recruit volunteers and evaluate their performance under their regular diet. Then the researchers will provide the volunteers with the new diet and repeat the evaluation. Which of the following statements is false? a. This study has only benefits; no risks are associated with it, and Institutional Review Board approval is not required. b. Informed consent is not necessary, because the participants can only benefit from such a study. c. This is a social and behavioral science project and, as such, does not require Institutional Review Board approval. d. All of the answer options are correct. ANSWER: d

Page 3

Name:

Class:

Date:

Chapter 12 1. I toss a two-sided coin and observe whether it lands heads up or tails up. Suppose the coin is a fair coin, meaning that the probability of heads up is 1/2 and the probability of tails up is 1/2. This means that: a. every occurrence of a head must be balanced by a tail in one of the next two or three tosses. b. if I flip the coin many, many times, the proportion of heads up will be approximately 1/2, and this proportion will tend to get closer and closer to 1/2 as the number of tosses increases. c. regardless of the number of flips, half will be heads up and half will be tails up. d. All of the answer options are correct. ANSWER: b 2. You toss a coin 100 times and observe that it lands heads down 65 times. The proportion of times it landed heads down is then 0.65. This proportion represents: a. the sample proportion of tosses that landed heads down in your 100 tosses. b. the correlation between the number of tosses and the number of times it landed heads down. c. the variance of the number of heads-down tosses. d. the probability that the coin lands heads down. ANSWER: a 3. A randomly selected sample of 100 horse owners found that 72 of them feed grass hay to their horses in the morning and alfalfa in the evening. The value 0.72 represents: a. the probability that a randomly selected horse owner will feed grass hay in the morning and alfalfa in the evening. b. the proportion of horse owners in the sample who feed grass hay in the morning and alfalfa in the evening. c. the probability that a horse will be fed grass hay in the morning and alfalfa in the evening. d. All of the answer options are correct. ANSWER: b 4. A randomly selected sample of 100 horse owners found that 72 of them feed their horses two flakes of grass hay in the morning, and one flake of alfalfa plus one flake of grass hay in the evening. The estimated probability that horse owners feed grass hay in the morning and alfalfa plus grass hay in the evening is: a. 0.72. b. 0.75. c. 0.5. d. 0.25. ANSWER: a 5. A randomly selected sample of 100 horse owners found that 72 of them feed one flake of alfalfa plus one flake of grass hay in the evening to their horses, while the rest feed one flake of alfalfa plus oat hay in the evening. The estimated probability that horse owners feed alfalfa plus oat hay in the evening is: a. 0.72. b. 0.5. c. 0.28. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 12 d. 0.75. ANSWER: c 6. Suppose you are told a coin is a fair coin, meaning that the probability of seeing heads should be 0.5 and the probability of seeing tails should be 0.5. You flip the coin 10 times and observe 7 heads and 3 tails. From this, what is your conclusion? a. The coin is not a fair coin. b. The coin is a fair coin. c. There is not enough evidence to tell whether the coin is fair, because the coin was tossed only 10 times. d. There is not enough evidence to tell whether the coin is fair, because you were the only person to toss the coin. ANSWER: c 7. A student uses a computer program designed to randomly print out a number between 1 and 1000. The number 679 appears on the screen. If the student were to repeat this process over and over, the process would best be described as: a. a truly random process. b. a pseudo-random process. c. not a random process at all. ANSWER: b 8. You randomly select 500 students and observe that 85 of them smoke. What is your estimate of the probability that a randomly selected student smokes? a. 0.27 b. 0.5, because there are two possible outcomes for every student surveyed (smoke or don’t smoke) c. 0.17 d. 1.2 ANSWER: c 9. When we draw a card from a deck, the outcome is uncertain. The card’s value is: a. random. b. predictable. c. deterministic. d. None of the answer options is correct. ANSWER: a 10. About 64% of teens aged 12 to 15 years regularly play video games. If we select a single teen in this age group, the probability that the teen regularly plays video games is: a. about 0.17. b. about 0.83. c. about 0.64. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 12 d. None of the answer options is correct. ANSWER: c 11. To say that a coin is fair means that when it is tossed, each of the outcomes (heads or tails) has a 50% probability of occurring. This means that: a. in the next 6 flips of the coin, exactly 3 of the outcomes will be heads. b. in the next 6 flips of the coin, at least 3 of the outcomes will be heads. c. in the next 6000 flips of the coin, approximately 3000 of the outcomes will be heads. d. in the next 6000 flips of the coin, exactly 3000 of the outcomes will be heads. ANSWER: c 12. A fair six-sided die is rolled and the sample space is given as S = {1, 2, 3, 4, 5, 6}. Which of the following statements is true? a. All outcomes in the sample space S are equally likely. b. The events A = {even number} and B = {odd number} are equally likely. c. The events A = {even number} and C = {number less than 4} are equally likely. d. All of the answer options are correct. ANSWER: d 13. A fair six-sided die is rolled and the sample space is given as S = {1, 2, 3, 4, 5, 6}. Let A = {1, 2} and B = {3, 4}. Which of the following statements is true? a. A and B are disjoint. b. P(A or B) = 4/6. c. P(A or B) = P(A) + P(B). d. All of the answer options are correct. ANSWER: d 14. Which of the following events are disjoint? a. P(A) = 0.3, P(B) = 0.25 and P(A or B) = 0.55 b. P(A) = 0.3, P(B) = 0.15 and P(A or B) = 0.35 c. P(A) = 0.6, P(B) = 0.5 and P(A or B) = 0.75 d. P(A) = 0.4, P(B) = 0.4 and P(A or B) = 0.7 ANSWER: a 15. A North American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green. If you bet on red, the probability of winning is 18/38 = 0.4737. The probability 0.4737 represents: a. the fact that you are more likely to win betting on red than you are to lose. b. the proportion of times that the event “winning” will occur in a very long series of individual bets on red. c. the fact that if you make 100 wagers on red, you will have 47 or 48 wins. d. nothing important, because every spin of the wheel results in one of three outcomes (red, black, or green). Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 12 ANSWER: b 16. A North American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green. Suppose you decide to bet on red on each of 10 consecutive spins of the roulette wheel. Suppose you lose the first five wagers. Which of the following is true? a. There should be more spins of red in the next five spins of the wheel, because there weren’t any on the first five spins. b. The wheel is not working properly—it favors outcomes that are not red. Hence, during the next five spins of the wheel, we’re likely to continue to see few red outcomes. c. We’re due for a win, so the sixth spin of the wheel is very likely to come up red. d. The outcomes of the first five spins tell us nothing about what will happen on the next five spins. ANSWER: d 17. I roll a four-sided die. The possible outcomes are 1, 2, 3, or 4, depending on the number of spots on the side of the die that is face down. This collection of all possible outcomes is called: a. a census. b. the probability. c. the sample space. d. the distribution. ANSWER: c 18. Assume that you are considering buying a car. There is a probability of 0.4 that you will purchase a new vehicle, and there is a probability of 0.5 that you will purchase a used vehicle. There is no probability that you will buy more than one vehicle. The probability that you will purchase no vehicle at all is: a. 0. b. 0.1. c. 0.9. d. 1. ANSWER: b 19. Assume that you are considering buying a car. There is a probability of 0.4 that you will purchase a new vehicle, and there is a probability of 0.5 that you will purchase a used vehicle. There is no probability that you will purchase more than one vehicle. The probability of the set of all outcomes is: a. 0. b. 0.3. c. 0.9. d. 1. ANSWER: d 20. Assume that you are considering buying a car. There is a probability of 0.4 that you will purchase a new vehicle, and there is a probability of 0.5 that you will purchase a used vehicle. There is no probability that you will purchase more than one vehicle. Which of the following is true? a. The probability that you will not buy a used vehicle is 0.5. Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 12 b. If you buy a new car, then you will not buy a used car. c. Purchasing a new car and purchasing a used car are disjoint events. d. All of the answer options are correct. ANSWER: d 21. An assignment of probabilities to events in a sample space must obey which of the following? a. The probability of any event must be a number between 0 and 1, inclusive. b. They must sum to 1 when adding over all events in the sample space. c. They must obey the addition rule for disjoint events. d. All of the answer options are correct. ANSWER: d 22. Event A occurs with probability 0.2. Event B occurs with probability 0.3. Event C occurs with probability 0.4. If A, B, and C are disjoint, then: a. P(A or B) = 0.5. b. P(A or C) = 0.6. c. P(A or B or C) = 0.9. d. All of the answer options are correct. ANSWER: d 23. I flip a coin twice and count the number of heads. Which of the following is a valid assignment of probabilities for the number of heads observed in two flips? a. Number of heads 0 1 2 Probability 1/10 5/10 4/10 b. Number of heads 0 1 2 Probability

1/4

2/4

1/4

c. Number of heads 0 1 Probability 1/3 1/3 d. All of the answer options are correct. ANSWER: d

2 1/3

24. A bowl contains 2 red and 2 green marbles. We pick a marble, record its color, and replace it. We repeat this procedure a second and a third time. The probability distribution for the number of red marbles is given by: a. Number of red marbles 0 1 2 3 Probability b. Number of red marbles Probability c. Number of red marbles Probability d. Number of red marbles

1/8

3/8

1/8

0 1/4

1 3/8

2 3/8

3 1/4

0 1/4

1 1/2

2 1/2

3 1/4

Page 5

Name:

Class:

Date:

Chapter 12 Probability ANSWER: d

1/8

3/4

3/8

1/8

25. A bowl contains 2 red and 2 green marbles. We pick a marble, record its color, and replace it. We repeat this procedure a second and a third time. The probability distribution for the number of red marbles is given below. Number of red marbles 0 1 2 3 Probability 1/8 3/8 3/8 1/8 For this distribution, the probability of exactly one red marble is given by: a. 1/8. b. 3/8. c. 7/8. d. 1/3. ANSWER: b 26. A bowl contains 2 red and 2 green marbles. We pick a marble, record its color, and replace it. We repeat this procedure a second and a third time. The probability distribution for the number of red marbles is given below. Number of red marbles 0 1 2 3 Probability 1/8 3/8 3/8 1/8 For this distribution, the probability of 2 or more red marbles is given by: a. 1/2. b. 3/8. c. 6/8. d. 1/4. ANSWER: a 27. According to the Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups: Age 15–17 18–24 25–34 35 or older Probability 0.007 0.573 0.26 0.16 If we randomly select a full-time student, what is the probability that the student is 25 or older? a. 0.26 b. 0.42 c. 0.74 d. The answer is impossible to determine from the information given. ANSWER: b 28. According to the Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups: Age 15–17 18–24 25–34 35 or older Probability 0.007 0.573 0.26 0.16 If we randomly select a full-time student, the probability that the student is not 18–24 years old is: a. 0.377. b. 0.427. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 12 c. 0.573. d. 0.993. ANSWER: b 29. According to the Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups: Age 15–17 18–24 25–34 35 or older Probability 0.007 0.573 0.26 0.16 If we randomly select a full-time student, the probability that the student is 20–34 years old is: a. 0.5. b. 0.703. c. 0.833. d. The answer cannot be determined from the information provided. ANSWER: d 30. A sample of horses admitted to a local veterinary hospital had the following distribution of mares, geldings, and stallions. Sex mares geldings stallions Percent 51.09 43.80 5.11 If we assume that the horses constitute a random sample of all horses in the state, then we estimate the probability that a randomly selected horse is a stallion to be: a. 5.11. b. 0.511. c. 0.0511. d. None of the answer options is correct. ANSWER: c 31. A random sample of horses admitted to a local veterinary hospital found the following distribution of mares, geldings, and stallions. Sex mares geldings stallions Percent 0.51 0.44 0.05 The probability that a horse newly arriving at the veterinary hospital is a male (gelding or stallion) is: a. 0.44. b. 0.05. c. 0.51. d. 0.49. ANSWER: d 32. At a small college, all entering first year students must take a foreign-language class, chosen from the languages Spanish, French, Swahili, Chinese, and Arabic. Because there is limited space in the foreignlanguage courses, a student cannot simultaneously enroll in more than one course. The probability distribution for the language studied by a randomly selected first year is summarized in the following table. Language studied Spanish French Swahili Chinese Arabic Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 12 Probability ? 0.12 0.09 0.19 The probability that the first year is studying Spanish is: a. 0.08. b. 0.52. c. 0.48. d. The answer cannot be determined from the information given. ANSWER: c

0.12

33. At a small college, all entering first year students must take a foreign-language class, chosen from the languages Spanish, French, Swahili, Chinese, and Arabic. Because there is limited space in the foreignlanguage courses, a student cannot simultaneously enroll in more than one course. The probability distribution for the language studied by a randomly selected first year is summarized in the following table. Language studied Spanish French Swahili Chinese Arabic Probability ? 0.12 0.09 0.19 0.12 The probability that the first year is studying Chinese or Swahili is: a. 0.28. b. 0.31. c. 0.72. d. 1. ANSWER: a 34. I choose a card at random from a well-shuffled deck of 52 cards. There is a 1/4 probability that the card chosen is a spade, a 1/4 probability that the card is a heart, a 1/4 probability that the card is a diamond, and a 1/4 probability that the card is a club. Both spades and clubs are black cards, whereas hearts and diamonds are red. The event that the card is a heart and the event that the card is a club are: a. disjoint events. b. impossible events. c. independent events. d. None of the answer options is correct. ANSWER: a 35. I choose a card at random from a well-shuffled deck of 52 cards. There is a 1/4 probability that the card chosen is a spade, a 1/4 probability that the card is a heart, a 1/4 probability that the card is a diamond, and a 1/4 probability that the card is a club. Both spades and clubs are black cards, whereas hearts and diamonds are red. The probability that the card chosen is not a spade is: a. 0.25. b. 0.5. c. 0.75. d. 1. ANSWER: c 36. A random variable can be described as: a. a probability of an event. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 12 b. a variable whose value is a numerical outcome of a random phenomenon. c. the proportion of times an event occurs over a long run of repeated trials. d. All of the answer options are correct. ANSWER: b 37. Suppose we roll two fair four-sided dice. Let X denote the sum of the two roll outcomes. For example, if the first roll yields 3 and the second roll yields 1, then X = 3 + 1 = 4. The probability distribution for X is given below. Value of X 2 3 4 5 6 7 8 Probability 1/16 2/16 3/16 4/16 3/16 2/16 1/16 The probability of rolling a pair of 4s (a 4 on the first die and a 4 on the second die) is: a. 1/16. b. 1/8. c. 3/16. d. 13/16. ANSWER: a 38. Suppose we roll two fair four-sided dice. Let X denote the sum of the two roll outcomes. For example, if the first roll yields 3 and the second roll yields 1, then X = 3 + 1 = 4. The probability distribution for X is given below. Value of X 2 3 4 5 6 7 8 Probability 1/16 2/16 3/16 4/16 3/16 2/16 1/16 P(X < 5) has the value: a. 1/16. b. 3/16. c. 6/16. d. 10/16. ANSWER: c 39. The management for a chain of restaurants recorded the number of appetizers, X, ordered by tables dining. They observed that X had the following probability distribution. Value of X 0 1 2 3 or more Probability 0.6 0.35 0.04 0.01 The probability that a randomly chosen table orders at least one appetizer is: a. 0.35. b. 0.39. c. 0.4. d. None of the answer options is correct. ANSWER: c 40. The management for a chain of restaurants recorded the number of appetizers, X, ordered by tables dining. They observed that X had the following probability distribution. Value of X 0 1 2 3 or more Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 12 Probability 0.6 What is P(X < 2)? a. 0.04 b. 0.35 c. 0.6 d. 0.95 ANSWER: d

0.35

0.04

0.01

41. You have three cards, labeled 1, 2, and 3. You select two of the cards at random and note the numbers on the two cards. Let X be the sum of the two numbers labeled on the selected cards. Which of the following is the correct set of probabilities for X? a. X 1 2 3 Probability 1/3 1/3 1/3 b. X Probability

3 1/3

4 1/3

5 1/3

c. X Probability

1 1/6

2 2/6

3 3/6

d. X Probability

3 1/6

4 2/6

5 3/6

ANSWER: b 42. A basketball player makes 70% of her free throws. When fouled, she gets to take two free throws. Let X represent the number of free throws made in two tries. The probability distribution for the number of free throws she makes in two attempts is summarized in the following table. Number of free throws made Probability

0.09

0.42

0.49

The probability that she makes at least one free throw is expressed as: a. P(X 1). b. P(X

1).

c. P(X < 1). d. P(X > 1). ANSWER: a 43. A basketball player makes 70% of her free throws. When fouled, she gets to take two free throws. Let X represent the number of free throws made in two tries. The probability distribution for the number of free throws she makes in two attempts is summarized in the following table. Number of free 0 1 2 throws made Probability 0.09 0.42 0.49 Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 12 The probability that she makes at least one free throw is: a. 0.67. b. 0.91. c. 0.95. d. 1. ANSWER: b 44. Horses are housed in pastures, pipe pens, or barn stalls at a local horse barn. Let A = {horse housed in barn stall}. Let the event B = {horse not housed in barn stall}. Which statement is true? a. B is the complement to A. b. B and A are mutually exclusive. c. P(A or B) = P(A) + P(B). d. All of the answer options are correct. ANSWER: d 45. Horses are housed in pastures, pipe pens, or barn stalls at a local horse barn. Let X = the number of horses housed in barn stalls. Then X is: a. a discrete random variable. b. a continuous random variable. c. an event. d. the sample space. ANSWER: a 46. The probability density of a random variable X is given in the following figure.

From this density, the probability that X is between 0.5 and 1.5 is: a. 1/3. b. 1/2. c. 3/4. d. 1. ANSWER: b 47. The probability density of a random variable X is given in the following figure.

Page 11

Name:

Class:

Date:

Chapter 12

The probability that X is at least 0.5 is: a. 0. b. 1/4. c. 1/2. d. 3/4. ANSWER: d 48. The density curve for a continuous random variable X has which of the following properties? a. The probability of any event is the area under the density curve and above the values of X that make up the event. b. The total area under the density curve for X must be exactly 1. c. The probability of any event of the form X = constant is 0. d. All of the answer options are correct. ANSWER: d 49. The amount of milk sold each day by a grocery store varies according to the Normal distribution with mean 130 gallons and standard deviation 12 gallons. On a randomly selected day, the probability that the store sells at least 154 gallons is: a. 0.0228. b. 0.1587. c. 0.8413. d. 0.9772. ANSWER: a 50. The high temperature X (in degrees Fahrenheit) on January days in Columbus, Ohio, varies according to the Normal distribution with mean 21 and standard deviation 10. The value of P(X < 10) is: a. 0.7433. b. 0.8643. c. 0.1357. d. 0. ANSWER: c 51. The high temperature X (in degrees Fahrenheit) on January days in Columbus, Ohio, varies according to the Normal distribution with mean 21 and standard deviation 10. If a January day in Columbus is randomly selected, what is the probability that the high temperature is between 15 and 25 degrees? a. 0.2743 Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 12 b. 0.6554 c. 0.3811 d. almost 1 ANSWER: c 52. You have lived in Columbus for more than 20 years and know that there is at least a 75% chance of a high temperature above freezing on a particular January day. This is an example of: a. the addition rule for disjoint events. b. a sample space. c. a personal probability. d. a random variable. ANSWER: c 53. According to the M&Ms website, each package of the milk chocolate candies typically contains 14% brown, 13% red, 14% yellow, 16% green, 24% blue, and 20% orange M&Ms. You go to the store and buy a standard package. When you open it, you find that it contains 51 M&Ms, distributed as follows. Color Brown Red Yellow Green Blue Orange Frequency 8 4 10 7 11 11 The variable “color” is: a. discrete. b. continuous. c. categorical. d. None of the answer options is correct. ANSWER: c 54. According to the M&Ms website, each package of the milk chocolate candies typically contains 14% brown, 13% red, 14% yellow, 16% green, 24% blue, and 20% orange M&Ms. You go to the store and buy a standard package. When you open it, you find that it contains 51 M&Ms, distributed as follows. Color Brown Red Yellow Green Blue Orange Frequency 8 4 10 7 11 11 Over the long run, you know that the probability of selecting a blue or an orange M&M will be 44%, because these outcomes are: a. discrete. b. disjoint. c. finite. d. None of the answer options is correct. ANSWER: b 55. According to the M&Ms website, each package of the milk chocolate candies typically contains 14% brown, 13% red, 14% yellow, 16% green, 24% blue, and 20% orange M&Ms. You go to the store and buy a standard package. When you open it, you find that it contains 51 M&Ms, distributed as follows. Color Brown Red Yellow Green Blue Orange Frequency 8 4 10 7 11 11 Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 12 Choosing one M&M from your bag is an example of: a. an event. b. an outcome. c. a set of outcomes. d. None of the answer options is correct. ANSWER: a 56. Every year, the veterinary hospital at a major research university treats a number of horses that have stones called enteroliths in their guts. A sample of 20 years shows that, on average, about 2% of horses presenting at the veterinary hospital are treated for enteroliths. In the long run, the probability that a horse arriving at the veterinary hospital has enteroliths is: a. 0.05. b. 0.02. c. 0.5. d. The answer cannot be determined from the information given. ANSWER: b 57. Every year, the veterinary hospital at a major research university treats a number of horses that have stones called enteroliths in their guts. A sample of 20 years shows that, on average, about 2% of horses presenting at the veterinary hospital are treated for enteroliths. Some breeds of horses seem more prone to developing enteroliths than others. Below is a table with the distribution of enteroliths among the breeds seen at the hospital. Quarter Breed Arabian Thoroughbred Appaloosa Morgan horse Probability 0.3 0.2 0.15 0.10 ? The probability that a horse arriving at the veterinary hospital is not an Arabian or a quarter horse is: a. 0.55. b. 0.25. c. 0.45. d. 0.75. ANSWER: c 58. A geneticist developed a new type of pest-resistant walnut tree. The geneticist wants to breed these trees to create more trees to sell. It turns out that when you try to breed these trees, 75% of the time the tree produced is pest-resistant, and 25% of the time it is susceptible (not pest-resistant). If a grower crossed creates 100 trees, the grower will get: a. exactly 70 resistant trees. b. somewhere between 67 and 73 resistant trees. c. somewhere between 64 and 73 resistant trees. d. The answer cannot be determined. ANSWER: d 59. A geneticist developed a new type of pest-resistant walnut tree. The geneticist wants to breed these trees to Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 12 create more trees to sell. It turns out that when you try to breed these trees, 75% of the time the tree produced is pest-resistant, and 25% of the time it is susceptible (not pest-resistant). If a grower creates 100 trees, the grower should expect to get: a. approximately 75 resistant trees. b. exactly 75 resistant trees. c. approximately 25 resistant trees. d. None of the answer options is correct. ANSWER: a 60. A geneticist developed a new type of pest-resistant walnut tree. The geneticist wants to breed these trees to create more trees to sell. It turns out that when you try to breed these trees, 75% of the time the tree produced is pest-resistant and 25% of the time it is susceptible (not pest-resistant). If a grower breeds a tree, the outcome is random and a probability model is given by outcomes: a. resistant with probability 0.5 and susceptible with probability 0.5. b. resistant with probability 0.75 and susceptible with probability 0.75. c. resistant with probability 0.25 and susceptible with probability 0.25. d. resistant with probability 0.75 and susceptible with probability 0.25. ANSWER: d 61. A geneticist developed a new type of pest-resistant walnut tree. The geneticist wants to breed these trees to create more trees to sell. It turns out that when you try to breed these trees, 75% of the time the tree produced is pest-resistant and 25% of the time it is susceptible (not pest-resistant). If a grower crosses two such trees, the outcome is random and a probability model is given by: a. resistant and susceptible. b. probabilities p = 0.70 and p = 0.3. c. P(resistant) = 0.75 and P(susceptible) = 0.25. d. P(resistant) = 0.7. ANSWER: c 62. A different geneticist developed a new type of pest-resistant walnut tree. The geneticist wants to breed these trees to create more trees to sell. It turns out that when you try to breed these trees, 50% of the time the tree is very resistant, 30% of the time the tree is somewhat resistant, and 20% of the time the tree is susceptible to invasion by pests. The sample space consists of which of the following outcomes? a. resistant, not resistant b. very resistant, not very resistant c. resistant, susceptible d. very resistant, somewhat resistant, susceptible ANSWER: d 63. A different geneticist developed a new type of pest-resistant walnut tree. The geneticist wants to breed these trees to create more trees to sell. It turns out that when you try to breed these trees, 50% of the time the tree is very resistant, 30% of the time the tree is somewhat resistant, and 20% of the time the tree is susceptible to invasion by pests The probability model for the breeding of a tree is: Copyright Macmillan Learning. Powered by Cognero.

Page 15

Name:

Class:

Date:

Chapter 12 a. P(susceptible) = 0.2, P(resistant) = 0.8. b. P(very resistant) = 0.5, P(somewhat resistant) = 0.3, P(susceptible)=0.2. c. P(very resistant) = 0.5, P(not very resistant) = 0.5. d. P(susceptible) = 0.2, P(not susceptible) = 0.8. ANSWER: b 64. A different geneticist developed a new type of pest-resistant walnut tree. The geneticist wants to breed these trees to create more trees to sell. It turns out that when you try to breed these trees, 50% of the time the tree is very resistant, 30% of the time the tree is somewhat resistant, and 20% of the time the tree is susceptible to invasion by pests The probability that a tree will be at least somewhat resistant is: a. P = 0.3. b. P = 0.5. c. P = 0.8. d. P = 0.7. ANSWER: c 65. A bowl contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the number of red marbles in the 4 picks, the random variable is: a. the number of red marbles. b. the number of red, blue, or green marbles. c. the number of green marbles. d. None of the answer options is correct. ANSWER: a 66. A bowl contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the number of red marbles in the 4 picks, the sample space is given by which of the following? a. 1, 2, 3, or 4 red marbles b. 4 marbles c. red, green, blue d. 0, 1, 2, 3, or 4 marbles ANSWER: d 67. A bowl contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the number of red marbles in the 4 picks, the probabilities associated with this experiment are P(0) = 0.24, P(1) = 0.41, P(2) = 0.265, P(3) = 0.076, and: a. P(4) = 0.001. b. P(4) = 0.005. c. P(4) = 0.009. d. The answer cannot be determined with information given. ANSWER: c 68. A bowl contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 12 number of red marbles in the 4 picks, the probabilities associated with this experiment are P(0) = 0.24, P(1) = 0.41, P(2) = 0.265, P(3) = 0.076, and P(4) = 0.009. The probability of at least 1 red marble is: a. 0.24. b. 0.76. c. 0.009. d. 0.41. ANSWER: b 69. A bowl contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the number of red marbles in the 4 picks, the probabilities associated with this experiment are P(0) = 0.24, P(1) = 0.41, P(2) = 0.265, P(3) = 0.076, and P(4) = 0.009. The probability of 2 or fewer red marbles is: a. 0.41. b. 0.24. c. 0.65. d. 0.915. ANSWER: d 70. A bowl contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the number of red marbles in the 4 picks, the probabilities associated with this experiment are P(0) = 0.24, P(1) = 0.41, P(2) = 0.265, P(3) = 0.076, and P(4) = 0.009. The probability of less than 2 red marbles is: a. 0.41. b. 0.65. c. 0.915. d. 0.991. ANSWER: b 71. An arborist is commissioned to study the amount of tree decay in a forest. The arborist obtains detailed information about the forest, the location, the annual rainfall, the type of tree species and other plants present, the pests and insects associated with tree death, and other information deemed relevant. On the basis of this information, the arborist reports that the proportion of decayed trees is 22%. Therefore, the arborist concludes that the probability of a randomly selected tree having decay is p = 0.22. This is an example of: a. a frequency-based probability. b. a random probability. c. a personal probability. d. a fixed probability. ANSWER: c 72. Two high school seniors find themselves with much time and nothing to do. They decide to devise a computer game in which a cursor moves randomly along the x axis between –1 and 1. The game they play is to stop the cursor at random points between –1 and 1 without looking at the screen. Such a game results in a uniform distribution over the interval between –1 and 1. Since the area under the density curve (here a flat line) equals 1, the height of the density curve is: a. 2. Copyright Macmillan Learning. Powered by Cognero.

Page 17

Name:

Class:

Date:

Chapter 12 b. 1. c. 0.5. d. 0.25. ANSWER: c 73. Two high school seniors find themselves with much time and nothing to do. They decide to devise a computer game in which a cursor moves randomly along the x axis between –1 and 1. The game they play is to stop the cursor at random points between –1 and 1 without looking at the screen. Such a game results in a uniform distribution over the interval between –1 and 1. Since the area under the density curve (here a flat line) equals 1, the height of the density curve is 0.5. The probability that the cursor will be between –0.75 and –0.25 or between 0.25 and 0.75 equals: a. 0. b. 0.25. c. 1. d. 0.5. ANSWER: d

Page 18

Name:

Class:

Date:

Chapter 13 1. A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice, and the outcomes of the two spins are independent. The probability that the ball lands on black the first time and on green the second time is: a. 0.0249. b. 0.2244. c. 0.277. d. 0.5263. ANSWER: a 2. A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice, and the outcomes of the two spins are independent. The probability that the ball lands on red at least once is: a. 0.4986. b. 0.723. c. 0.7756. d. 0.9474. ANSWER: b 3. A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that like trance music but not dubstep is: a. 5%. b. 10%. c. 15%. d. 20%. ANSWER: b 4. A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that like either dubstep or trance is: a. 40%. b. 55%. c. 70%. d. 100%. ANSWER: a 5. A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that like neither trance music nor dubstep is: Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 13 a. 0%. b. 20%. c. 40%. d. 60%. ANSWER: d 6. A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that didn’t select any of the music options available on the survey was: a. 0%. b. 20%. c. 40%. d. 60%. ANSWER: c 7. A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that preferred either dubstep or trance is calculated by: a. P(Dubstep) + P(Trance). b. P(Dubstep) + P(Trance) + P(Dubstep and Trance). c. P(Dubstep) + P(Trance) – P(Dubstep and Trance). d. None of the answer options is correct. ANSWER: c 8. A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The conditional probability that a student likes dubstep, given that the student likes trance music, is: a. 55%. b. 60%. c. 65%. d. 70%. ANSWER: b 9. A group of first years at a local university consider joining the equestrian team. It is known that, of students who join the team, 35% percent choose Western riding, 45% choose dressage, and 50% choose jumping. Twenty percent choose both dressage and jumping, while 10% choose Western and dressage. No one chooses Western and jumping. There are no horses suitable for two styles, and each student is assigned to one horse. What is the probability that a student chooses dressage or jumping? a. 0.95 b. 0.75 Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 13 c. 0.23 d. 0.9 ANSWER: b 10. A group of first years at a local university consider joining the equestrian team. It is known that, of students who join the team, 35% percent choose Western riding, 45% choose dressage, and 50% choose jumping. Twenty percent choose both dressage and jumping, while 10% choose Western and dressage. No one ever chooses Western and jumping. What is the probability that a student chooses neither dressage nor Western riding? a. 0.3 b. 0.5 c. 0.2 d. 0.05 ANSWER: a 11. A group of first years at a local university consider joining the equestrian team. It is known that, of students who join the team, 35% percent choose Western riding, 45% choose dressage, and 50% choose jumping. Twenty percent choose both dressage and jumping, while 10% choose Western and dressage. No one ever chooses Western and jumping. If two students decide to join the team, what is the probability that both are Western and dressage riders, if they decide independently? a. 0.1 b. 0.2 c. 0.01 d. 0.8 ANSWER: c 12. A group of first years at a local university consider joining the equestrian team. It is known that, of students who join the team, 35% percent choose Western riding, 45% choose dressage, and 50% choose jumping. Twenty percent choose both dressage and jumping, while 10% choose Western and dressage. No one ever chooses Western and jumping. If two students decide to join the team, what is the probability that one student joins jumping only and the other student joins the Western team, if they decide independently? a. 0.175 b. 0.125 c. 0.0375 d. 0.105 ANSWER: d 13. A group of first years at a local university consider joining the equestrian team. It is known that, of students who join the team, 35% percent choose Western riding, 45% choose dressage, and 50% choose jumping. Twenty percent choose both dressage and jumping, while 10% choose Western and dressage. No one ever chooses Western and jumping. If two students decide to join the team, what is the probability that one student joins the dressage team and the other student does not? a. 0.2275 Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 13 b. 0.1925 c. 0.2475 d. 0.1525 ANSWER: c 14. A group of first years at a local university consider joining the equestrian team. It is known that, of students who join the team, 35% percent choose Western riding, 45% choose dressage, and 50% choose jumping. Twenty percent choose both dressage and jumping, while 10% choose Western and dressage. No one ever chooses Western and jumping. If five students decide to join the team, what is the probability that at least one student joins the dressage team? a. 0.0185 b. 0.0503 c. 0.0412 d. 0.9497 ANSWER: d 15. A system has two components that operate in parallel, as shown in the following diagram.

Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probabilities of failure for Components 1 and 2, during one period of operation, are 0.2 and 0.03, respectively. Let F1 denote the event that Component 1 fails during one period of operation and F2 denote the event that Component 2 fails during one period of operation. The component failures are independent. The event corresponding to the above system failing during one period of operation is: a. F1 and F2. b. F1 or F2. c. not F1 or not F2. d. not F1 and not F2. ANSWER: a 16. A system has two components that operate in parallel, as shown in the following diagram.

Page 4

Name:

Class:

Date:

Chapter 13 0.2 and 0.03, respectively. Let F1 denote the event that Component 1 fails during one period of operation and F2 denote the event that Component 2 fails during one period of operation. The component failures are independent. The event corresponding to the above system functioning properly during one period of operation is: a. F1 and F2. b. F1 or F2. c. not F1 or not F2. d. not F1 and not F2. ANSWER: c 17. A system has two components that operate in parallel, as shown in the following diagram.

Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probabilities of failure for Components 1 and 2, during one period of operation, are 0.2 and 0.03, respectively. Let F1 denote the event that Component 1 fails during one period of operation and F2 denote the event that Component 2 fails during one period of operation. The component failures are independent. The probability that the system functions properly during one period of operation is closest to: a. 0.994. b. 0.97. c. 0.94. d. 0.776. ANSWER: a 18. A system has two components that operate in parallel, as shown in the following diagram.

Because the components operate in parallel, at least one of the components must function properly if the system Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 13 is to function properly. The probabilities of failure for Components 1 and 2, during one period of operation, are 0.2 and 0.03, respectively. Let F1 denote the event that Component 1 fails during one period of operation and F2 denote the event that Component 2 fails during one period of operation. The component failures are independent. The probability that the system fails during one period of operation is closest to: a. 0.23. b. 0.224. c. 0.06. d. 0.006. ANSWER: d 19. Spelling mistakes in a text are either “nonword errors” or “word errors.” A nonword error produces a string of letters that is not a word, such as “the” typed as “teh.” Word errors produce the wrong word, such as “loose” typed as “lose.” Nonword errors make up 25% of all errors. A human proofreader will catch 80% of nonword errors and 50% of word errors. What percent of errors will the proofreader catch? a. 20% b. 37.5% c. 57.5% d. 80% ANSWER: c 20. Spelling mistakes in a text are either “nonword errors” or “word errors.” A nonword error produces a string of letters that is not a word, such as “the” typed as “teh.” Word errors produce the wrong word, such as “loose” typed as “lose.” Nonword errors make up 25% of all errors. A human proofreader will catch 80% of nonword errors and 50% of word errors. Of all the errors that the proofreader catches, what percent are word errors? a. 28.7% b. 57.5% c. 65.2% d. 87.0% ANSWER: c 21. The following table gives the sex and age group of college students at a midwestern university. Female Male Total 15 to 17 years 89 61 150 18 to 24 years 5,668 4,697 10,365 25 to 34 years 1,904 1,589 3,493 35 years or 1,660 970 2,630 older Total 9,321 7,317 16,638 A student is to be selected at random. The estimated probability that the selected student is 25 to 34 years old is: a. 0.21. b. 0.25. c. 0.56. d. 0.623. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 13 ANSWER: a 22. The following table gives the sex and age group of college students at a midwestern university. Female Male Total 15 to 17 years 89 61 150 18 to 24 years 5,668 4,697 10,365 25 to 34 years 1,904 1,589 3,493 35 years or 1,660 970 2,630 older Total 9,321 7,317 16,638 A student is to be selected at random. The estimated probability that the selected student is a female who is 15 to 17 years old is: a. 0.005. b. 0.01. c. 0.56. d. 0.593. ANSWER: a 23. The following table gives the sex and age group of college students at a midwestern university. Female Male Total 15 to 17 years 89 61 150 18 to 24 years 5,668 4,697 10,365 25 to 34 years 1,904 1,589 3,493 35 years or 1,660 970 2,630 older Total 9,321 7,317 16,638 A student is to be selected at random. Given that the selected student is female, the estimated conditional probability that she is 25 to 34 years old is: a. 0.545. b. 0.204. c. 0.114. d. 0.008. ANSWER: b 24. The following table gives the sex and age group of college students at a midwestern university. Female Male Total 15 to 17 years 89 61 150 18 to 24 years 5,668 4,697 10,365 25 to 34 years 1,904 1,589 3,493 35 years or 1,660 970 2,630 older Total 9,321 7,317 16,638 A student is to be selected at random. All of the outcomes counted in this table are: a. discrete. Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 13 b. disjoint. c. finite. d. None of the answer options is correct. ANSWER: b 25. Veterinarians suspect that enteroliths (calcifications in the gut of horses) are related to diet—in particular, alfalfa. To investigate this suspicion, a group of veterinarians collected information on the diet of horses and whether the horses developed enteroliths. The table below displays the findings (a case is a horse with enteroliths, a control is a horse without enteroliths). Percent of Alfalfa in Diet Disease status < 25% 25%–50% > 50% Total Case 0.05 0.07 0.08 0.20 Control 0.40 0.25 0.15 0.80 The probability that a randomly selected horse gets more than 50% alfalfa is: a. 0.33. b. 0.5. c. 0.8. d. 0.23. ANSWER: d 26. Veterinarians suspect that enteroliths (calcifications in the gut of horses) are related to diet—in particular, alfalfa. To investigate this suspicion, a group of veterinarians collected information on the diet of horses and whether the horses developed enteroliths. The table below displays the findings (a case is a horse with enteroliths, a control is a horse without enteroliths). Percent of Alfalfa in Diet Disease status < 25% 25%–50% > 50% Total Case 0.05 0.07 0.08 0.20 Control 0.40 0.25 0.15 0.80 The probability that a randomly selected horse has enteroliths, given that it is fed more than 50% alfalfa, is: a. 0.23. b. 0.348. c. 0.08. d. 0.2. ANSWER: b 27. Veterinarians suspect that enteroliths (calcifications in the gut of horses) are related to diet—in particular, alfalfa. To investigate this suspicion, a group of veterinarians collected information on the diet of horses and whether the horses developed enteroliths. The table below displays the findings (a case is a horse with enteroliths, a control is a horse without enteroliths). Percent of Alfalfa in Diet Disease status < 25% 25%–50% > 50% Total Case 0.05 0.07 0.08 0.20 Control 0.40 0.25 0.15 0.80 The probability that a randomly selected horse is fed more than 50% alfalfa, given that it has enteroliths, is: Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 13 a. 0.2. b. 0.23. c. 0.08. d. 0.4. ANSWER: d 28. Veterinarians suspect that enteroliths (calcifications in the gut of horses) are related to diet—in particular, alfalfa. To investigate this suspicion, a group of veterinarians collected information on the diet of horses and whether the horses developed enteroliths. The table below displays the findings (a case is a horse with enteroliths, a control is a horse without enteroliths). Percent of Alfalfa in Diet Disease status < 25% 25%–50% > 50% Total Case 0.05 0.07 0.08 0.20 Control 0.40 0.25 0.15 0.80 There is a relationship between being fed alfalfa and having enteroliths because: a. P(enteroliths | > 50% alfalfa) > P(enteroliths | 25%–50% alfalfa) > P(enteroliths | < 25% alfalfa). b. fewer horses get more than 50% alfalfa. c. the proportion of horses that have enteroliths and eat more than 50% alfalfa is the largest probability in the "Case" row of the table. d. None of the answer options is correct. ANSWER: a 29. Event A occurs with probability 0.1. Event B occurs with probability 0.6. If A and B are independent, then: a. P(A and B) = 0.7. b. P(A and B) = 0.06. c. P(A and B) = 0.64. d. P(A or B) = 0.7. ANSWER: b 30. Event A occurs with probability 0.2. Event B occurs with probability 0.9. Events A and B: a. are disjoint. b. cannot be independent. c. cannot be disjoint. d. are reciprocating. ANSWER: c 31. A stack of four cards contains two red cards and two black cards. I select two cards, one at a time, and do not replace the first card selected before selecting the second card. Consider the events: A = the first card selected is red. B = the second card selected is red. The events A and B are: a. independent. Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 13 b. disjoint. c. conditional. d. None of the answer options is correct. ANSWER: d 32. In a particular game, a six-sided fair die is tossed. If the number of spots showing is six, you win $6; if the number of spots showing is five, you win $3; if the number of spots showing is four, you win $2; and if the number of spots showing is three, you win $1. If the number of spots showing is one or two, you win nothing. You play the game twice. The probability that you win something both times you play is: a. 1/6. b. 1/3. c. 4/9. d. 1/4. ANSWER: c 33. Students at a local university have the option of taking first year seminars during their first year in college. First year seminars are restricted to first years, and this rule is strictly enforced. A survey of the first years revealed the following: Among the social science majors, 50% chose to take a first year seminar; among the humanities majors, 65% chose to take a first year seminar; and among the physical science majors, it was 30%. First years make up 32% of undergraduates. The probability of taking a first year seminar, if a student is a physical science major, is: a. a total probability. b. a complete probability. c. a joint probability. d. a conditional probability. ANSWER: d 34. Students at a local university have the option of taking first year seminars during their first year in college. First year seminars are restricted to first years, and this rule is strictly enforced. A survey of the first years revealed the following: Among the social science majors, 50% chose to take a first year seminar; among the humanities majors, 65% chose to take a first year seminar; and among the physical science majors, it was 30%. First years make up 32% of undergraduates. The probability that a student is a first year, given that the student is enrolled in a first year seminar, is: a. 1. b. 0.32. c. 0.53. d. The answer cannot be determined from the information provided. ANSWER: a 35. In a particular game, a six-sided fair die is tossed. If the number of spots showing is six, you win $6; if the number of spots showing is five, you win $3; if the number of spots showing is four, you win $2; and if the number of spots showing is three, you win $1. If the number of spots showing is one or two, you win nothing. You play the game twice. The probability that you win at least $9 in total for your game play is: Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 13 a. 1/6. b. 1/3. c. 1/36. d. 1/12. ANSWER: d 36. Suppose we toss a coin and roll a die. Let A be the event that the number of spots showing on the die is three or less, and let B be the event that the coin comes up heads. The events A and B are: a. disjoint. b. conditional. c. independent. d. reciprocals. ANSWER: c 37. An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. The conditional probability of B, given A, is: a. 5/6. b. 1/5. c. 1/6. d. The answer cannot be determined from the information given. ANSWER: b 38. An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. We may conclude that: a. events A and B are independent. b. events A and B are disjoint. c. either A or B always occurs. d. None of the answer options is correct. ANSWER: c 39. Event A occurs with probability 0.3, and event B occurs with probability 0.4. If A and B are independent, we may conclude that: a. P(A and B) = 0.12. b. P(A | B) = 0.3. c. P(B | A) = 0.4. d. All of the answer options are correct. ANSWER: d 40. After observing the defects within individual candies in many bags of M&Ms, investigators have determined that 11% of all candies are defective, that the probability of observing an M&M with a missing letter is 22%, and that the probability of observing a cracked M&M, given that you already know it is defective, is 70%. You can calculate the probability that you randomly select an M&M that is cracked, because: Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 13 a. the events are discrete. b. the events are independent. c. the outcomes are disjoint. d. None of the answer options is correct. ANSWER: d 41. In the Virginia instant lottery, there are 10 different $5 Scratcher games. Your favorite, “Hit the Jackpot,” is advertised to have a 1-in-4.37 chance of winning and a 1-in-664,457 chance of hitting the top prize of $200,000. If you buy five of these tickets and outcomes are independent, the probability of winning at least once in these five draws is: a. 0.353. b. 0.459. c. 0.727. d. 0.771. ANSWER: c 42. In the Virginia instant lottery, there are 10 different $5 Scratcher games. Your favorite, “Hit the Jackpot,” is advertised to have a 1-in-4.37 chance of winning, and a 1-in-664,457 chance of hitting the top prize of $200,000. If you buy five of these tickets and outcomes are independent, the probability that you lose all five times is: a. 0.229. b. 0.273. c. 0.459. d. 0.771. ANSWER: b 43. In the Virginia instant lottery, there are 10 different $5 Scratcher games. Your favorite, “Hit the Jackpot,” is advertised to have a 1-in-4.37 chance of winning, and a 1-in-664,457 chance of hitting the top prize of $200,000. If you buy five of these tickets and outcomes are independent, the probability that you win all five times is: a. 6.27%. b. 0.627%. c. 0.0627%. d. 0.0063%. ANSWER: c 44. In the Virginia instant lottery, there are 10 different $5 Scratcher games. Your favorite, “Hit the Jackpot,” is advertised to have a 1-in-4.37 chance of winning, and a 1-in-664,457 chance of hitting the top prize of $200,000. If you buy five of these tickets and outcomes are independent, the probability that you will not win the jackpot is: a. 0.9. b. 0.95. Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 13 c. 0.001. d. 0.999. ANSWER: d 45. University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A study of previous years finds that the probability that a student gets a Bachelor of Science degree is P(Science) = 0.3, and the probability that a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability that a student gets no degree is P(no) = 0.2. The probability that a student gets a Bachelor of Arts and Science degree is: a. 0.2. b. 0.3. c. 0.1. d. 0.6. ANSWER: c 46. University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A study of previous years finds that the probability that a student gets a Bachelor of Science degree is P(Science) = 0.3, and the probability that a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability that a student gets no degree is P(no) = 0.2. The probability that a student gets a Bachelor of Arts degree or a Bachelor of Science degree is: a. 0.9. b. 0.8. c. 0.3. d. 0.6. ANSWER: b 47. University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A study of previous years finds that the probability that a student gets a Bachelor of Science degree is P(Science) = 0.3, and the probability that a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability that a student gets no degree is P(no) = 0.2. The probability that a student gets only a Bachelor of Arts degree is: a. 0.5. b. 0.6. c. 0.3. d. 0.1. ANSWER: a 48. University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A study of previous years finds that the probability that a student gets a Bachelor of Science Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 13 degree is P(Science) = 0.30, and the probability that a student gets a Bachelor of Arts degree is P(Arts) = 0.60. If getting a Bachelor of Science degree is independent of getting a Bachelor of Arts degree, the probability of getting a Bachelor of Arts and Science degree is: a. 0.1. b. 0.18. c. 0.2. d. None of the answer options is correct. ANSWER: b 49. University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A study of previous years finds that the probability that a student gets a Bachelor of Science degree is P(Science) = 0.3, and the probability that a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability that a student gets no degree is P(no) = 0.2. Some probability calculations show the probability of getting a Bachelor of Arts and Science degree to be P(Arts & Science) = 0.1. Given this result, we conclude that: a. getting a Bachelor of Science is independent of getting a Bachelor of Arts. b. getting a Bachelor of Arts and getting a Bachelor of Science are mutually exclusive. c. getting a Bachelor of Arts and getting a Bachelor of Science are disjoint. d. getting a Bachelor of Arts and getting a Bachelor of Science are not independent. ANSWER: d 50. University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A study of previous years finds that the probability that a student gets a Bachelor of Science degree is P(Science) = 0.3, and the probability that a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability that a student gets no degree is P(no) = 0.2. Some probability calculations show the probability of getting a Bachelor of Arts and Science degree to be P(Arts & Science) = 0.1. The probability of getting a Bachelor of Arts and Science degree, given that a student is getting a Bachelor of Science degree, is: a. 0.333. b. 0.167. c. 0.111. d. 0.125. ANSWER: a 51. University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which require meeting graduation criteria for both degrees. A study of previous years finds that the probability that a student gets a Bachelor of Science degree is P(Science) = 0.3, and the probability that a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability that a student gets no degree is P(no) = 0.2. Some probability calculations show the probability of getting a Bachelor of Arts and Sciences to be P(Arts & Science) = 0.1. Getting a Bachelor of Arts degree and getting a Bachelor of Science degree are: a. disjoint events. Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 13 b. independent events. c. adverse events. d. dependent events. ANSWER: d 52. University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A study of previous years finds that the probability that a student gets a Bachelor of Science degree is P(Science) = 0.3, and the probability that a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The probability of getting a Bachelor of Science degree, given that a student is getting a Bachelor of Arts degree, is given by P(Science | Arts) = 0.12. The probability of a student getting both a Bachelor of Arts degree and a Bachelor of Science degree is: a. 0.12. b. 0.6. c. 0.72. d. 0.3. ANSWER: c 53. University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A study of previous years finds that the probability that a student gets a Bachelor of Science degree is P(Science) = 0.3, and the probability that a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The probability of getting a Bachelor of Science degree, given that a student is getting a Bachelor of Arts degree, is given by P(Science | Arts) = 0.3. The probability that a student will get no degree is: a. 0.1. b. 0.28. c. 0.3. d. 0.4. ANSWER: b 54. Let A be the event that a flight from New York to San Francisco arrives on time, and let B be the event that it is a clear day in San Francisco. Suppose the probability of a clear day is P(B) = 0.6 and the probability that a plane arrives on time is P(A) = 0.7. We also know that the probability that a plane arrives on time on a cloudy day is P(A | BC) = 0.5. The probability that a plane arrives on time and it is a cloudy day is: a. 0.6. b. 0.5. c. 0.2. d. 0.42. ANSWER: c 55. Let A be the event that a flight from New York to San Francisco arrives on time, and let B be the event that it is a clear day in San Francisco. Suppose the probability of a clear day is P(B) = 0.6 and the probability that a plane arrives on time is P(A) = 0.7. We also know that the probability that a plane arrives on time on a cloudy Copyright Macmillan Learning. Powered by Cognero.

Page 15

Name:

Class:

Date:

Chapter 13 day is P(A | BC) = 0.5. The events A and B are: a. dependent events. b. independent events. c. disjoint events. d. complementary events. ANSWER: a 56. Let A be the event that a flight from New York to San Francisco arrives on time, and let B be the event that it is a clear day in San Francisco. Suppose the probability of a clear day is P(B) = 0.6. We also know that the probability that a plane arrives on time on a clear day is P(A | B) = 0.9, and on a cloudy day it is P(A | BC) = 0.5. The probability that a plane arrives on time is: a. 0.6. b. 0.4. c. 0.5. d. 0.74. ANSWER: d 57. Let A be the event that a flight from New York to San Francisco arrives on time, and let B be the event that it is a clear day in San Francisco. Suppose the probability of a clear day is P(B) = 0.6. We also know that the probability that a plane arrives on time on a clear day is P(A | B) = 0.9, and on a cloudy day it is P(A | BC) = 0.5. The probability that a plane arrives late is: a. 0.26. b. 0.74. c. 0.6. d. 0.4. ANSWER: a 58. Let A be the event that a flight from New York to San Francisco arrives on time, and let B be the event that it is a clear day in San Francisco. Suppose the probability of a clear day is P(B) = 0.6. We also know that the probability that a plane arrives on time on a sunny day is P(A | B) = 0.9 and on a cloudy day it is P(A | BC) = 0.5. The probability that it is a clear day, given that the plane was on time, is: a. 0.54. b. 0.6. c. 0.73. d. 0.2. ANSWER: c 59. Let A be the event that a flight from New York to San Francisco arrives on time, and let B be the event that it is a clear day in San Francisco. Suppose the probability of a clear day is P(B) = 0.6. We also know that the probability that a plane arrives on time on a sunny day is P(A | B) = 0.9, and on a cloudy day it is P(A | BC) = 0.5. The probability that it is a cloudy day, given that the plane was late, is: a. 0.77. b. 0.5. Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 13 c. 0.54. d. 0.46. ANSWER: a

Page 17

Name:

Class:

Date:

Chapter 14 1. Suppose we toss a fair coin repeatedly. We continue to do this until a tail is observed. Let X be the number of tosses required. Then X has: a. a binomial distribution, with mean 0.5. b. a binomial distribution, with mean 2. c. a binomial distribution, with variance 0.707. d. None of the answer options is correct. ANSWER: d 2. A small class has 10 students. Of these students, 7 are first years and 3 are sophomores. You write the name of each student on a small card. The cards are shuffled thoroughly, and you choose one at random, observe the name of the student, and replace the card in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe the name, and replace the card in the set. This is done a total of five times. Let X be the number of cards observed in these five trials with a name corresponding to a first year student. The random variable X has which of the following probability distributions? a. the Normal distribution, with mean 3 and variance 1 b. the binomial distribution, with parameters n = 5 and p = 0.3 c. the binomial distribution, with parameters n = 5 and p = 0.7 d. None of the answer options is correct. ANSWER: c 3. For which of the following counts would a binomial probability model be reasonable? a. the number of phone calls received in a one-hour period b. the number of hearts in a hand of 5 cards dealt from a standard deck of 52 cards that has been thoroughly shuffled c. the number of 7s in a randomly selected set of five digits from your table of random digits d. All of the answer options are correct. ANSWER: c 4. Two students taking a multiple-choice exam with 20 problems and four choices for each question have the same incorrect answer on eight of the problems. The probability that Student B guesses the same incorrect answer as Student A on a particular question is 1/4. If the student is guessing, it is reasonable to assume guesses for different problems are independent. The instructor for the class suspects the students exchanged answers. The teacher decides to present a statistical argument to substantiate the accusation. A possible model for the number of incorrect questions that agree is: a. a binomial distribution with n = 8 and p = 0.25. b. a binomial distribution with n = 20 and p = 0.4. c. a Normal distribution with = 8 and = 0.25. d. a Normal distribution with = 20 and = 0.4. ANSWER: a 5. Two students taking a multiple-choice exam with 20 problems and four choices for each question have the same incorrect answer on seven of eight incorrectly answered problems. The probability that Student B guesses the same incorrect answer as Student A on a particular question is 1/4. If the student is guessing, the guess for Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 14 one problem is independent of the guess for the other problems. The probability of getting agreement on seven or more out of eight questions is: a. 0.9996. b. 0.0004. c. 0.25. d. None of the answer options is correct. ANSWER: b 6. Two students taking a multiple-choice exam with 20 problems and four choices for each question have the same incorrect answer on seven of eight incorrectly answered problems. The probability that Student B guesses the same incorrect answer as Student A on a particular question is 1/4. If the student is guessing, the guess for one problem is independent of the guess for the other problems. The number of guesses by Student B that agree with those of Student A has mean and variance given by: a. = 2 and = 1.5. b.

= 2 and

= 1.52.

= 4 and

= 1.5.

= 2 and

= 1.5.

ANSWER: a 7. The leading veterinarian at a local veterinary hospital decides to investigate whether there is an increase in West Nile virus infection in horses in the area. The horses diagnosed with West Nile infection are counted for the period April 15 through July 15. If X represents that count, a possible distribution for X is given by: a. a binomial distribution. b. a Normal distribution. c. a uniform distribution. d. None of the answer options is correct. ANSWER: d 8. A set of 20 cards consists of 12 red cards and 8 black cards. The cards are shuffled thoroughly, and you choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe its color, and replace it in the set. This is done a total of six times. Let X be the number of red cards observed in these six trials. The variance of X is: a. 6. b. 3.6. c. 2.4. d. 1.44. ANSWER: d 9. A deck of cards is shuffled, and you choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe its color, and replace it in the set. This process is repeated until you get a red card, with X denoting the number of draws required. The Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 14 random variable X has which of the following probability distributions? a. the Normal distribution, with mean 26 and variance 13 b. the binomial distribution, with parameters n = 52 and p = 0.5 c. the binomial distribution, with parameters n = 26 and p = 0.5 d. None of the answer options is correct. ANSWER: d 10. Which of the following statements is not true about the binomial distribution? a. A random variable having a binomial distribution is a finite count, and the minimum value is zero. b. The smallest value can be zero or an integer above zero. c. The overall experiment consists of independent and identical trials. d. The mean does not have to be an integer, even though the variable is a count. ANSWER: b 11. If X has a binomial distribution with 20 trials and a mean of 6, then the success probability p is: a. 0.3. b. 0.5. c. 0.75. d. This cannot be determined without taking a sample. ANSWER: a 12. If X is a binomial distribution with n = 20 and p = 1/4, the standard deviation of X is: a. 14.063. b. 5. c. 3.75. d. 1.936. ANSWER: d 13. Opinion polls find that 20% of American adults claim they don’t get enough sleep. Suppose you take a random sample of 200 American adults, and you count the number X in your sample who claim they do not get enough sleep. The mean of X is: a. 32. b. 40. c. 160. d. 168. ANSWER: b 14. Opinion polls find that 20% of American adults claim they don’t get enough sleep. Suppose you take a random sample of 200 American adults, and you count the number X in your sample who claim they do not get enough sleep. The standard deviation of X is: a. 5.66. b. 6.32. Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 14 c. 32. d. 40. ANSWER: a 15. A local veterinary clinic typically sees that 15% of its horses have West Nile virus. If 10 horses are admitted during July, what is the probability that a randomly selected horse among the 10 newly admitted horses has West Nile virus? a. 0.1 b. 0.5 c. 0.15 d. 0.9 ANSWER: c 16. A local veterinary clinic typically sees that 15% of its horses have West Nile virus. If 10 horses are admitted during July, what is the probability at least 1 of the 10 horses has been infected with West Nile virus? a. 0.923 b. 0.177 c. 0.348 d. 0.803 ANSWER: d 17. A local veterinary clinic typically sees that 15% of its horses have West Nile virus. If 10 horses are admitted during July, what is the probability that 2 or fewer horses among the 10 horses admitted have been infected with West Nile virus? a. 0.8202 b. 0.1937 c. 0.3874 d. 0.3487 ANSWER: a 18. Opinion polls find that 20% of American adults claim they never have time to relax. Suppose you take a random sample of 200 American adults, and you count the number X in your sample who claim they never have time to relax. Using the Normal approximation, the probability that X is at least 50 is: a. less than 0.0001. b. about 0.962. c. about 0.2. d. about 0.038. ANSWER: d 19. A local veterinary clinic typically sees that 15% of its horses have West Nile virus. Last month, 100 horses were admitted, and 20 of them had been infected with West Nile virus. The probability of seeing 20 or more horses with West Nile virus was calculated based on a Normal distribution with = 15 and = 12.75. Which of Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 14 the following statements is true? a. Using the Normal approximation to the binomial distribution is justified, because X = 20 > 10. b. Using the Normal approximation to the binomial distribution is justified, because n is large and exact calculations are too tedious. c. Using the Normal approximation to the binomial distribution is justified, because np = 15 and n(1 − p) = 85. d. All of the answer options are correct. ANSWER: d 20. A local veterinary clinic recently had 25 horses admitted from the same barn. It was determined that most cases of West Nile virus infection in the group of 25 horses were caused by infection by another horse. In this case, modeling the number of cases diagnosed with a binomial distribution is not appropriate, because: a. the success of different trials needs to be mutually exclusive and that is not the case here. b. the success of individual trials needs to be independent. c. the success of individual trials needs to be positive. d. n = 25 is a very small sample. ANSWER: b 21. At a large midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The mean of X is: a. 0.4. b. 0.8. c. 1.2. d. 1.6. ANSWER: b 22. At a large midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The standard deviation of X is: a. 0.71 b. 0.768. c. 0.8. d. 0.88. ANSWER: d 23. At a large midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The probability that X is at least 1 is: a. 0.22. b. 0.44. c. 0.56. d. 0.77. ANSWER: c Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 14 24. Suppose we select a simple random sample of size n = 100 from a large population having proportion p of successes. Let X be the number of successes in the sample. For which value of p would it be safe to assume that the sampling distribution of X is approximately Normal? a. 0.01 b. 1/9 c. 0.975 d. 0.9999 ANSWER: b 25. Suppose X is a random variable with the binomial distribution with n = 4 and p = 1/4. The probability that X is greater than or equal to 1 is: a. 0.9961. b. 0.6836. c. 0.3164. d. 0.0039. ANSWER: b 26. A college basketball player makes 70% of his free throws. At the end of a game, his team is losing by two points. He is fouled attempting a three-point shot and is awarded three free throws. Assuming each free throw is independent, what is the probability that he makes at least two of the free throws? a. 0.784 b. 0.7 c. 0.441 d. 0.216 ANSWER: a 27. A college basketball player makes 5/6 of her free throws. Assuming free throws are independent, the probability that she makes exactly three of her next four free throws is: a. . b.

ANSWER: c 28. Suppose we flip a fair coin 10 times. The probability that heads occurs exactly the same number of times as Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 14 tails on the 10 flips is: a. 0.1667. b. 0.2461. c. 0.3125. d. 0.5. ANSWER: b 29. A local politician claims that one in five automobile accidents involves a teenage driver. He is advocating increasing the age at which teenagers can drive alone. Over a two-month period there are 67 accidents in your city, and only nine of them involve a teenage driver. If the politician is correct, what is the chance that you would observe nine or fewer accidents involving a teenage driver? a. about 0.05 b. about 0.09 c. about 0.16 d. about 0.11 ANSWER: b 30. A college basketball player makes 80% of his free throws. Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that he makes at least 90 of these attempts? a. about 0.9 b. about 0.7 c. about 0.3 d. about 0.006 ANSWER: d 31. Twenty percent of American households own three or more cars. A random sample of 144 American households is selected. Let X be the number of households selected that own three or more cars. The standard deviation of X is: a. 2. b. 4.8. c. 23.04. d. 28.8. ANSWER: b 32. Twenty percent of American households own three or more cars. A random sample of 144 American households is selected. Let X be the number of households selected that own three or more cars. The mean of X is: a. 2. b. 4.8. c. 23.04. d. 28.8. Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 14 ANSWER: d 33. Twenty percent of American households own three or more cars. A random sample of 144 American households is selected. Let X be the number of households selected that own three or more cars. Using the Normal approximation, the probability that at least 34 of the households selected own at least three or more cars is: a. 0.14. b. 0.409. c. 0.591. d. 0.86. ANSWER: a 34. An article in Parenting magazine reported that 60% of Americans needed a vacation after visiting their families for the holidays. Suppose this is the true proportion of Americans who feel this way. A random sample of 100 Americans is taken. Using the Normal approximation, what is the probability that less than 50% of the people in the sample feel that they need a vacation after visiting their families for the holidays? a. 0.4 b. 0.1446 c. 0.0207 d. 0.0062 ANSWER: c 35. Which of the following statements is true about a binomial experiment? a. The number of trials can vary. b. There are only two possible outcomes: success and failure. c. The probability of success and failure can change from trial to trial. d. Each trial in the experiment may depend on previous trials. ANSWER: b 36. Zener cards are often used to test the psychic ability of individuals. In the Zener deck, there are five different patterns displayed, and each has a 1/5 probability of being drawn from a well-shuffled deck. The five patterns are: circle, plus sign, wavy lines, empty box, and star. One hundred trials were conducted, and your very impressive friend guessed right on 41 of those trials. What proportion of the cards would you expect your friend to guess correctly? a. 0% b. 20% c. 80% d. 100% ANSWER: b 37. Zener cards are often used to test the psychic ability of individuals. In the Zener deck, there are five different patterns displayed, and each has a 1/5 probability of being drawn from a well-shuffled deck. The five patterns are: circle, plus sign, wavy lines, empty box, and star. One hundred trials were conducted, and your Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 14 very impressive friend guessed right on 41 of those trials. Given this sample, can we use the Normal approximation to the binomial? a. Yes, because np 10. b. Yes, because np

10 and n(1 – p)

c. No, because n(1 – p) d. No, because np

10.

10 and n(1 – p)

10.

ANSWER: b 38. A hobby gardener planted 20 rose bushes; 8 of them produced red roses, and the other 12 produced white roses. The gardener randomly samples 5 rose bushes to be treated with a new plant food. He wants to calculate the probability that only white rose bushes get selected. Which of the following distributions can he use to calculate this probability? a. the Normal distribution b. the binomial distribution c. the Normal approximation to the binomial distribution d. None of the answer options is correct. ANSWER: d 39. A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is: a. the binomial distribution. b. the Normal distribution. c. the Normal approximation to the binomial. d. None of the answer options is correct. ANSWER: a 40. A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. Assuming rose bushes are selected independently, the number of pink rose bushes can be modeled by a binomial distribution. The probability of getting 1 pink rose bush is: a. p = 0.5. b. p = 0.8. c. p = 0.3. d. p = 0.2. ANSWER: c 41. A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 14 Assuming rose bushes are selected independently, we can use the binomial distribution for calculations. The probability of getting at least 3 pink rose bushes is: a. 0.5. b. 0.617. c. 0.348. d. 0.259. ANSWER: b 42. A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is given by the binomial distribution. The mean number of pink rose bushes is: a. 10. b. 5. c. 3. d. 7. ANSWER: c 43. A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is given by the binomial distribution. The standard deviation is: a. 1.45. b. 2.1. c. 3. d. 5. ANSWER: a 44. A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is given by the binomial distribution. Probability calculations are quicker when using the Normal approximation to the binomial distribution. Which of the following is false? a. The approximation requires np 10 and n(1 – p) 10. b. The sample size here is too small to use the Normal approximation to the binomial. c. The approximation requires np 30. d. The Normal approximation works better if the success probability p is close to p = 0.5. ANSWER: c 45. A study investigated the use of social media by first year college students. One question asked whether the Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 14 person answering ever stayed up late to chat with friends on social media and ended up sleep deprived. It was thought that at least 80% of first year college students would stay up late. If the study sampled 400 students, what is the mean number of students staying up late in random samples of n = 400 in the first year college student population? a. 80 b. 160 c. 240 d. 320 ANSWER: d 46. A study investigated the use of social media by first year college students. One question asked if the person answering ever stayed up late to chat with friends on social media and ended up sleep deprived. It was thought that at least 80% of all people first year college students would stay up late. If the study sampled 400 students, which of the following statements is true? a. The number of students in the sample who stay up late follows a binomial distribution with = 320 and variance = 64. b. The number of students in the sample who stay up late can be approximated by a Normal distribution with mean = 320 and variance = 64. c. The number of students in the sample who stay up late can be approximated by a Normal distribution with mean = 320 and variance = 8. d. All of the answer options are correct. ANSWER: d 47. Suppose a flu epidemic is sweeping a campus and many students are sick. Student health services finds that 30% of students are ill. A nurse samples a dormitory with 30 students and wants to calculate the probability that at least 10 students are sick. Which of the following statements is false? a. The binomial distribution cannot be used in this example, because the probability that 1 student is sick is not independent of another student in the dorm also being sick. b. The Normal approximation to the binomial cannot be used, because the binomial distribution is not an appropriate model. c. The Normal approximation to the binomial could not be used even if the binomial were an appropriate model, because np = 30 0.3 = 9 and this violates one criterion for using the Normal approximation. d. The binomial distribution can be used here, because our variable of interest is a finite count with minimum 0 and maximum 30. ANSWER: d 48. A group of economists surveys consumers of smartphones to see which devices consumers prefer. The question asked of shoppers is whether they are purchasing a Windows device or another type. The economists count the number of shoppers expressing preference for a Windows device. The survey samples about 50 shoppers from among several million. Which of the following criteria for using a binomial model is violated? a. There are more than two possibilities for smartphones, and the binomial allows only two categories: Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 14 success and failure. b. This is sampling without replacement, so the observations are dependent despite the large population. c. The binomial has to be a finite count between zero and some fixed upper value. d. None of the criteria listed is violated. ANSWER: d 49. An experiment consisted of 10 draws, with replacement, from an urn containing four red marbles and six green marbles. The probability that at least three and at most six red marbles are drawn is: a. 0.563. b. 0.778. c. 0.605. d. 0.82. ANSWER: b

Page 12

Name:

Class:

Date:

Chapter 15 1. A veterinary researcher takes an SRS of 60 horses with colic from a certain clinic. The average age of these horses is 12 years. The average age of all horses seen at this clinic was determined to be 10 years. The researcher concludes that horses with colic are older. The value 12 is: a. a population mean. b. a sample mean. c. a variance of the sample mean. d. None of the answer options is correct. ANSWER: b 2. A veterinary researcher takes an SRS of 60 horses with colic from a certain clinic. The average age of these horses is 12 years. The average age of all horses seen at that clinic was determined to be 10 years. The researcher concludes that horses with colic are older. The value 10 years is: a. a population mean. b. a sample mean. c. a sample distribution. d. a sample variance. ANSWER: a 3. The average age of all horses seen at a certain veterinary clinic was determined to be 10 years, with a standard deviation of 8 years. Suppose we take a simple random sample of 60 horses seen at the clinic. The probability that the mean age of horses in that sample is 12 or larger is: a. 0.0100. b. 0.1264. c. 0.0264. d. 0.9736. ANSWER: c 4. A simple random sample of 25 recent birth records was selected from a local hospital. In the sample, the average birth weight was 119.6 ounces. Suppose the standard deviation for all birth weights for this hospital is known to be 6.5 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean . For a sample of size 25, the standard deviation of the sampling distribution of the mean is: a. 6.52 ounces. b. 1.30 ounces. c. 0.38 ounces. d. 0.02 ounces. ANSWER: b 5. A simple random sample of 25 recent birth records was selected from a local hospital. In the sample, the average birth weight was 119.6 ounces. Suppose the standard deviation for all birth weights for this hospital is known to be 6.5 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean . If the sample size of birth records increases, how does the sampling distribution change? Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 15 a. The shape of the distribution will change, but it is not possible to determine what the new distribution will be without knowing the new data. b. The shape of the distribution will change, but it is dependent on the new data that are collected. c. The sampling distribution will remain Normal, regardless of the sample size, and will have the same average and standard deviation as the sampling distribution computed from the smaller sample. d. The sampling distribution will remain Normal and the mean will remain the same, regardless of the sample size, but its standard deviation will be smaller than that of the sampling distribution based on the smaller sample. ANSWER: d 6. A simple random sample of 25 recent birth records was selected from a local hospital. In the sample, the average birth weight was 119.6 ounces. Suppose the distribution for all birth weights for this hospital is known to be Normal, with mean and standard deviation 6.5 ounces. Based on the 25 recent birth records, the sampling distribution of the sample mean x can be represented by: a. N(119.6, 1.30). b. N(119.6, 6.5). c. N( , 1.30). d. N( , 6.5). ANSWER: c 7. A random sample of n = 25 airline passengers was collected. Each passenger was on a different flight, and researchers recorded the time it took the passenger to board the flight. The average boarding time for this sample was 42 minutes. Previous studies had determined boarding times to be Normally distributed, with = 38 minutes and = 36 minutes. The sampling distribution of , the sample average in samples of size n = 25, is: a. N(42, 36). b. N(38, 36). c. N(38, 7.2). d. N(38, 1.2). ANSWER: c 8. A study was conducted to reassess boarding times of flights. The consulting firm given the task of conducting the study decided that taking a simple random sample of flights was too time-consuming. Instead, the firm chose to take a convenience sample of flights during winter break, when passengers are more cheerful and less likely to be annoyed by the presence of someone with a stopwatch. The company found that in their sample, boarding took an average of 50 minutes. The staff scheduling the flights were somewhat surprised, because a previous study (a simple random sample) had shown boarding to take an average of 38 minutes. A probable explanation is that: a. The current study is biased, because people traveling during winter break might tend to take longer to board. b. The current study is biased, because a convenience sample was taken instead of a simple random sample. c. The current study is not representative of the distribution of all flights, because the investigators chose not to take an SRS. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 15 d. All of the answer options are correct. ANSWER: d 9. The law of large numbers states that as the number of observations drawn at random from a population with finite mean increases, the mean of the observed values: a. gets larger and larger. b. gets smaller and smaller. c. tends to get closer and closer to the population mean . d. fluctuates steadily between 1 standard deviation above and 1 standard deviation below the mean. ANSWER: c 10. The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age of these residents is to be computed. We know the random variable

has approximately a Normal distribution because:

a. of the central limit theorem. b. of the law of large numbers. c. of the 68−95−99.7 rule. d. the population from which we’re sampling has a Normal distribution. ANSWER: a 11. The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age of these residents is to be computed. The probability that the average age, , of the 100 residents selected is less than 68.5 years is: a. 0.805. b. 0.568. c. 0.195. d. 0.043. ANSWER: c 12. On a production line, batches of 20 metal discs are randomly selected each hour for inspection. The diameter of each disc is measured, and the average diameter of the 20 discs is recorded. The distribution of diameters is uniform. Once a week, all of the hourly values for average diameter are gathered, and the distribution is plotted. According to the central limit theorem, what kind of distribution will this be? a. It will be a uniform distribution. b. It will be a Normal distribution. c. It could be either option (a) or option (b), depending on what happened on the production line that week. d. It would be neither option (a) nor option (b) but a different distribution. ANSWER: b Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 15 13. Suppose you’re in a class of 35 students. The instructor takes a simple random sample of 7 students and observes their heights. Imagine all of the different samples possible. Let X denote the tallest height in the sample. The distribution of all values taken by X in all possible samples of 7 students selected from the 35 students in your class is called: a. the probability that X is obtained. b. the sampling distribution of X. c. the standard deviation of values. d. the parameter. ANSWER: b 14. Suppose you interview 10 randomly selected workers and ask how many miles they commute to work. You’ll compute the sample mean commute distance. Now imagine repeating the survey many, many times, each time recording a different sample mean commute distance. In the long run, a histogram of these sample means represents: a. the bias, if any, that is present in the sampling method. b. the true population average commute distance. c. a simple random sample. d. the sampling distribution of the sample mean. ANSWER: d 15. Suppose that two very large companies (A and B) each select random samples of their employees. Company A has 5,000 employees and Company B has 15,000 employees. In both surveys, the company will record the number of sick days taken by each sampled employee. Suppose the population standard deviation of the number of sick days is the same for both companies. If each company randomly selects 50 employees for the survey, which of the following is true about the sampling distributions of the sample means (the mean number of sick days)? a. The sampling distributions of the sample means will have about the same standard deviation. The standard deviation for a sampling distribution of a sample mean depends only on the sample size, not on the population (company) size. b. Since Company A is surveying a higher percent of its employees, the standard deviation of the sampling distribution for its sample mean will be smaller than that for Company B (the larger company). Larger companies should take larger samples. c. Since Company B is a larger company, the standard deviation for its sampling distribution of the sample mean will be smaller. The larger a population, the smaller the standard deviation of a sample mean’s sampling distribution. d. None of the answer options is correct. ANSWER: a 16. Suppose that two very large companies (A and B) each select random samples of their employees. Company A has 5,000 employees and Company B has 15,000 employees. In both surveys, the company will record the number of sick days taken by each sampled employee. Suppose the population standard deviation of the number of sick days is the same for both companies. If each firm randomly selects 3% of its employees, which of the following is true about the sampling distributions of the sample means? Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 15 a. The standard deviation of the sampling distribution of the sample mean will be smaller for the larger company (Company B) because a larger sample is being selected. b. The sampling distributions of the sample means will have about the same standard deviation because, in both cases, 3% of the employees are selected. c. The smaller company (Company A) will have a sampling distribution with a smaller standard deviation. d. None of the answer options is correct. ANSWER: a 17. A simple random sample of 1,000 American adults found that the average number of hours spent watching television during a typical week was 13.8. A simple random sample of 500 Canadians yielded an average of 12.5 hours per week of television viewing. Assume that for the American and Canadian distributions for weekly television, viewing times have the same standard deviations. The sampling variability associated with these sample means is: a. smaller for the sample of Canadians, because the population of Canada is less than half that of the United States. b. larger for the sample of Canadians, because the sample size is smaller. c. smaller for the sample of Canadians, because their population is smaller. d. larger for the sample of Canadians, because Canadian citizens are more widely dispersed throughout their country than American citizens are in the United States. Hence, Canadians have more variable views. ANSWER: b 18. The incomes in a certain large population of college teachers have a Normal distribution, with mean $65,000 and standard deviation $10,000. Sixteen teachers are selected at random from this population to serve on a committee. What is the probability that their average salary is more than $67,500? a. 0.0228 b. 0.1587 c. 0.8413 d. essentially 0 ANSWER: b 19. In a large population of college-educated adults, the mean IQ is 112, with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign. The distribution of the sample mean IQ is: a. approximately Normal, with mean 112 and standard deviation 25. b. approximately Normal, with mean 112 and standard deviation 1.443. c. approximately Normal, with mean 112 and standard deviation 0.083. d. approximately Normal, with mean equal to the observed value of the sample mean and standard deviation 25. ANSWER: b 20. In a large population of college-educated adults, the mean IQ is 112 with standard deviation 25. Suppose Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 15 300 adults from this population are randomly selected for a market research campaign. The probability that the sample mean IQ is greater than 115 is: a. 0.019. b. 0.452. c. 0.528. d. 0.981. ANSWER: a 21. The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal, with mean 8.1 ounces and standard deviation 0.2 ounce. A sample of 10 of these cheese wedges is selected. The distribution of the sample mean of the weights of the cheese wedges is: a. approximately Normal, with mean 8.1 and standard deviation 0.020. b. approximately Normal, with mean 8.1 and standard deviation 0.2. c. approximately Normal, with mean 8.1 and standard deviation 0.063. d. impossible to determine, because the sample size is too small. ANSWER: c 22. The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal, with mean 8.1 ounces and standard deviation 0.2 ounce. A sample of 10 of these cheese wedges is selected. What is the standard deviation of the sampling distribution of the mean? a. 0.075 ounce b. 0.315 ounce c. 0.0633 ounce d. 0.963 ounce ANSWER: c 23. The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal, with mean 8.1 ounces and standard deviation 0.2 ounce. A sample of 10 of these cheese wedges is selected. The company then decides, instead, to sample batches of 20 cheese wedges, with the sampling to be repeated every time workers start a new shift at the dairy. How will the distribution of the sample means of the weights of the cheese wedges change from the previous batches, which contained only 10 samples? a. The shape of the distribution may change completely based on the new data. b. The distribution will still be Normal, but it will be more peaked around the sample mean, and the standard deviation will be smaller. c. The distribution will still be Normal, but it will be more peaked around the sample mean, and the standard deviation will be larger. d. It is not possible to tell from the information provided. ANSWER: b 24. The sampling distribution of a statistic is: a. the probability that the statistic is obtained in repeated random samples. b. the mechanism that determines whether randomization was effective. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 15 c. the distribution of values taken by a statistic in all possible samples of the same size from the same population. d. the extent to which the sample results differ systematically from the truth. ANSWER: c 25. A statistic is said to be unbiased if: a. the person computing it doesn’t favor any particular outcome. b. the mean of its sampling distribution is equal to the true value of the parameter being estimated. c. the person who calculated the statistic and the subjects whose responses make up the statistic were truthful. d. it is used only for honest purposes. ANSWER: b 26. The variability of a statistic is described by: a. the spread of its sampling distribution. b. the amount of bias present. c. the vagueness in the wording of the question used to collect the sample data. d. the stability of the population it describes. ANSWER: a 27. Researchers doing a study comparing time spent on social media and time spent studying randomly sampled 200 students at a major university. They found that the students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day studying. The value 2.3 hours represents: a. the average number of hours students at the university spent on social media. b. the average number of hours students at a typical university spend on social media. c. the average number of hours students in the sample spent on social media. d. None of the answer options is correct. ANSWER: c 28. Researchers doing a study comparing time spent on social media and time spent studying randomly sampled 200 students at a major university. They found that the students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day studying. Which of the following statements is false? a. The value 1.8 represents a parameter. b. The value 1.8 represents a statistic. c. The value 1.8 represents the average number of hours the students in the sample spent studying. d. The students in the sample spent an average of 2.3 hours per day on social media. ANSWER: a 29. Researchers doing a study comparing time spent on social media and time spent studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day studying. If all the students at the university in fact spent 2.2 hours per day studying, with a standard deviation of 2 hours, then the sampling distribution of the sample Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 15 average hours spent studying has mean: a. 2.3. b. 1.8. c. 2.0. d. 2.2. ANSWER: d 30. Researchers doing a study comparing time spent on social media and time spent studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day studying. If all the students at the university in fact spent 2.2 hours per day studying, with a standard deviation of 2 hours, the sampling distribution of the time spent studying has the approximate distribution: a. N(1.8, 2). b. N(2.2, 2). c. N(1.8, 0.141). d. N(2.2, 0.141). ANSWER: d 31. Researchers doing a study comparing time spent on social media and time spent studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day studying. If all the students at the university in fact spent 2.2 hours per day studying, with a standard deviation of 2 hours, the shape of the sampling distribution of the sample average time spent studying is: a. Normal, centered at 2.2. b. Normal, centered at 2.2 only if the studying times are Normally distributed. c. Normal, centered at 1.8. d. Normal, centered at 1.8 only if all samples have a sample average of 1.8 hours studying. ANSWER: a 32. Researchers doing a study comparing time spent on social media and time spent studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day studying. If all the students at the university in fact spent 2.2 hours per day studying, with a standard deviation of 2 hours, which of the following statements is true? a. The sample average of 1.8 hours studying is biased, because it is not equal to 2.2. b. The sample average is unbiased, because a proper random sample was taken from the population. c. The sample average is in error, because students clearly study more. d. There is not enough information to choose an answer option. ANSWER: b 33. Researchers doing a study comparing time spent on social media and time spent studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day studying. If all the students at the university in fact spent 2.2 hours per day studying, with a standard deviation of 2 hours, the probability of getting a sample average of Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 15 1.8 or less is: a. 0.0023. b. 0.4207. c. 0.5893. d. 0.9977. ANSWER: a 34. Researchers doing a study comparing time spent on social media and time spent studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day studying. If all the students at the university in fact spent 2.2 hours per day studying, with a standard deviation of 2 hours, and we find that observing a sample mean of 1.8 hours studying has an extremely low probability, we say that the observed time is: a. statistically wrong. b. statistically unlikely. c. statistically significant. d. statistically rare. ANSWER: c 35. Which of the following does not determine the sampling distribution? a. the population size b. the sample size c. the population mean d. the population variance ANSWER: a 36. Which of the following statements is false? a. By the central limit theorem, the sample mean from a population with finite mean and variance will be approximately Normally distributed for sufficiently large samples. b. By the central limit theorem, a sample mean must be based on samples from a population that is Normally distributed. c. By the law of large numbers, the sample mean will be close to the true mean in most samples for large sample sizes. d. If the true population mean is given by , then the mean of the sampling distribution of the sample average is also in proper random samples from the population. ANSWER: b

Page 9

Name:

Class:

Date:

Chapter 16 1. The critical value from the standard Normal distribution is with area under the standard Normal curve to the right of equal to 0.05 is: a. 1.645. b. 1.96. c. 2.326. d. 2.576. ANSWER: a 2. I collected a random sample of size n from a population and computed a 95% confidence interval for the population mean using a Normal distribution. I am worried that my margin of error is too large. What could I do to produce a new confidence interval with a smaller smaller margin of error based on the same data? a. I could use a larger confidence level. b. I could use a smaller confidence level. c. I could use the same confidence level but compute the interval n times; approximately 5% of these intervals will be larger. d. Nothing can guarantee absolutely that I will get a smaller interval; I can only say the chance of obtaining a smaller interval is 0.05. ANSWER: b 3. In general, confidence intervals have the form: a. estimate + z* standard error. b. estimate standard error. c. estimate z* margin of error. d. estimate

margin of error.

ANSWER: d 4. To calculate a 99% confidence interval using a Normal distribution, the value z* in the margin of error should equal: a. 1.645. b. 1.96. c. 2.33. d. 2.576. ANSWER: d 5. Suppose that for a certain population, = 5. We take an SRS of n = 100 from this population, and we want to make a confidence interval for the mean. The confidence level is chosen to be 98%. The margin of error for estimating a mean is given by: a. 1.163. b. 0.1163. c. 2.326. d. 0.2326. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 16 ANSWER: a 6. Suppose that for a certain population, = 5. We take an SRS of n = 100 from this population, and we want to make a confidence interval for the mean. The confidence level is chosen to be 98%. The margin of error for estimating a mean is given by 1.163. To reduce the margin of error to 0.3877, we should: a. increase the sample size to 300. b. increase the sample size to 400. c. increase the sample size to 900. d. decrease the sample size by one-third to 34 (rounding up). ANSWER: c 7. An SRS of size n was taken to estimate mean body mass index (BMI) for girls between 13 and 19 years of age. The 95% confidence interval obtained using a Normal distribution had the lower limit 19.5 and upper limit 26.3. Which statement is not necessarily true? a. Approximately 95% of all girls between 13 and 19 years of age have BMI between 19.5 and 26.3. b. The margin of error of the confidence interval is 3.4. c. The critical value for the confidence interval is z* = 1.96. d. Approximately 95% of all SRS of size n contain the mean BMI for all girls between 13 and 19 years of age. ANSWER: a 8. If the confidence level is increased from 90% to 99% for a simple random sample of size n, the width of the confidence interval for the mean will: a. decrease. b. stay the same. c. increase. d. The answer cannot be determined from the information given. ANSWER: c 9. A 95% confidence interval for the mean number of hours freshmen spent on social media per day was calculated to be (2.5 hours, 3.1 hours). The confidence interval was based on an SRS of size n = 50. The standard deviation is given by: a. 0.3. b. 1.96. c. 0.2772. d. 1.0823. ANSWER: d 10. Researchers partnering with local animal shelters calculate a 99% confidence interval for the average age of dogs that are adopted from county shelters. The interval is 1.3 to 3.4 years. Based on this information, we conclude that: a. 99% of all dogs adopted from county shelters are between 1.3 and 4.4 years old. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 16 b. we can be 100% sure that the average age of dogs adopted at county shelters is between 1.3 and 3.4 years. c. we are 99% confident the true mean age of dogs adopted at county shelters is between 1.3 and 3.4 years old. d. All of the answer options are correct. ANSWER: c 11. Researchers partnering with local animal shelters calculate a 99% confidence interval for the average age of dogs that are adopted from county shelters. The interval is 1.3 to 3.4 years. What does this confidence interval tell us? a. The margin of error is 1.05 years. b. The critical value z* = 2.576. c. The confidence coefficient is 99%. d. All of the answer options are correct. ANSWER: d 12. You measure the lifetime of a random sample of 64 tires of a certain brand, for which the standard deviation of the lifetime of all tires of the brand is known. In a follow-up study of the same brand, more tires were available for testing, so you were able to measure the lifetimes of a random sample of 100 tires rather than 64. Assume that the population standard deviation did not change from the time of the original study to the time of the follow-up study and that you used the same confidence level for both intervals. Which statement is true? a. The margin of error for the follow‑up confidence interval would increase. b. The margin of error for the follow-up confidence interval would decrease. c. The margin of error for the follow-up confidence interval would stay the same because the level of confidence has not changed. d. It is impossible to say how the margin of error would change. It all depends on the value of the sample mean. ANSWER: b 13. Suppose that the population of the scores of all high school seniors who took the SAT Math test this year follows a Normal distribution, with mean μ and standard deviation = 100. You read a report that says, “On the basis of a simple random sample of 100 high school seniors who took the SAT Math test this year, a confidence interval for is 512.00 25.76.” The confidence level for this interval is: a. 90%. b. 95% c. 99%. d. > 99.9%. ANSWER: c 14. A 99% confidence interval for the mean of a population is computed from a random sample and found to be 6 3. We may conclude that: a. there is a 99% probability that is between 3 and 9. Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 16 b. there is a 99% probability that the true mean is 6, and there is a 99% chance that the true margin of error is 3. c. if we took many additional random samples and computed a 99% confidence interval for from each, approximately 99% of these intervals would contain . d. All of the answer options are correct. ANSWER: c 15. A medical researcher treats 400 subjects with high cholesterol using a new medicine. After two months of taking the drug, the average decrease in cholesterol level is = 90. Previous research suggests that the decrease in cholesterol from using this medicine follows a Normal distribution, with unknown mean and standard deviation = 30. A 95% confidence interval for is: a. 90 1.96. b. 90

2.94.

c. 90

3.92.

d. 90

58.8.

ANSWER: b 16. A medical researcher treats 400 subjects with high cholesterol with a new medicine. After two months of taking the medicine, the average decrease in cholesterol level is = 90. Previous research suggests that the decrease in cholesterol from using this medicine follows a Normal distribution, with unknown mean and standard deviation = 30. Which of the following would produce a confidence interval with a smaller margin of error than the 95% confidence interval 90 2.94? a. Giving the medicine to only 100 subjects rather than to 400, since 100 people are easier to manage and control. b. Giving the medicine to 500 subjects rather than to 400. c. Computing a 99% confidence interval rather than a 95% confidence interval; the increase in confidence indicates that we have a better interval. d. None of the answer options is correct. ANSWER: b 17. You measure the lifetime of a random sample of 64 tires of a certain brand. The sample mean is

= 50

months. Suppose that the lifetimes for tires of this brand follow a Normal distribution, with unknown mean and standard deviation = 5 months. A 99% confidence interval for is: a. 49.8 to 50.2. b. 48.78 to 51.22. c. 48.39 to 51.61. d. 40.2 to 59.8. ANSWER: c 18. You recently measured the lifetime of a random sample (Sample 1) of 64 tires of a certain brand. In a Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 16 follow-up study, more tires were available for testing, so you were able to measure the lifetimes of a random sample (Sample 2) of 100 tires rather than 64. Which of the following statements is true? a. The margin of error for your 99% confidence interval would increase from Sample 1 to Sample 2 (smaller for Sample 1 than for Sample 2). b. The margin of error for your 99% confidence interval would decrease from Sample 1 to Sample 2 (smaller for Sample 2 than for Sample 1). c. The margin of error for your 99% confidence interval would stay the same, since the level of confidence has not changed. d. The value of σ would decrease. ANSWER: b 19. To assess the accuracy of a laboratory scale, a standard weight known to weigh 1 gram is repeatedly weighed a total of n times. We take the mean of the n weights. Suppose the scale readings are Normally distributed, with unknown mean m and standard deviation = 0.01 gram. How large should n be so that a 95% confidence interval for m has a margin of error of 0.0001? a. 100 b. 196 c. 10,000 d. 38,416 ANSWER: d 20. A company produces precision 1000-millimeter rulers. The actual distribution of the lengths of the rulers produced by this company is Normal, with mean and standard deviation = 0.02 millimeter. Suppose I select a simple random sample of four of the rulers produced by the company and I measure their lengths in millimeters. The sample yields = 1000. A 90% confidence interval for is: a. 1000

0.0082.

b. 1000

0.0115.

c. 1000

0.0165.

d. 1000

0.0196.

ANSWER: c 21. The time (in days) until maturity of a certain variety of tomato plant is Normally distributed, with mean and standard deviation = 2.4. I select a simple random sample of four plants of this variety and measure the time until maturity. The sample yields = 65. A 95% confidence interval for (in days) is: a. 65

1.97.

b. 65

2.35.

c. 65

3.95.

d. 65

4.7.

Page 5

Name:

Class:

Date:

Chapter 16 ANSWER: b 22. The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed, with mean and standard deviation = 10. A simple random sample of 25 children from this population is taken, and each child is given the WISC. The mean of the 25 scores is = 104.32. Based on these data, a 95% confidence interval for is: a. 104.32 0.78. b. 104.32

3.29.

c. 104.32

3.92.

d. 104.32

19.6.

ANSWER: c 23. The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed, with mean and standard deviation = 10. A simple random sample of 25 children from this population is taken, and each child is given the WISC. The mean of the 25 scores is = 104.32. Suppose the histogram below represents the 25 WISC scores.

Based on this histogram, we would conclude that: a. the 95% confidence interval 104.32 3.92 is very reliable. b. the 95% confidence interval 104.32

3.92 is not very reliable.

c. the 95% confidence interval 104.32

3.92 is actually a 99% confidence interval.

Page 6

Name:

Class:

Date:

Chapter 16 d. the 95% confidence interval 104.32

3.92 is actually a 90% confidence interval.

ANSWER: b 24. Suppose we want a 90% confidence interval for the average amount of time (in minutes) spent per week on homework by the students in a large introductory statistics course at a major university. The interval is to have a margin of error of 3 minutes. The amount of time spent has a Normal distribution, with a standard deviation = 40 minutes. The number of observations required is closest to: a. 22. b. 482. c. 683. d. 1180. ANSWER: b 25. Twenty-five seniors from a large metropolitan school district volunteer to allow their SAT Math scores to be used in a study. These 25 seniors had a mean SAT Math score of = 450. Suppose we know that the standard deviation of the population of SAT Math scores for seniors in the district is = 100. Assuming that the population of SAT Math scores for seniors in the district is approximately Normally distributed, a 90% confidence interval for the mean SAT Math score for the population of seniors computed from these data is: a. 450 32.9. b. 450

39.2.

c. 450

164.5.

d. not “trustworthy” based on these data, so we should not compute one. ANSWER: d 26. The records of the 100 postal employees at a certain postal station in a large city show that the average time these employees have worked for the postal service is = 9 years. Assume we know that the time the population of U.S. postal service employees have spent with the postal service is approximately Normal, with standard deviation = 5 years, but we do not know how the 100 records were obtained. A 95% confidence interval for the mean time that the population of U.S. postal service employees have spent with the postal service is: a. 9 0.82. b. 9

0.98.

c. 9

9.8.

d. not “trustworthy” based on these data, so we should not compute one. ANSWER: d 27. Two researchers plan to construct a 99% confidence interval for the mean of a Normal population with (known) standard deviation . Researcher A will use a random sample of 50 individuals. Researcher B will use a random sample of 800 individuals. The margin of error for Researcher A’s estimate is _______ times that for Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 16 Researcher B’s estimate. a. 2. b. 4. c. 16. d. None of the answer options is correct. ANSWER: b 28. Suppose a 95% confidence interval is given by (15, 20). The margin of error is: a. 5. b. 2.5. c. 1.96. d. 1.65. ANSWER: b 29. A 95% confidence is given by (15, 20). The interval is based on a sample of size n = 25. If we want to reduce the margin of error by half, we need to: a. reduce the sample size by half. b. double the sample size. c. quadruple the sample size. d. reduce the sample size to one-quarter of the current sample size. ANSWER: c 30. A sample of n = 25 diners at a local restaurant had a mean lunch bill of $16. Assume that we know that the distribution of all lunch bills at the diner is Normal with a standard deviation of = $5. The margin of error for a 98% confidence interval is given by: a. 2.575. b. 2.33. c. 1.96. d. 1.65. ANSWER: b 31. A sample of n = 25 diners at a local restaurant had a mean lunch bill of $16. We knew that the distribution of all lunch bills at the diner is Normal with a standard deviation of = $5. We obtained a confidence interval to estimate the mean lunch bill for all diners at the restaurant. Which action will not reduce the margin of error? a. increasing the sample size b. increasing the confidence level c. sampling from a different random sample of n = 25 diners ANSWER: c 32. A sample of n = 25 diners at a local restaurant had a mean lunch bill of $16. We knew that the distribution of all lunch bills at the diner is Normal with a standard deviation of = $5, and computed a confidence interval for the mean lunch bill for all diners at this restaurant. Which is not required for the confidence interval to be Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 16 trustworthy? a. The population standard deviation

is known.

b. The sample size is at least 30. c. The sample was random. ANSWER: b 33. A sample of n = 25 diners at a local restaurant had a mean lunch bill of $16 with a standard deviation of $4. We obtain a 95% confidence interval as (14.43, 17.57). Which of the following statements correctly interprets this interval? a. 95% of all lunches will cost between $14.43 and $17.57. b. 95% of the time, the average price for a lunch will be between $14.43 and $17.57. c. 95% of all samples of size n = 25 will have an average lunch price between $14.43 and $17.57. d. None of the answer options is correct. ANSWER: d

34. What is the correct formula for a confidence interval for a mean using a Normal distribution? a. b. c. d. ANSWER: a 35. Suppose we wish to compare lunch prices at two restaurants. We decide to randomly sample n = 50 lunches from each restaurant, obtain the prices, compute the sample mean, and proceed to calculate confidence intervals for the mean lunch price at each restaurant using a Normal distribution. Which of the following statements is true? a. If the populations of all lunch prices at both restaurants have the same variance, the confidence intervals will be the same. b. If the populations of all lunch prices at both restaurants have the same variance, the margins of error will be the same. c. If the populations of all lunches at one restaurant have a standard deviation twice that of the populations of all lunches at the other restaurant, then we need to sample twice as many lunches to get the same margin of error. d. All of the answer options are correct. ANSWER: b

Page 9

Name:

Class:

Date:

Chapter 17 1. Which of the following statements is true for tests of significance? a. If p is less than the significance level , then we have evidence that suggests rejecting the null hypothesis. b. If p is greater than the significance level , then we have evidence that supports rejecting the null hypothesis. c. If the P-value is less than the significance level , then we have evidence that supports rejecting the null hypothesis. d. If the P-value is greater than the significance level , then we have evidence that supports rejecting the null hypothesis. ANSWER: c 2. In a hypothesis test, a small P-value provides evidence: a. against the null hypothesis in favor of the alternative hypothesis. b. against the alternative hypothesis in favor of the null hypothesis. c. against the null hypothesis and the alternative hypothesis. d. for the null hypothesis and the alternative hypothesis. ANSWER: a 3. If a hypothesis test is significant at level = 0.05, what is true of the P-value? a. P-value > 0.05 b. P-value > 0.01 c. P-value 0.05 d. P-value

0.01

ANSWER: c 4. A P-value is always computed assuming that: a. the alternative hypothesis is true. b. the alternative hypothesis may be true. c. the null hypothesis may be true. d. the null hypothesis is true. ANSWER: d 5. The P-value measures the strength of evidence: a. against the null hypothesis. b. against the alternative hypothesis. c. sometimes against the null hypothesis and sometimes against the alternative hypothesis. d. The interpretation depends on whether we reject the null hypothesis. ANSWER: a 6. Which of the following is an acceptable statement of a null and an alternative hypothesis for testing a hypothesis about a mean? Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 17 a.

d. All of the answer options are correct. ANSWER: d 7. The following is an acceptable statement of a null and an alternative hypothesis about a mean: a. b. c. d. None of the answer options is correct. ANSWER: d 8. A statistician wishes to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course. The statistician decides to randomly select 20 students in the class and have them take the exam early. The average score for these students on the exam is 78%. The hypothesis the statistician wants to test is: a. . b.

ANSWER: c 9. A statistician wishes to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course. The statistician decides to randomly select 20 students in the class and have them take the exam early. The average score for these students on the exam is 78%. Suppose the standard deviation in the population is known to be = 15%. The P-value for the hypothesis is: a. 0.814. b. 0.186. c. 0.371. d. The answer cannot be determined with the information provided. ANSWER: b 10. A statistician wishes to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course. The statistician decides to randomly select 20 students in the class and have them take the exam early. The average score for these students on the exam is 72%. Suppose the standard deviation in the population is known to be = 15%. The statistician calculates the test statistic to be −0.8944. If the statistician chose to do a two-sided alternative, the P-value would be calculated by: a. finding the area to the left of −0.8944 and doubling it. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 17 b. finding the area to the left of −0.8944. c. finding the area to the right of −0.8944 and doubling it. d. finding the area to the right of the absolute value of −0.8944 and dividing it by 2. ANSWER: a 11. In formulating hypotheses for a statistical test of significance, the null hypothesis is often: a. a statement of “no effect” or “no difference.” b. the probability of observing the data you actually obtained. c. a statement that the data are all 0. d. 0.05. ANSWER: a 12. Suppose we are testing the null hypothesis

and the alternative

, for a Normal

population with = 5. A random sample of 25 observations is drawn from the population, and we find that the sample mean of these observations is = 17.6. The P-value is closest to: a. 0.0668. b. 0.0082. c. 0.0164. d. 0.1336. ANSWER: c 13. The mean area of the several thousand apartments in a new development by a certain builder is advertised to be 1100 square feet. A tenant group thinks this is inaccurate and suspects that the actual average area is less than 1100 square feet. To investigate this suspicion, the group hires an engineer to measure a sample of apartments. The appropriate null and alternative hypotheses, and , for are: a.

d. The hypotheses cannot be specified without knowing the size of the sample used by the engineer. ANSWER: b 14. Is the mean age at which American children first read now under 4 years? If the population of all American children has a mean age of years until they begin to read, which of the following null and alternative hypotheses would be tested to answer this question? a. b. c. d.

, assuming our sample size is n

ANSWER: b Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 17 15. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 110 and standard deviation = 20. You suspect that incoming first years have a mean µ that is different from 110, because they are often excited yet anxious about entering college. To verify ( or debunk) your suspicion, you test the hypotheses . You give the SSHA to 50 students who are incoming first years and find their mean score. The P-value of the test of the null hypothesis is: a. the probability (assuming the null hypothesis is true) that the test statistic will take a value at least as extreme as that actually observed. b. the probability (assuming the null hypothesis is false) that the test statistic will take a value at least as extreme as that actually observed. c. the probability that the null hypothesis is true. d. the probability that the null hypothesis is false. ANSWER: a 16. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 110 and standard deviation = 20. You suspect that incoming first years have a mean µ that is different from 110, because they are often excited yet anxious about entering college. To verify (or debunk) your suspicion, you test the hypotheses . You give the SSHA to 50 students who are incoming first years and find their mean score. If you observe a sample mean of

= 115.35, what is the

corresponding P-value? a. 0.058 b. 0.029 c. 0.787 d. None of the answer options is correct. ANSWER: a 17. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 110 and standard deviation = 20. You suspect that incoming first years have a mean that is different from 110, because they are often excited yet anxious about entering college. To verify (or debunk) your suspicion, you test the hypotheses . You give the SSHA to 50 students who are incoming first years and find their mean score. Suppose you observed the same sample mean

115.35, but it was based on a sample of 100 students. What would the corresponding P-value be? a. 0.0037 b. 0.0074 c. 0.9926 d. None of the answer options is correct. ANSWER: b Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 17 18. In a statistical test of hypotheses, we say the data are statistically significant at level if: a. = 0.05. b.

is small.

c. the P-value is less than . d. the P-value is larger than . ANSWER: c 19. In a test of statistical hypotheses, the P-value tells us: a. whether the null hypothesis is true. b. whether the alternative hypothesis is true. c. the largest level of significance at which the null hypothesis can be rejected. d. the smallest level of significance at which the null hypothesis can be rejected. ANSWER: d 20. A university administrator obtains a random sample of the academic records of athletes at a certain university. The administrator is interested in determining whether the average GPA (grade point average) of athletes at the school is higher than the state average GPA for athletes. Suppose the average GPA of athletes in the state is 3.0. The administrator reports that there is no evidence that the average GPA of athletes from the school was higher than the mean GPA in the state (P = 0.287). This means that: a. The average GPAs for athletes in this school and in the state are identical, except for 28.7% of the athletes. b. The average GPA for the school is at most 0.287 different from the average GPA for the state. c. The chance of obtaining an average school GPA as large as that observed in the sample, if the average school GPA was the same as the state average GPA, is 0.287. d. The chance that a randomly chosen student would have a GPA significantly different from 3.0 is 0.287. ANSWER: c 21. The level of calcium in the blood of healthy young adults follows a Normal distribution, with mean = 10 milligrams per deciliter and standard deviation = 0.4. A clinic measures the blood calcium of 25 healthy pregnant young women at their first visit for prenatal care. The mean of these 25 measurements is = 9.6. Is this evidence that the mean calcium level in the population from which these women come is less than 10? To answer this, test the hypotheses . The P-value of your test is: a. less than 0.0002. b. 0.3085. c. 0.617. d. greater than 0.99. ANSWER: a 22. Suppose the time that it takes a certain large bank to approve a home loan is Normally distributed, with mean (in days) and standard deviation = 1. The bank advertises that it approves loans in 5 days, on average, Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 17 but measurements on a random sample of 500 loan applications to this bank gave a mean approval time of

5.3 days. Is this evidence that the mean time to approval is actually longer than advertised? To answer this, test the hypotheses, : µ> 5, at significance level = 0.01. You conclude that: a.

should be rejected.

should not be rejected.

should be rejected.

d. there is a 5% chance that the null hypothesis is true. ANSWER: a 23. The time needed for college students to complete a certain paper-and-pencil maze follows a Normal distribution, with a mean of 80 seconds and a standard deviation of 16 seconds. You wish to find out whether the mean time is changed by meditation, so you have a group of 8 college students meditate for 30 minutes and then complete the maze. It takes them an average of = 74 seconds to complete the maze. Use this information to test the hypotheses a.

should be rejected.

should not be rejected.

should be accepted.

at significance level = 0.02. You conclude that:

d. This is a borderline case, and no decision should be made. ANSWER: b 24. You conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level = 0.05. You may conclude that: a. the test would also be significant at level = 0.10. b. the test would also be significant at level = 0.01. c. both option (a) and option (b) are true. d. neither option (a) nor option (b) is true. ANSWER: a 25. The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed, with mean and standard deviation = 10. I wish to test whether the mean for this population differs from the national average of 100, so I use the hypotheses and , based on an SRS of size 25 from the population. I calculate a 95% confidence interval for µ and find it to be 100.76 to 106.24. Which of the following statements is true? a. I would reject at level 0.05. b. I would reject

at level 0.05.

c. The P-value is 0.05. d. A mistake has almost certainly been made—the confidence interval must contain = 100 at least 95% of the time. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 17 ANSWER: a 26. The time needed for college students to complete a certain paper-and-pencil maze follows a Normal distribution, with a mean of 70 seconds and a standard deviation of 15 seconds. You wish to find out whether the mean time is changed by meditation, so you have a group of 9 college students meditate for 30 minutes and then complete the maze. You compute the average of their times to complete the maze and use this information to test the hypotheses mean completion time of

at significance level = 0.05. If you observe a sample

= 78.55, the P-value obtained is:

a. less than 0.01. b. between 0.01 and 0.025. c. between 0.025 and 0.05. d. between 0.05 and 0.1. ANSWER: d 27. A marketing consultant is hired by a major restaurant chain that wants to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. To address the CEO’s conjecture, the marketing manager should: a. calculate a margin of error. b. carry out a test of significance. c. ask more customers and refute the CEO’s claim if the average is not above $13.50. d. refuse the assignment. ANSWER: b 28. A marketing consultant is hired by a major restaurant chain that wants to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. To address the CEO’s conjecture, the marketing manager decides to carry out a test of significance. The null hypothesis should be: a. . b.

ANSWER: a 29. A marketing consultant is hired by a major restaurant chain that wants to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 17 per customer to be

= $14.50. Based on previous surveys, the restaurant informs the marketing manager that

the standard deviation is = $3.50. To address the CEO’s conjecture, the marketing manager decides to carry out a test of significance. The null hypothesis is given by . The hypothesis test is set up to provide the marketing manager with: a. evidence in favor of the null hypothesis. b. evidence against the alternative hypothesis in favor of the null hypothesis. c. evidence against the null hypothesis in favor of the alternative. d. proof that the null hypothesis is true. ANSWER: c 30. A marketing consultant is hired by a major restaurant chain that wants to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. Lunch bills are Normally distributed. To address the CEO’s conjecture, the marketing manager carries out a test of significance. The test statistic to use is given by which of the following formulas? a.

ANSWER: d 31. A marketing consultant is hired by a major restaurant chain that wants to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. Lunch bills are Normally distributed. To address the CEO’s conjecture, the marketing manager carried out a test of

. Using the test statistic

, the

P-value for the hypothesis test equals: a. 0.025. b. 0.077. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 17 c. 0.144. d. 0.923. ANSWER: b 32. A marketing consultant is hired by a major restaurant chain that wants to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. To address the CEO’s conjecture, the marketing manager carried out a test of vs. and obtained a P-value = 0.077. At a significance level of = 0.05, this result: a. proves without a doubt that the average lunch bill exceeds $13.50. b. proves without a doubt that the average lunch bill does not exceed $13.50. c. provides evidence against the alternative hypothesis in favor of the null hypothesis. d. does not provide evidence against the null hypothesis in favor of the alternative hypothesis. ANSWER: d 33. A marketing consultant is hired by a major restaurant chain that wants to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. To address the CEO’s conjecture, the marketing manager carried out a test of the hypothesis vs. and obtained a P-value of p = 0.077. This result is significant at: a.

= 0.1.

= 0.01.

= 0.05.

= 0.02.

ANSWER: a 34. Which of the following assumptions is required for a one-sample z test for a mean? a. We need to have an SRS from the target population. b. The target population needs to be Normally distributed. c. We need to know the population standard deviation. d. All of the answer options are correct. ANSWER: d 35. A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was = 78 with standard deviation = 10. One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know whether teaching a smaller class was more effective and (hence) students performed better. We can consider the small Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 17 class as an SRS of the students who took the large class over the years. The average midterm score was The hypothesis should be: a.

= 83.

ANSWER: c 36. A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was = 68 with standard deviation = 20. One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know whether teaching a smaller class affected scores in any way. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was = 78. The hypothesis the teacher tested was

vs.

. P-value for this hypothesis was found to be:

a. 0.0124. b. 0.0248. c. 0.0062. d. 0.0233. ANSWER: a

Page 10

Name:

Class:

Date:

Chapter 18 1. The margin of error in a confidence interval refers to error related to: a. sampling. b. nonresponse. c. measurement. d. All of the answer options are correct. ANSWER: a 2. A group of veterinary researchers plans a study to estimate the average daily number of packages delivered to homes in a city in Texas. Previous research has shown the variability in the number to be = 2. The researchers wish the margin of error to be no larger than 0.5 for a 99% confidence interval. To obtain such a margin of error, the researchers need at least: a. 53 observations. b. 106 observations. c. 54 observations. d. 107 observations. ANSWER: d 3. A group of veterinary researchers plans a study to estimate the average number of enteroliths in horses suffering from them. The number of enteroliths is determined by surgery or by ultrasound. This requires the participation of a surgeon and a radiologist in the study. To ensure correct counts, the researchers decide that they should enroll only horses seen at the best veterinary hospital in the country, which will typically see the most severe cases. The researchers will enroll the first 100 horses seen, beginning on the day the study is funded. The resulting interval is probably biased because: a. a sample of 100 horses is too small to obtain an unbiased estimate. b. the best veterinary hospital is likely to see the most severe cases, with larger numbers of enteroliths. c. the first 100 horses seen is not an SRS of all horses with enteroliths and, therefore, is not representative. d. All of the answer options are correct. ANSWER: b 4. Which of the following quantities must be known before calculating the margin of error? a. the population variance b. the population mean c. the population size d. All of the answer options are correct. ANSWER: a 5. If you are willing to incorrectly reject the null hypothesis one time out of every 20 times that you conduct the same test of significance, which of the following is always true? a. The power of the test is too low. b. The effect size must be small for the power of the test to be high. c. The level of significance that you have set is = 0.05. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 18 d. The level of significance that you have set is = 0.025. ANSWER: c 6. What is required for the power of the test to remain constant as the effect size gets smaller? a. The sample size must increase. b. The sample size must decrease. c. The sample size must increase, and the significance level must increase. d. The sample size must decrease, and the significance level must increase. ANSWER: a 7. A “false positive,” in which an effect is detected when in reality there is none, is an example of: a. a Type I error. b. a Type II error. c. the power of the test. d. None of the answer options is correct. ANSWER: a 8. A “false negative,” in which no effect is detected when in reality one exists, is an example of: a. a Type I error. b. a Type II error. c. the power of the test. d. None of the answer options is correct. ANSWER: b 9. Suppose the probability that you fail to reject the null hypothesis when you should have rejected it is 20%, meaning there is a 20% chance that there is a real effect that you were unable to detect. The power of the test is: a. . b. 0.8. c. 0.9. d. It is not possible to determine the power without knowing the sample size. ANSWER: b 10. All other factors being equal, which error would you choose to decrease? a. b. c. d. Choosing is always a matter of judgment and context, so the choice will be different for different data and different situations. ANSWER: d 11. The significance level is defined as: Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 18 a. the probability of a Type I error. b. the probability of a Type II error. c. the probability that the power of the test is at least 0.9. d. None of the answer options is correct. ANSWER: a 12. When one is designing a significance test, which of the following will increase the power of the test? a. increasing the significance level. b. increasing the sample size. c. increasing the effect size. d. None of the answer options is correct. ANSWER: b 13. Before conducting a significance test, which of the following should you do? a. Set an appropriate significance level. b. Determine the sample size needed for your inference to be successful to the standards you want to meet. c. Inspect the data for outliers or other issues that might challenge the assumptions of the particular statistical test you wish to use. d. All of the answer options are correct. ANSWER: d 14. A researcher wishes to determine whether the use of an herbal extract improves memory. Subjects will take the herbal extract regularly during a 10-week period, and then each subject will take a standard memory test. Suppose the scores on this test, for all potential subjects taking the herbal extract, follow a Normal distribution, with mean and standard deviation = 6. Suppose also that, in the general population of all people, scores on the memory test follow a Normal distribution, with mean 50 and standard deviation = 4. The researcher, therefore, decides to test the hypotheses , . To do so, the researcher has 100 subjects follow the 10-week protocol, meaning they take the supplement for 10 weeks and then take the memory test. The mean score for these subjects is = 55.2, and the P-value is less than 0.0001. Which of the following is an appropriate conclusion? a. The researcher has conclusively proved that the use of this herbal extract improves memory. b. The researcher has strong evidence that people who use this herbal extract, on average, have higher memory test scores than those who don’t use this extract. However, the difference may or may not be important. c. The researcher has strong evidence that the use of this herbal extract improves memory, and because the P-value is so small, the difference must be substantial. d. None of the answer options is correct. ANSWER: b 15. A researcher wishes to determine whether the use of an herbal extract improves memory. Subjects will take the herbal extract regularly during a 10-week period, and then each subject will take a standard memory test. Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 18 Suppose the scores on this test, for all potential subjects taking the herbal extract, follow a Normal distribution, with mean and standard deviation = 6. Suppose also that, in the general population of all people, scores on the memory test follow a Normal distribution, with mean 50 and standard deviation = 4. The researcher, therefore, decides to test the hypotheses , . To do so, he has 100 subjects follow the 10week protocol, meaning they take the supplement for 10 weeks and then take the memory test. The mean score for these subjects is = 55.2, and the P-value is less than 0.0001. Suppose that another researcher attempts to replicate this study. This researcher uses a sample of 10 subjects and observes a sample mean memory score of 55.2, which is the same as the sample mean described in the first study. Which of the following is an appropriate conclusion? a. The second researcher has obtained the same sample mean as the first researcher, so the P-value will be the same as that of the first researcher. b. The second researcher has obtained the same sample mean as the first researcher, but the P-value will be smaller than that of the first researcher. c. The second researcher has obtained the same sample mean as the first researcher, but the P-value will be greater than that of the first researcher. d. None of the answer options is correct. ANSWER: c 16. In testing hypotheses, if the consequences of failing to reject a null hypothesis that is actually false are very serious, we should: a. use a very large level of significance. b. use a very small level of significance. c. insist that the P-value be smaller than the level of significance. d. insist that the level of significance be smaller than the P-value. ANSWER: b 17. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean 115 and standard deviation = 25. You suspect that incoming first years have a mean that is different from 115, since they are often excited yet anxious about entering college. To verify your suspicion, you test the hypotheses , . You give the SSHA to 25 incoming first years and find their mean score. Based on this, you reject

at significance level = 0.01. Which of the following would

be most helpful in assessing the practical significance of your results? a. Test the hypotheses again, this time using significance level = 0.001. b. Report the P-value of your test. c. Take another sample and retest, just to make sure the results are not due to chance. d. Construct a 99% confidence interval for to see the magnitude of the difference between 115 and your sample results. ANSWER: d 18. After diagnosis for a certain type of cancer, the average survival time on the standard treatment is two years. A medical researcher is working on a new treatment. In an early trial, she tries the new treatment on three Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 18 subjects, who have an average survival time after diagnosis of four years. Although the survival time doubled, the results are not statistically significant, even at the 0.10 significance level, because: a. the placebo effect is present, which limits statistical significance. b. the sample size is small. c. although the survival time has doubled, the actual increase is really two years. d. the calculation was in error; the researchers forgot to include the sample size. ANSWER: b 19. A certain type of automobile has an average highway gas mileage of 30 miles per gallon (mpg). An engineer designs an improved engine, which has an average highway gas mileage of 30.2 mpg, based on a sample of 3600 cars with the new engine. Although the difference is quite small, the effect is statistically significant because: a. new designs typically have less variability than standard designs, so small differences can appear to be statistically significant. b. the sample size is very large. c. the mean of 30.2 is large compared to the gas mileage of most cars. d. All of the answer options are correct. ANSWER: b 20. In people with cholesterol levels over 200, the decrease in cholesterol level after eating a certain brand of oatmeal for breakfast for one month is Normally distributed, with mean (in milligrams) and standard deviation = 3. The brand advertises that eating its oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 10 points for people with cholesterol levels over 200. However, you believe that the mean decrease in cholesterol is actually less than advertised. To explore this, you test the hypotheses , , and you obtain a P-value of 0.052. Which of the following is true? a. At the = 0.05 significance level, you have proved that b. You have failed to obtain any evidence for c. There is some evidence against

is true.

, and a study using a larger sample size may be worthwhile.

d. This should be viewed as a pilot study, and the data suggest that further investigation of the hypotheses will not be fruitful at the = 0.05 significance level. ANSWER: c 21. In assessing the validity of any test of hypotheses, it is good practice to: a. examine the data using exploratory data analysis to make sure the probability distribution used for the test makes sense. b. test the hypotheses at several different levels of significance. c. test both one-sided and two-sided hypotheses to help guarantee consistency. d. All of the answer options are correct. ANSWER: a 22. In assessing the validity of any test of hypotheses, it is good practice to: Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 18 a. examine the data using exploratory data analysis to make sure the probability distribution used for the test makes sense. b. determine exactly how the study was conducted. c. determine what assumptions the researchers made. d. All of the answer options are correct. ANSWER: d 23. A radio show in the United States conducts a phone-in survey each morning. Listeners are asked to call in with a response to the question of the day. One morning in 2020, listeners were asked whether they supported or opposed term limits for members of Congress. Remarkably, 88% of listeners who called in favored term limits. We may safely conclude that: a. there is overwhelming approval for congressional term limits among Americans generally. b. if all Americans were asked their opinions, it is unlikely that the results would differ from those obtained in the poll. c. there is strong evidence that the majority of Americans believe there should be congressional term limits. d. a great majority of those with strong enough feelings on the issue to call in are in favor of congressional term limits, but we cannot generalize any of this survey’s results to a larger population. ANSWER: d 24. Does 30 minutes of meditation every day provide significant improvement in mental performance? To investigate this issue, a researcher conducted a study with 150 adult subjects, who meditated for 30 minutes each day for a period of six months. At the end of the study, 300 variables related to mental performance were measured on each subject. The resulting means were compared to known means for these variables in the population of all adults. Sixteen of these variables were significantly better (in the sense of statistical significance) at the = 0.05 level for the meditation group as compared to the population as a whole, and three variables were significantly better at the = 0.01 level for the meditation group as compared to the population as a whole. It would be correct to conclude that: a. there is very good statistical evidence that 30 minutes of meditation each day provides some improvement in mental performance. b. there is very good statistical evidence that 30 minutes of meditation each day provides improvement for the variables that were significant at the = 0.01 level. We should be somewhat cautious about making claims for the variables that were significant at the = 0.05 level. c. these results would have provided very good statistical evidence that 30 minutes of meditation each day provides some improvement in mental performance, if the number of subjects had been larger. It is premature to draw statistical conclusions from studies in which the number of subjects is less than the number of variables measured. d. None of the answer options is correct. ANSWER: d 25. If we accept the null hypothesis when, in fact, it is false, we have: a. committed a Type I error. b. committed a Type II error. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 18 c. a probability of being correct that is equal to the P-value. d. a probability of being correct that is equal to 1 P-value. ANSWER: b 26. A Type I error consists of: a. rejecting the null hypothesis when it is true. b. accepting the null hypothesis when it is false. c. incorrectly specifying the null hypothesis. d. incorrectly specifying the alternative hypothesis. ANSWER: a 27. The power of a statistical test of hypotheses is: a. the smallest significance level at which the data will allow you to reject the null hypothesis. b. equal to 1 P-value. c. the extent to which the test will reject both one-sided and two-sided hypotheses. d. defined for a particular alternative value of the parameter of interest and is the probability that a fixed level α significance test will reject the null hypothesis when the particular alternative value of the parameter is true. ANSWER: d 28. Which of the following will reduce the value of the power in a statistical test of hypotheses? a. decreasing the probability of a Type II error b. decreasing the sample size c. rejecting the null hypothesis only if the P-value is smaller than the level of significance d. All of the answer options are correct. ANSWER: b 29. A researcher plans to conduct a significance test at the = 0.10 significance level. The researcher designs the study to have a power of 0.7 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type I error is: a. 0.1. b. 0.7. c. 0.9. d. equal to the P-value and cannot be determined until the data have been collected. ANSWER: a 30. A researcher plans to conduct a significance test at the = 0.10 significance level. The researcher designs the study to have a power of 0.7 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type II error for the particular alternative value of the parameter at which the power was computed is: a. 0.1. b. 0.3. Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 18 c. 0.7. d. equal to 1 ANSWER: b

P-value and cannot be determined until the data have been collected.

31. A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. To address the CEO’s conjecture, the marketing manager carried out a hypothesis test of vs. and obtained a P-value = 0.077. The study meets all conditions for inference: a. if the customers constitute an SRS and the variance is small. b. if the customers constitute an SRS and the population distribution of lunch prices is Normal. c. if the population of lunch prices is Normal and the variance is known. d. if the population of lunch prices is Normal and the sample is not too small. ANSWER: b 32. A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. To address the CEO’s conjecture, the marketing manager carried out a hypothesis test of vs. and obtained a P-value = 0.077. To illustrate his results, the director also wanted to calculate a 95% confidence interval with a margin of error m = $1.00. The required sample size is: a. 30. b. 100. c. 25. d. 48. ANSWER: d 33. A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. To address the CEO’s conjecture, the marketing manager carried out a hypothesis test of vs. and obtained a P-value = 0.077. At level of significance = 0.05, the null hypothesis is not rejected. However, the marketing manager later finds that, in fact, the average lunch price is above $13.50. The failure of the sample of 25 lunch prices to detect this fact was: a. a Type I error. b. a Type II error. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 18 c. an error of the third kind. d. caused by bad data. ANSWER: b 34. A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be = $14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is = $3.50. To address the CEO’s conjecture, the marketing manager carried out a hypothesis test of vs. and obtained a P-value = 0.077. The marketing manager chooses a significance level of = 0.10. If he uses this significance level throughout his work, how often will he reject a true null hypothesis? a. He will reject 10% of all true null hypotheses. b. He will reject 1% of all true null hypotheses. c. He will reject 5% of all true null hypotheses. d. The frequency of his rejection is not known; it depends on getting good samples. ANSWER: a 35. A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was = 68 with standard deviation = 20. One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know whether teaching a smaller class affected scores in any way. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was = 78. The hypothesis the teacher tested was

vs.

. To reduce the probability of a Type I error, the teacher should:

a. increase the sample size. b. decrease the sample size. c. choose a two-sided alternative. d. do nothing; a Type I error is not affected by sample size. ANSWER: d 36. A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was = 68 with standard deviation = 20. One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know whether teaching a smaller class affected scores in any way. We can consider the small class as a SRS of the students who took the large class over the years. The average midterm score was = 78. The hypothesis the teacher tested was

vs.

. A power calculation done prior to collecting the sample showed the

probability of Type II error to be 0.1. If the null hypothesis is not rejected, the teacher can conclude that: a. the null hypothesis is true, no doubt about it. b. there is no evidence against the null or in favor of the alternative. c. the alternative hypothesis is proved wrong. d. the null hypothesis is proved wrong. Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 18 ANSWER: b

Page 10

Name:

Class:

Date:

Chapter 20 1. A 99% confidence interval for the mean of a population is computed from a random sample and found to be 6 3. We may conclude that: a. there is a 99% probability that is between 3 and 9. b. there is a 99% probability that the true mean is 6, and there is a 99% chance that the true margin of error is 3. c. if we took many, many additional random samples and, from each, computed a 99% confidence interval for , approximately 99% of these intervals would contain . d. All of the answer options are correct. ANSWER: c 2. I collect a random sample of size n from a population. From the data collected, I compute a 95% confidence interval for the mean of the population. Which of the following would produce a new confidence interval with smaller width (smaller margin of error) based on these same data? a. using a larger confidence level b. using a smaller confidence level c. using the same confidence level, but computing the interval n times—approximately 5% of these intervals will be larger d. none of these. Nothing can guarantee a smaller interval; one can only say the chance of obtaining a smaller interval is 0.05. ANSWER: b 3. A veterinarian collects data on the number of times race horses are raced during their careers. The veterinarian finds that the average number of races a horse enters is = 15.3, with a standard deviation of s = 6.8 in a sample of n = 20 horses. For a 95% confidence interval, the veterinarian should choose the critical value to be: a. 1.96. b. 1.645. c. 2.093. d. 1.729. ANSWER: c 4. A veterinarian collects data on the number of times race horses are raced during their careers. The veterinarian finds that the average number of races a horse enters is = 15.3, with a standard deviation of s = 6.8 in a sample of n = 20 horses. The veterinarian notices one horse that has raced 45 times. This outlier poses a problem. What should the veterinarian do? a. Drop the outlier, recalculate the sample mean and the standard deviation, and then proceed with a t interval. b. Choose a z interval instead of a t interval, because a z interval is not affected by outliers. c. Increase the confidence level. d. None of the answer options is correct. ANSWER: d Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 20 5. A veterinarian collects data on the number of times race horses are raced during their careers. The veterinarian finds that the average number of races a horse enters is = 15.3, with a standard deviation of s = 6.8 in a sample of n = 20 horses. Rounded to three digits, the standard error of the sample mean

is:

a. 1.521. b. 1.560. c. 0.340. d. 0.358. ANSWER: a 6. A veterinarian collects data on the number of times race horses are raced during their careers. The veterinarian finds that the average number of races a horse enters is = 15.3, with a standard deviation of s = 6.8 in a sample of n = 20 horses. A 95% confidence for , the average number of times a horse races, is given by: a. (12.32, 18.28). b. (11.38, 19.22). c. (12.12, 18.48). d. (10.95, 19.65). ANSWER: c 7. A veterinarian wishes to compare the number of times race horses are reported to be lame during a 12-month period to the incidence of lameness in similar horses that are not raced. The veterinarian decides to pair horses based on age, breed, and the area where the horse is trained. The veterinarian obtains 20 horses: 10 that are raced and 10 that are not raced. The veterinarian calculates a 95% confidence interval for the mean number of reports of lameness in racing horses using the 10 horses that are raced; for horses that are not raced using the 10 horses that are not raced; and for the mean difference in the number of reports of lameness using the pairs of horses. The veterinarian should: a. report the two confidence intervals for the 10 horses raced and for the 10 horses not raced. b. take the difference in the upper and lower limits of the confidence intervals for the 10 horses raced and for the 10 horses not raced. c. report the confidence interval for the paired differences. d. All of the answer options are correct. ANSWER: c 8. A veterinarian wishes to compare the number of times race horses are reported to be lame during a 12-month period with the incidence of lameness in similar horses that are not raced. The veterinarian is particularly interested in whether the exercise schedule used in racing contributes to lameness, rather than the total amount of exercise. The veterinarian feels horses to be compared should be similar with regard to age, breed, and the number of weekly hours spent exercising. Which of the following study types should be used? a. a matched design, in which a race horse is chosen, and a horse that is the same age, is the same breed, and is exercised the same number of hours is chosen for comparison b. a horse is chosen and raced for one year but is not raced the next year c. a group of race horses is chosen and then, from a nearby barn, a group of horses that do not race is Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 20 chosen d. None of the answer options is correct. ANSWER: a 9. A veterinarian wishes to compare the number of times race horses are reported to be lame during a 12-month period with the incidence of lameness in jumping horses that are not raced. The veterinarian chooses nine race horses and selects, for each race horse, a jumping horse that is the same age, is the same breed, and is exercised a similar number of hours each week. The table below contains the observed number of times each horse was lame.

The number of degrees of freedom for a confidence interval for estimating the difference in the mean number of times a race horse is lame and a jumping horse is lame is: a. 18. b. 16. c. 9. d. 8. ANSWER: d 10. A veterinarian wishes to compare the number of times race horses are reported to be lame during a 12month period with the incidence of lameness in jumping horses that are not raced. The veterinarian chooses nine race horses and selects, for each race horse, a jumping horse that is the same age, is the same breed, and is exercised a similar number of hours each week. The table below contains the observed number of times each horse was lame.

A 90% confidence interval for the mean difference in the number of times a horse is lame is given by: a. ( 1.329, 2.663). b. ( 1.59, 2.923). c. ( 3.405, 4.738). d. ( 2.459, 3.792). Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 20 ANSWER: b 11. A 95% confidence interval for the difference in the mean number of times race horses are lame and the number of times jumping horses are lame over a 12-month period is calculated to be ( 2.13, 3.47). Therefore, it can be concluded that: a. we have convincing evidence that race horses are lame more often than jumping horses, because the interval contains more positive than negative values. b. we have convincing evidence that race horses and jumping horses are lame equally often, on average, because the confidence interval contains zero. c. the sample is too small for us to draw any conclusion. d. no conclusion can be drawn, because a confidence interval cannot contain negative and positive values. ANSWER: b 12. A medical researcher treats 400 subjects who have high cholesterol using a new medicine. The average decrease in cholesterol level is = 90 mg/dl after two months of taking the medicine. Assume that this decrease in cholesterol follows a Normal distribution, with unknown mean and standard deviation s = 30. The researcher wants to see whether there was any statistically significant reduction in cholesterol levels as a result of this medicine. The appropriate hypotheses are: a. . b.

d. None of the answer options is correct. ANSWER: a 13. The time (in number of days) until maturity of a certain variety of tomato plant is Normally distributed, with mean and standard deviation s = 2.4. You select a simple random sample of forty plants of this variety and measure the time until maturity. The sample yields = 65. You read on the package of seeds that these tomatoes reach maturity, on average, in 61 days. You want to test to see whether your seeds are reaching maturity later than expected, which might indicate that your package of seeds is too old. The appropriate hypotheses are: a. . b.

ANSWER: a 14. You are thinking of employing a t procedure to test hypotheses about the mean of a population using a significance level of 0.05. You suspect the distribution of the population is not Normal and may be moderately skewed. Which of the following statements is correct? Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 20 a. You should not use the t procedure, because the population does not have a Normal distribution. b. You may use the t procedure, provided your sample size is large (at least 40). c. You may use the t procedure, but you should probably claim that the significance level is only 0.1. d. You may not use the t procedure because, although t procedures are robust to non-Normality for confidence intervals, they are not robust for tests of hypotheses. ANSWER: b 15. A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of 143 with standard deviation s = 21. The question is whether this is sufficient evidence that the diet is effective in meeting the target. Assume the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean . The appropriate hypotheses are: a. . b.

ANSWER: b 16. A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of 143 with standard deviation s = 21. The question is whether this is sufficient evidence that the diet is effective in meeting the target. Assume the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean . The appropriate degrees of freedom for this test are: a. 27. b. 28. c. 20. d. 149. ANSWER: a 17. A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of 143 with standard deviation s = 21. The question is whether this if sufficient evidence that the diet is effective in meeting the target. Assume the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean . Based on the data, the value of the one-sample t statistic is: a. 0.33. b. 1.76. c. 1.76. Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 20 d. 0.33. ANSWER: c 18. A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of 143 with standard deviation s = 21. The question is whether this is sufficient evidence that the diet is effective in meeting the target. Assume the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean . The P-value for the one-sample t test is: a. larger than 0.1. b. between 0.1 and 0.05. c. between 0.01 and 0.05. d. below 0.01. ANSWER: c 19. A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of 143 with standard deviation s = 21. The question is whether this is sufficient evidence that the diet is effective in meeting the target. Assume the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean . Given a P-value between 0.01 and 0.05, what conclusion should you draw at the 5% level of significance? a. Accept the null hypothesis, because the P-value is less than the level of significance. b. Fail to reject the null hypothesis, because the P-value is less than the level of significance. c. Reject the null hypothesis, because the P-value is less than the level of significance. d. No conclusion can be drawn without knowing the exact P-value. ANSWER: c 20. The one-sample t statistic from a sample of n = 23 observations for the one-sided test of

versus

has the value t = 2.24. Based on this information: a. P-value > 0.1. b. 0.01 < P-value < 0.025. c. we would reject the null hypothesis at = 0.025. d. both “0.01 < P-value < 0.025” and “we would reject the null hypothesis at α = 0.025” are correct. ANSWER: d 21. The one-sample t statistic from a sample of n = 23 observations for the two-sided test of

versus

has the value t = 2.24. If the standard deviation from the sample is 2.4, what is the mean of these n = 23 observations? a. 14 b. 15 Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 20 c. 16 d. The mean cannot be determined from the information given. ANSWER: c 22. Which of the following is an example of a matched pairs design? a. A teacher compares the pretest and posttest scores of students. b. A teacher compares the scores of students who had a computer-based method of instruction with the scores of other students who had a traditional method of instruction. c. A teacher compares the scores of students in her class on a standardized test with the national average score. d. A teacher calculates the average of students' scores on a pair of tests and wishes to see whether this average is larger than 80%. ANSWER: a 23. A medical researcher wishes to investigate the effectiveness of exercise versus diet in bringing about weight loss. Two groups of 25 overweight adults are used, with a subject in each group matched to a similar subject in the other group on the basis of a number of physiological variables. One group is placed on a regular program of vigorous exercise with no restriction on diet, and the other group is placed on a strict diet with no requirement to exercise. The weight loss after 20 weeks is determined for each subject, and the difference between the matched pairs of subjects (the weight loss of each subject in the exercise group minus the weight loss of the matched subject in the diet group) is computed. The mean of these differences in weight loss is found to be 2 pounds with standard deviation s = 6 pounds. Is this evidence of a difference in mean weight loss for the two methods? To test this, consider the population of differences (the weight loss an overweight adult would experience after 20 weeks on the exercise program minus the weight loss the same adult would experience after 20 weeks on the strict diet). Let be the mean of this population of differences, and assume their distribution is approximately Normal. We test the hypotheses versus using the matched pairs t test. The Pvalue for this test is: a. larger than 0.1. b. between 0.1 and 0.05. c. between 0.05 and 0.01. d. below 0.01. ANSWER: b 24. A veterinarian wishes to compare the number of times race horses are reported to be lame during a 12month period with the incidence of lameness in jumping horses that are not raced. The veterinarian chooses nine race horses and selects, for each race horse, a jumping horse that is the same age, is the same breed, and is exercised a similar number of hours each week. The table below contains the observed number of times each horse was lame.

Page 7

Name:

Class:

Date:

Chapter 20

The veterinarian tests the hypotheses

versus

, where

is the average difference in the

number of times race horses are lame minus the number of times jumping horses are lame. The P-value is: a. > 0.3. b. between 0.3 and 0.2. c. between 0.2 and 0.1. d. < 0.1. ANSWER: b 25. A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. Valid inferences require which of the following? a. a random sample of U.S. citizens, since the study is conducted in the United States b. a sample size of at least 30 subjects c. that the population of patients at the regional hospital be at least 20 times the sample size d. All of the answer options are correct. ANSWER: c 26. A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. If we wish to calculate a 95% confidence interval based on the t distribution and we have a sample of n = 20 subjects, we require which of the following from the population of score averages? a. Averages of the 50 questions should be Normally distributed in the population of all patients. b. Averages should have a known variance. c. Averages should be near the halfway point, which is 2.5. d. All of the answer options are correct. ANSWER: a 27. A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. A prior Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 20 study conducted at the hospital showed that averaging scores over 50 questions produces a Normal population distribution. If we obtain a sample of n = 15 subjects and wish to calculate a 95% confidence interval, the critical value t* is: a. 2.131. b. 2.145. c. 1.761. d. 1.753. ANSWER: b 28. A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. A sample of n = 15 patients produced the following statistics: and . A 99% confidence interval is given by: a. (2.37, 4.22). b. (2.64, 3.97). c. (2.69, 3.91). d. (2.5, 4.1). ANSWER: a 29. A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. A prior survey of patients had found the mean score for the population of patients to be = 2.9. After careful review of these data, the hospital nutritionist decided that patients could benefit from nutrition education. The current survey was implemented after patients were subjected to this education, and it produced the following sample statistics for the 15 patients sampled: and . We would like to know whether the education improved nutrition behavior. The hypotheses to be tested are: a. . b.

ANSWER: c 30. A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. A prior survey of patients had found the mean score for the population of patients to be = 2.9. After careful review of these data, the hospital nutritionist decided that patients could benefit from nutrition education. The current survey was implemented after patients were provided with this education, and it produced the following sample Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 20 statistics for the 15 patients sampled:

and

improved nutrition behavior. We test the hypotheses

. We would like to know whether the education versus

. The t test to be used has the

value: a. 1.35. b. 2.36. c. 1.29. d. 1.29. ANSWER: d 31. A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. The current survey was implemented after patients were subjected to this education, and it produced the following sample statistics for 15 patients sampled: and . We would like to know whether the education improved nutrition behavior. We test the hypotheses

versus

. The value of the t test is

1.29, and: a. P-value > 0.1. b. 0.05 ≤ P-value < 0.1. c. 0.025 ≤ P-value < 0.05. d. 0.25 ≤ P-value < 0.01. ANSWER: a 32. A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. The current survey was implemented after patients were provided with to this education, and 100 patients were included in the sample. The t test for the hypotheses versus was t = 2.88. The P-value is significant at: a. = 0.1. b.

= 0.05.

= 0.01.

d. All of the answer options are correct. ANSWER: d 33. A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. The researchers were interested in comparing the diets of long-time married couples. They randomly sampled 10 such couples and proceeded to test the hypothesis that the scores of the two partners in such couples were Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 20 similar. The appropriate procedure is called: a. a couple comparison. b. a two-sample t test. c. a paired t test. d. a bivariate t test. ANSWER: c 34. When a study involves a test about a mean, data should always be scrutinized for possible outliers or heavily skewed data. The t test and the t interval rely on certain assumptions. Which of the following statements is true? a. The most important step in ensuring validity is obtaining a simple random sample from the population of interest. b. As long as the sample size is at least 15 and there are no outliers among the data, we can use a t test. c. As long as the sample size is at least 40, we can use the t test even if the data exhibit skewness. d. All of the answer options are correct. ANSWER: d

Page 11

Name:

Class:

Date:

Chapter 21 1. Do SAT coaching classes help students to improve their test scores? To explore this, forty students were selected randomly from all of the students signed up for an SAT coaching class. For each student, we recorded their first SAT score (before the class) and their second SAT score (after the coaching class). Information for the first four students in the data set are provided below. Student 1 Student 2 Student 3 Student 4 First SAT score 920 830 960 910 Second SAT score 1010 800 1000 980 To analyze these data, we should use: a. the one-sample t test. b. the matched pairs t test. c. the two-sample t test. d. any of the answer options—we just need to use the t distribution because is unknown. ANSWER: b 2. A golf club is interested in determining whether there is a difference in golfer performance using two different brands of golf clubs, Brand A and Brand B. To test this, 62 golfers are asked to play a round of golf each on two consecutive Saturday afternoons. During the first round, one of two brands of clubs is to be used. During the second round, the other club brand is to be used. The order in which a golfer uses each brand is determined randomly. Scores for each round are recorded, and the results for the first four golfers are given below. Golfer Brand 1 Brand 2 1 93 95 2 88 86 3 112 111 4 79 77 To determine whether the mean scores differ by brand of club, we would use: a. the one-sample t test. b. the matched pairs t test. c. the two-sample t test. d. any of the answer options—it is at the experimenter’s discretion. ANSWER: b 3. A researcher is interested in the causes of migraine headaches in teenagers. The researcher suspects that high sugar intake might be related to migraines in teens. To investigate that suspicion, 50 teenagers who are known to have migraines are randomly selected, and an additional 50 who do not have migraines are also randomly selected. The researcher then computes the number of grams of sugar each teen has eaten over the past month. If the researcher calculates a two-sample confidence interval by hand for the difference in the mean number of grams of sugar consumed by teens with and without migraines, the number of degrees of freedom she should use is: a. 49. b. 2. c. 50. d. 25. ANSWER: a Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 21 4. A researcher is interested in the causes of migraine headaches in teenagers. The researcher suspects that high sugar intake might be related to migraines in teens. To investigate that suspicion, 50 teenagers who are known to have migraines are randomly selected, and an additional 50 who do not have migraines are also randomly selected. The researcher then computes the number of grams of sugar each teen has eaten over the past month. The researcher calculates a two-sample confidence interval for the difference in means and finds that it does not include zero. Therefore, she can conclude that: a. all teens consume exactly the same amount of sugar each month, whether or not they have migraines. b. all 100 teens consume different amounts of sugar each month. c. there is a difference in the average amount of sugar consumed by teens with and without migraines. d. there is evidence that, on average, teens with and without migraines consume the same amount of sugar. e. there is evidence that, on average, teens with and without migraines do not consume the same amount of sugar. ANSWER: e 5. A researcher is interested in the causes of migraine headaches in teenagers. The researcher suspects that high sugar intake might be related to migraines in teens. To investigate that suspicion, 50 teenagers who are known to have migraines are randomly selected, and an additional 50 who do not have migraines are also randomly selected. The researcher then computes the number of grams of sugar each teen has eaten over the past month. n s Migraine group 50 3200 320 No-migraine group 50 2620 210 Based on the given data, a 95% confidence interval for the difference in average amount of sugar consumed in the migraine group versus the no-migraine group is given by: a. (437.9, 686.1), b. (488.9, 671.2), c. (471.2, 688.8), d. (260, 900), ANSWER: b 6. A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 23 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data follows. n s Treatment group (new drug) 21 23.48 8.01 Control group (old drug) 23 18.52 7.15 Without using software, how would you estimate the number of degrees of freedom for this problem? a. Use the smaller value, 20, chosen from the two options 20 and 22. b. Use the larger value, 22, chosen from the two options 20 and 22. c. Use the smaller value, 21, chosen from the two options 21 and 23. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 21 d. Use the larger value, 23, chosen from the two options 21 and 23. ANSWER: a 7. A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 23 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data follows. n s Treatment group (new drug) 21 23.48 8.01 Control group (old drug) 23 18.52 7.15 A 95% confidence interval for the difference in reduction of blood pressure between these two drugs (using Option 2 and the conservative method for degrees of freedom) is: a. 0.17 to 9.75 points. b. 0.45 to 9.46 points. c. 1.26 to 8.66 points. d. 1.35 to 8.57 points. ANSWER: a 8. A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 23 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data follows. n s Treatment group (new drug) 21 23.48 8.01 Control group (old drug) 23 18.52 7.15 The researcher suspects that the new drug results in greater average reduction in blood pressure than the old drug does. Based on these data, the appropriate two-sample t statistic is: a. 1.84. b. 2.16. c. 2.31. d. 4.7. ANSWER: b 9. A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 23 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data follows. n s Treatment group (new drug) 21 23.48 8.01 Control group (old drug) 23 18.52 7.15 The P-value for a two-sample t test using these data, using Option 2 for degrees of freedom, is: a. larger than 0.05. Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 21 b. between 0.025 and 0.05. c. between 0.04 and 0.05. d. between 0.02 and 0.025. ANSWER: d 10. A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 23 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data follows. n s Treatment group (new drug) 21 23.48 8.01 Control group (old drug) 23 18.52 7.15 Which of the following would lead us to believe that the t procedures were not safe to use here? a. The two population distributions being studied are slightly non-Normal. b. The sample medians and means for the two groups are slightly different. c. The two population distributions are heavily skewed and far from Normal. d. Some subjects did not follow protocol, and these could be outliers in the data. ANSWER: c 11. A sports writer wished to see whether a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 20 adult volunteers. These volunteers were randomly divided into two groups of 10 subjects each. Group 1 kicked a football that was filled with helium to the recommended pressure. Group 2 kicked a football that was filled with air to the recommended pressure. The mean yardage for Group 1 was = 32 yards with a standard deviation s1 = 9 yards. The mean yardage for Group 2 was

= 27 yards with a standard deviation s2 = 6 yards.

Assume the two groups of kicks are independent. Let and represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium-filled and an air-filled football. Assume that two-sample t procedures are safe to use. A 99% confidence interval for (using the conservative value for the degrees of freedom) is: a. 0.7 to 10.5 yards. b. 3.8 to 13.8 yards c. 6.1 to 16.1 yards d. 6.7 to 16.7 yards ANSWER: c 12. A sports writer wished to see whether a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 20 adult volunteers. These volunteers were randomly divided into two groups of 10 subjects each. Group 1 kicked a football that was filled with helium to the recommended pressure. Group 2 kicked a football that was filled with air to the recommended pressure. The mean yardage for Group 1 was = 32 yards with a standard deviation s1 = 9 yards. The mean yardage for Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 21 Group 2 was

= 27 yards with a standard deviation s2 = 6 yards.

Assume the two groups of kicks are independent. Let and represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium-filled and an air-filled football. Assume that two-sample t procedures are safe to use. Suppose the researcher had wished to test the hypotheses , . The numerical value of the two-sample t statistic is: a. 0.36. b. 1.46. c. 2.57. d. 4.08. ANSWER: b 13. A sports writer wished to see whether a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 20 adult volunteers. These volunteers were randomly divided into two groups of 10 subjects each. Group 1 kicked a football that was filled with helium to the recommended pressure. Group 2 kicked a football that was filled with air to the recommended pressure. The mean yardage for Group 1 was = 32 yards with a standard deviation s1 = 9 yards. The mean yardage for Group 2 was

= 27 yards with a standard deviation s2 = 6 yards.

Assume the two groups of kicks are independent. Let and represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium-filled and an air-filled football. Assume that two-sample t procedures are safe to use. Suppose the researcher had wished to test the hypotheses , . The P-value for the test (use the conservative Option 2 for the degrees of freedom) is: a. larger than 0.1. b. between 0.05 and 0.1. c. between 0.01 and 0.05. d. below 0.01. ANSWER: b 14. Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, seven rooms were carpeted and seven were left uncarpeted. The rooms were similar in size and function. After a suitable period, the concentration of bacteria in the air was measured (in units of bacteria per cubic foot) in all of these rooms. The data and summaries follow. s Carpeted rooms Uncarpeted rooms

184 175

22.0 16.9

A 95% confidence interval for the difference in mean bacterial concentration in the air of carpeted rooms versus uncarpeted rooms (using the conservative value for the degrees of freedom) is: a. −7.47 to 31.47. b. −11.7 to 29.7. Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 21 c. −16.66 to 34.66. d. −18.89 to 42.89. ANSWER: c 15. Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, seven rooms were carpeted and seven were left uncarpeted. The rooms were similar in size and function. After a suitable period, the concentration of bacteria in the air was measured (in units of bacteria per cubic foot) in all of these rooms. The data and summaries follow. s Carpeted rooms 184 22.0 Uncarpeted rooms 175 16.9 The researcher wants to investigate whether the presence of carpet is associated with either an increase or a decrease in the mean bacterial concentration in air. The numerical value of the two-sample t statistic for this test is: a. 0.414. b. 0.858. c. 1.312. d. 3.818. ANSWER: b 16. A researcher is interested in the causes of migraine headaches in teenagers. The researcher suspects that high sugar intake might be related to migraines in teens. To investigate that suspicion, 50 teenagers who are known to have migraines are randomly selected, and an additional 50 who do not have migraines are also randomly selected. The researcher then computes the number of grams of sugar each teen has eaten over the past month. She is interested in comparing the mean of the migraine group (M) to that of the no-migraine group (O). The researcher should test which of the following hypotheses? a. . b.

ANSWER: a 17. A researcher is interested in the causes of migraine headaches in teenagers. The researcher suspects that high sugar intake might be related to migraines in teens. To investigate that suspicion, 50 teenagers who are known to have migraines are randomly selected, and an additional 50 who do not have migraines are also randomly selected. The researcher then computes the number of grams of sugar each teen has eaten over the past month. She is interested in comparing the mean of the migraine group (M) to that of the no-migraine group (O). The researcher tests the following hypotheses: . Migraine group No-migraine group Copyright Macmillan Learning. Powered by Cognero.

n 50 50

3200 2620

s 320 210 Page 6

Name:

Class:

Date:

Chapter 21 For the data given, the test statistic is: a. 0.193 b. 10.6. c. 1.96. d. 1.645. ANSWER: b 18. A researcher is interested in the causes of migraine headaches in teenagers. The researcher suspects that high sugar intake might be related to migraines in teens. To investigate that suspicion, 50 teenagers who are known to have migraines are randomly selected, and an additional 50 who do not have migraines are also randomly selected. The researcher then computes the number of grams of sugar each teen has eaten over the past month. She is interested in comparing the mean of the migraine group (M) to that of the no-migraine group (O). For which of the following reasons would the researcher be unable to use a two-sample t test? a. The two means and are not the same. b. The number of grams of sugar consumed by teens has a highly symmetric distribution. c. The distribution of the grams of sugar consumed is highly skewed. d. The variances of the number of grams of sugar in alfalfa are very different across the two groups. ANSWER: c 19. Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, seven rooms were carpeted and seven were left uncarpeted. The rooms were similar in size and function. After a suitable period, the concentration of bacteria in the air was measured (in units of bacteria per cubic foot) in all of these rooms. The P-value for this test is greater than 0.25. Which of the following is a reasonable conclusion? a. There isn’t much evidence to support a conclusion that the presence of carpet is associated with an increase or decrease in the mean concentration of bacteria in the air. b. There is fairly strong evidence to support a conclusion that the presence of carpet is associated with an increase or decrease in the mean concentration of bacteria in the air. c. There are outliers in these data, so we can’t rely on the two-sample t test. d. This test is unreliable, because the populations we’re sampling from are heavily skewed. ANSWER: a 20. When should you use a pooled two-sample t test? a. never, because its assumptions are inaccurate for all real-world data sets b. only when you do not have software available to perform the unequal-variances two-sample t test c. only when the variances within each of the two groups are different from each other d. always, because it is easier to calculate the pooled value of the t statistic ANSWER: b 21. Which of the following conditions must be met to perform the two-sample t test? a. The two random samples must be selected from two distinct populations. b. The two random samples must be selected from the same population. Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 21 c. There can be no skewness in either of the distributions. d. There must be skewness in both of the distributions. ANSWER: a 22. DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data follow. Poisoned rats: 12.207 16.869 25.050 22.429 8.456 20.589 Unpoisoned rats: 11.074 9.686 12.064 9.351 8.182 6.642 Let be the mean nerve sensitivity for rats poisoned with DDT. Let be the mean nerve sensitivity for rats not poisoned with DDT. Which of the following is the alternative hypothesis for the relevant significancetesting problem? a. b. c. d. ANSWER: a 23. DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data follow. Poisoned rats: 12.207 16.869 25.050 22.429 8.456 20.589 Unpoisoned rats: 11.074 9.686 12.064 9.351 8.182 6.642 Let be the mean nerve sensitivity for rats poisoned with DDT. Let be the mean nerve sensitivity for rats not poisoned with DDT. The numerical value of the standard error of the difference in sample means is: a. 1.3. b. 2.71. c. 4.05. d. 9.02. ANSWER: b 24. DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data follow. Poisoned rats: 12.207 16.869 25.050 22.429 8.456 20.589 Unpoisoned rats: 11.074 9.686 12.064 9.351 8.182 6.642 Let be the mean nerve sensitivity for rats poisoned with DDT. Let be the mean nerve sensitivity for rats not poisoned with DDT. The numerical value of the t statistic is: a. 0.57. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 21 b. 1.93. c. 6. d. 2.99. ANSWER: d 25. DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data follow. Poisoned rats: 12.207 16.869 25.050 22.429 8.456 20.589 Unpoisoned rats: 11.074 9.686 12.064 9.351 8.182 6.642 Let be the mean nerve sensitivity for rats poisoned with DDT. Let be the mean nerve sensitivity for rats not poisoned with DDT. The conservative degrees of freedom (Option 2) is: a. 4. b. 5. c. 6. d. 7. ANSWER: b 26. DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data follow. Poisoned rats: 12.207 16.869 25.050 22.429 8.456 20.589 Unpoisoned rats: 11.074 9.686 12.064 9.351 8.182 6.642 Let be the mean nerve sensitivity for rats poisoned with DDT. Let be the mean nerve sensitivity for rats not poisoned with DDT. Using Table C and the conservative version for degrees of freedom (Option 2), the P-value is: a. larger than 0.1. b. between 0.1 and 0.05. c. between 0.05 and 0.01. d. below 0.01. ANSWER: c 27. DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data follow. Poisoned rats: 12.207 16.869 25.050 22.429 8.456 20.589 Unpoisoned rats: 11.074 9.686 12.064 9.351 8.182 6.642 Let be the mean nerve sensitivity for rats poisoned with DDT. Let be the mean nerve sensitivity for rats not poisoned with DDT. The P-value for this test was between 0.05 and 0.01. Which of the following is a reasonable conclusion? Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 21 a. There isn’t much evidence to support a conclusion that the mean nerve sensitivity is greater in rats exposed to DDT than in rats not exposed to DDT. b. There is fairly strong evidence to support a conclusion that the mean nerve sensitivity is greater in rats exposed to DDT than in rats not exposed to DDT. c. There are outliers in these data, so we can’t rely on the two-sample t test. d. This test is unreliable, because the populations we’re sampling from are heavily skewed. ANSWER: b 28. An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students and then randomly divided them into two groups of five each. One group was provided the interactive tool, and the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let mean score that would be observed if all students used the interactive tool, and let mean score that would be observed if all students worked an extra problem. The number of degrees of freedom, using a t table for the hypothesis , is: a. 10. b. 8. c. 5. d. 4. ANSWER: d 29. An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students and then randomly divided them into two groups of five each. One group was provided the interactive tool, and the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let mean score that would be observed if all students used the interactive tool, and let mean score that would be observed if all students worked an extra problem. For testing , it has been suggested in the past to use a version of the t test that calculates a pooled variance estimate. Such an assumption requires that: a. the population standard deviations and be equal. b. the population means

and

be equal.

c. the sample standard deviations s1 and s2 be equal. Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 21 d. the sample means

and

be equal.

ANSWER: a 30. An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students and then randomly divided them into two groups of five each. One group was provided the interactive tool, and the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let mean score that would be observed if all students used the interactive tool, and let mean score that would be observed if all students worked an extra problem. In the past, a method called the pooled two-sample t test was commonly used for the comparison of two means. It requires equality of population variances. This test should be avoided because: a. the assumption of equal variances is not likely to hold in many practical applications. b. the approximate t test that does not require equality of variances is a valid test, even if variances are equal. c. it is difficult, on the basis of a sample, to judge equality of variance, because the F test for equality is not robust to deviations from Normality. d. All of the answer options are correct. ANSWER: d 31. An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students and then randomly divided them into two groups of five each. One group was provided the interactive tool, and the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let mean score that would be observed if all students used the interactive tool, and let mean score that would be observed if all students worked an extra problem. You are determined to use a two-sample pooled t test. To convince yourself that the test is valid to use, you will carry out an F test for equality of variances. This test is not a good test to use because: a. the test is very sensitive to departures from equality of variances. b. the test is too robust to detect outliers. c. the test is not robust against departures from Normality. d. All of the answer options are correct. ANSWER: c 32. An instructor gave students the option to purchase an interactive program that allows them to answer Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 21 questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students and then randomly divided them into two groups of five each. One group was provided the interactive tool, and the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let mean score that would be observed if all students used the interactive tool, and let mean score that would be observed if all students worked an extra problem. The standard error of the difference of sample means equals: a. 11.07. b. 7. c. 7.25. d. 10.05. ANSWER: b 33. An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students and then randomly divided them into two groups of five each. One group was provided the interactive tool, and the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let mean score that would be observed if all students used the interactive tool, and let mean score that would be observed if all students worked an extra problem. The value of the test statistic for the hypothesis equals: a. 1.915. b. 1.432. c. 2.145. d. 1.645. ANSWER: a 34. An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students and then randomly divided them into two groups of five each. One group was provided the interactive tool, and the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 21 scores. Let mean score that would be observed if all students used the interactive tool, and let mean score that would be observed if all students worked an extra problem. The number of degrees of freedom, using technology of the test statistic for the hypothesis , is: a. 4. b. 8. c. 7.92. d. 3.96. ANSWER: c 35. An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students and then randomly divided them into two groups of five each. One group was provided the interactive tool, and the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let mean score that would be observed if all students used the interactive tool, and let mean score that would be observed if all students worked an extra problem. The P-value for the hypothesis is: a. P > 0.05. b. 0.05 P > 0.025. c. 0.025

P > 0.01.

d. 0.01

ANSWER: b 36. An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students and then randomly divided them into two groups of five each. One group was provided the interactive tool, and the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let mean score that would be observed if all students used the interactive tool, and let mean score that would be observed if all students worked an extra problem. The hypothesis to be tested is . After rechecking the exam scores, the instructor notes that the lowest score in the extra problem group is actually only 16. The two-sample t test should not be used because: a. the data can’t be paired since there are five in each group. b. the t test is not robust enough for samples of size five each. Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 21 c. the t test for small samples is not robust to outliers. d. All of the answer options are correct. ANSWER: c 37. When the two-sample t test is said to be robust, to which of the following properties does this description not refer? a. In large samples (each sample larger than n = 40), outliers do not affect the P-value. b. In large samples (each sample larger than n = 40), the assumption of Normality for the population distribution is not necessary. c. In large samples (each sample larger than n = 40), it is not necessary to have independent samples. d. In large samples (each sample larger than n = 40), the population distributions can be skewed. ANSWER: c 38. Suppose a statistician has a client who conducted a statistical analysis related to a research project, for which she prepared a manuscript and submitted it to a scientific journal. This manuscript was rejected on the grounds of an inappropriate statistical analysis. The client had used a two-sample t test. Which of the following might have been a reason why the journal rejected her manuscript? a. The client used a pooled t test when it was obvious that the variances were unlikely to be equal on the basis of a sample. b. The client had small samples, and there were outliers in the data. c. The samples were not collected independently from two different populations. d. All of the answer options are correct. ANSWER: d 39. Which of the following statements is false? a. The two-sample t test can be used for independent samples and for paired data (there are two sets of numbers, after all). b. The two-sample t test can be used, even if the population distributions are not Normal, as long as the samples sizes are large. c. The pooled-variance version of the two-sample t test is not good to use—variances are unlikely to be the same in different populations. d. The F test for equality of variances is sensitive to departures from Normality and should not be used. ANSWER: a

Page 14

Name:

Class:

Date:

Chapter 22 1. Eggs that are contaminated with salmonella can cause food poisoning among consumers. A large egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory reports that 11 of the 200 eggs (or 5.5%) had salmonella contamination. Unknown to the producer, 0.2% (two-tenths of 1%) of all eggs shipped had salmonella. In this situation: a. 0.2% is a parameter and 5.5% is a statistic. b. 5.5% is a parameter and 0.2% is a statistic. c. both 0.2% and 5.5% are statistics. d. both 0.2% and 5.5% are parameters. ANSWER: a 2. Which of the following statements is true? a. A statistic characterizes a population, and a parameter describes a sample. b. A parameter characterizes a population, and a statistic describes a sample. c. You can obtain both statistics and parameters from either a sample or a population. d. None of the answer options is correct. ANSWER: b 3. In a survey of sleeping habits, 8400 adults were selected randomly and contacted by telephone. Based on a medical association’s recommended amount of sleep for adults, respondents were asked, “Do you typically sleep more than six hours during the night?” Of those surveyed, only 46% reported that they did. Which of the following is true with respect to this scenario? a. 8400 is the size of the population being studied. b. 46% is a statistic and represents an estimate of the unknown value of a parameter of interest. c. 46% is a parameter and represents an estimate of the unknown value of a statistic of interest. d. None of the answer options is correct. ANSWER: b 4. In a survey of sleeping habits, 8400 adults were selected randomly and contacted by telephone. Based on a medical association’s recommended amount of sleep for adults, respondents were asked, “Do you typically sleep more than six hours during the night?” Of those surveyed, only 46% reported that they did. Suppose the researchers who conducted the survey decide to conduct it again, but now they will interview only 5000 people. In the first survey of 8400 people, the observed proportion was 46%. Which of the following is true about the sample proportion for the second survey? a. By the law of large numbers, it will again be 46%. b. By the law of large numbers, the smaller (second) survey will certainly produce a sample proportion further from the true population proportion than the larger (first) survey. c. The proportion computed from the sample of 5000 people will be more accurate, because smaller samples tend to be more homogeneous than larger samples. d. None of the answer options is correct. ANSWER: d 5. The law of large numbers states that as the number of observations drawn at random from a population with Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 22 proportion p increases, the sample proportion

of the observed values:

a. gets larger and larger. b. gets smaller and smaller. c. tends to get closer and closer to the population proportion p. d. fluctuates steadily between 1 standard deviation above and 1 standard deviation below the observed proportion . ANSWER: c 6. As the number of estimates you have for p increases, what happens to the distribution of all ? a. It becomes more Normal. b. Its center more closely approximates the true population proportion p. c. Its standard deviation is approximately equal to the square root of

d. All of the answer options are correct. ANSWER: d 7. Students conducted a survey and found out that 36% of their peers on campus had tattoos, but only 4% of their peers were smokers. If 100 students were surveyed, can these students use the Normal approximation to construct a confidence interval for the proportion of students in the population who have tattoos? a. Yes, because both np and are less than 15. b. Yes, because both np and

are greater than 15.

c. No, because either np or

is less than 15.

d. No, because either np or

is greater than 15.

ANSWER: b 8. Students conducted a survey and found out that 36% of their peers on campus had tattoos, but only 4% of their peers were smokers. If 100 students were surveyed, can these students use the Normal approximation to construct a confidence interval for the proportion of students in the population who are smokers? a. Yes, because both np and are less than 15. b. Yes, because both np and

are greater than 15.

c. No, because either np or

is less than 15.

d. No, because either np or

is greater than 15.

ANSWER: c 9. Students conducted a survey and found out that 36% of their peers on campus had tattoos, but only 4% of their peers were smokers. If 200 students were surveyed, can these students use the Normal approximation to Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 22 construct a confidence interval for the proportion of students in the population who have tattoos? a. Yes, because both np and are less than 15. b. Yes, because both np and

are greater than 15.

c. No, because either np or

is less than 15.

d. No, because either np or

is greater than 15.

ANSWER: b 10. Students conducted a survey and found out that 36% of their peers on campus had tattoos, but only 4% of their peers were smokers. The standard error of

of tattooed students in the 100-student sample is:

a. 4%. b. 5%. c. 6%. d. It is not possible to tell from the information provided. ANSWER: b 11. A news organization previously stated that three of four people believed that the state of the economy was the country’s most significant concern. Now, the news organization wants to test to see whether the proportion of people who feel that way has changed. The most appropriate hypotheses are: a. . b.

ANSWER: d 12. A TV news program conducts a call-in poll about a proposed city ban on smoking in public places. Of the 2467 callers, 1900 were opposed to the ban. Which of the following statements are true with respect to using this sample to estimate p, the proportion of all TV news viewers that favor such a ban on smoking in public places? a. There is no way that this sample can be viewed as an SRS of all TV news viewers, so we can’t use this sample to estimate p. b. The population is much larger than the sample, so it’s okay to use this sample to estimate p. c. n is so large that both the count of successes, and the count of failures, , are 15 or more, so it’s okay to use this sample to estimate p. d. There appear to be no violations of any of the assumptions made in using the methods of this chapter, so we should now be able to use this sample to estimate p. ANSWER: a Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 22 13. The American Veterinary Medical Association conducted a survey of veterinary clinics to estimate the proportion of clinics that do not treat large animals (such as cows and horses). The survey was mailed to a random sample of 120 veterinary clinics throughout the country, and of these, 88 responded that they do not treat large animals. Typically, 70% of the veterinary clinics in the world do not treat large animals. You wish to test whether American veterinary clinics are more likely not to provide this service. The most appropriate hypotheses are: a. . b.

ANSWER: c 14. A doctor studying causes of diabetes in teens suspects that eating too much sugar may be a culprit. The doctor hypothesizes that more than 75% of all teens with diabetes consume more than twice as much sugar as is suggested by national guidelines. The proper hypotheses are: a. . b.

ANSWER: c 15. A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. For the bill to pass, at least 50% of voters need to be in favor of the levy. The board randomly selected 850 residents in the community and contacted them by telephone. Of the 850 residents surveyed, 410 supported the property tax levy. A z test for proportions will be used to test the hypothesis that the bill will pass. This is: a. appropriate, because n > 30. b. appropriate, because . c. appropriate, because both d. not appropriate, because

and

. .

ANSWER: c 16. A group of students in a seminar are interested in investigating what proportion of first year students had visited the campus prior to enrolling. They interview a group of n = 25 first year students and find that 14 had made a visit to the campus. Since the sample size is small, the confidence interval for p should: a. use t* with degrees of freedom df = 24. b. use z* from the Normal distribution using the large-sample method. c. use z* with the plus four method. Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 22 d. All of the answer options are correct. ANSWER: c 17. A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. They randomly selected 850 residents in the community and contacted them by telephone. Of the 850 residents surveyed, 410 supported the property tax levy. Let p represent the proportion of residents in the community who support the property tax levy. A 90% confidence interval for p is: a. 0.4489 to 0.5159. b. 0.4542 to 0.5105. c. 0.4487 to 0.5161. d. 0.4463 to 0.5185. ANSWER: b 18. A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. They randomly selected 850 residents in the community and contacted them by telephone. Of the 850 residents surveyed, 410 supported the property tax levy. Let p represent the proportion of residents in the community who support the property tax levy. How large a sample n would you need to estimate p with margin of error 0.04 and 95% confidence? (Assume that you don’t know anything about the value of p.) a. 256 b. 423 c. 601 d. 1037 ANSWER: c 19. According to the National Institute on Alcohol Abuse and Alcoholism, and the National Institutes of Health, 41% of college students nationwide engage in binge drinking behavior—having had five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at their college college that binge drinks is lower than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 162 admitted to having engaged in binge drinking. The college president is more interested in testing the suspicion that the proportion of students at the college who binge drink is lower than the national proportion of 0.41. The appropriate P-value is: a. between 0.05 and 0.1. b. between 0.025 and 0.05. c. between 0.01 and 0.025. d. below 0.01. ANSWER: d 20. According to the National Institute on Alcohol Abuse and Alcoholism, and the National Institutes of Health, 41% of college students nationwide engage in binge drinking behavior—having had five or more drinks on one occasion during the past two weeks. A college president wonders whether the proportion of students enrolled at the college who binge drink is lower than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 162 admitted to having engaged in Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 22 binge drinking. The college president is more interested in testing the suspicion that the proportion of students at the college who binge drink is lower than the national proportion of 0.41. Based on a P-value that you have computed, which of the following conclusions is reasonable? a. There is little evidence to support a conclusion that the proportion of students at this particular college who binge drink is lower than the national proportion of 0.41. b. There is moderate, but not strong, evidence that the proportion of binge-drinking students at this college is lower than the national proportion of 0.41. c. There is strong evidence that the proportion of students at this college who binge drink is lower than the national proportion of 0.41. d. We can’t reach any reasonable conclusion, because the assumptions necessary for a significance test for a proportion are not met in this case. ANSWER: c 21. In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1472 U.S. adults (presumably selected randomly) during 2020 revealed that 677 had never smoked cigarettes. Suppose you wished to test whether there has been a change since 1965 in the proportion of U.S. adults who have never smoked cigarettes. You test the hypotheses , . The P-value of the test is: a. greater than 0.1. b. between 0.05 and 0.1. c. between 0.01 and 0.05. d. below 0.01. ANSWER: b 22. In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1472 U.S. adults (presumably selected randomly) during 2020 revealed that 677 had never smoked cigarettes. Suppose you wished to test whether there has been a change since 1965 in the proportion of U.S. adults who have never smoked cigarettes. You test the hypotheses , . The P-value of the test is: a. greater than 0.1. b. between 0.05 and 0.1. c. between 0.01 and 0.05. d. below 0.01. ANSWER: a 23. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects, prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion p is less than 0.1, the inspector will reject the shipment. The inspector will test the hypotheses , . The instructor selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Suppose that 12 of the potatoes sampled are found to have major defects. The P-value of this test is: a. 0.059. b. 0.029. c. 0.04. d. less than 0.01. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 22 ANSWER: b 24. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects, prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion p is less than 0.1, the inspector will reject the shipment. The inspector will test the hypotheses , . The instructor selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Suppose that 12 of the potatoes sampled are found to have major defects. Which of the following is true? a. The inspector will decide to accept the shipment, because there’s strong evidence that the proportion of potatoes with serious defects is less than 0.1. b. The inspector might reach the wrong conclusion about the shipment of potatoes, whether the inspector accepts the shipment or not. c. The inspector’s sample size is large enough for valid inference here. d. All of the answer options are true. ANSWER: d 25. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects, prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion p is less than 0.1, the inspector will reject the shipment. The inspector will test the hypotheses , . The instructor selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Suppose that 12 of the potatoes sampled are found to have major defects. Which of the following assumptions for inference about a proportion using a hypothesis test are violated? a. The data are an SRS from the population of interest. b. The population is at least 10 times as large as the sample. c. n is large enough that both np0 and are 10 or more, where p0 is the proportion with major defects if the null hypothesis is true. d. There appear to be no violations. ANSWER: d 26. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects, prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion p is less than 0.1, the inspector will reject the shipment. The inspector will test the hypotheses , . The instructor selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Suppose that 12 of the potatoes sampled are found to have major defects. If the P-value of this test is between 0.01 and 0.05, which of the following statements is true? a. If the null were true, there is less than a 1% chance that if we took another SRS and performed this test again, we would find results that are at least as extreme as what was observed with this sample. b. If the null were true, there is less than a 5% chance that if we took another SRS and performed this test again, we would find results that are at least as extreme as what was observed with this sample. c. There is a less than a 5% chance of observing defective potatoes in any given sample. d. We cannot conclude that there is evidence that we should accept the shipment. ANSWER: b Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 22 27. In the four-step process for tests of significance, what do you do differently for a two-tailed test? a. Nothing—one-tailed and two-tailed tests are executed identically. b. In the “Solve” step, you must multiply the test statistic by 2 before proceeding. c. In the “Solve” step, you must multiply the P-value by 2 before proceeding. d. In the “Conclude” step, you must state that your results are twice as likely. ANSWER: c 28. If you don’t know anything about the value of p, which of the following assumptions can you use if you wish to compute an appropriate sample size? a. You must collect some sample data to provide an accurate estimate for p. b. Assume p and q are both 0.5, which will result in the smallest possible estimated sample size. c. Assume p and q are both 0.5, which will result in the largest possible estimated sample size. d. There is no way to compute an appropriate sample size. ANSWER: c 29. A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. They randomly selected 850 residents in the community and contacted them by telephone. Of the 850 residents surveyed, 410 supported the property tax levy. Let p represent the proportion of residents in the community who support the property tax levy. What is the sample proportion? a. 0 b. 0.41 c. 0.482 d. 0.5 ANSWER: c 30. A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. They randomly selected 850 residents in the community and contacted them by telephone. Of the 850 residents surveyed, 410 supported the property tax levy. Let p represent the proportion of residents in the community who support the property tax levy. What is the margin of error for a 90% confidence interval? a. 0.017 b. 0.028 c. 0.033 d. 0.056 ANSWER: b 31. You are conducting research for a popular blog to find out the proportion of readers who are satisfied with the site’s newly designed navigation. You want to make sure that you increase your chances of capturing the true proportion of readers who are satisfied, but the margin of error is too large. Which of the following would you do? a. Use a larger confidence level but choose a smaller margin of error. b. To increase your confidence, you must be willing to accept a smaller margin of error. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 22 c. To get a smaller margin of error, you must be willing to accept lower confidence. d. All of the answer options are correct. ANSWER: c 32. Each person in a random sample of 2000 “likely voters” (as defined by a professional polling organization) was questioned about her or his political views. Of those surveyed, 1308 felt that “the economy’s state” was the most urgent national concern. Using the plus four estimate, we estimate the proportion of likely voters who felt that the economy’s state was the most urgent national concern to be: a. 0.357. b. 0.5. c. 0.654. d. 0.732. ANSWER: c 33. Each person in a random sample of 2000 “likely voters” (as defined by a professional polling organization) was questioned about her or his political views. Of those surveyed, 1308 felt that “the economy’s state” was the most urgent national concern. The standard error SE of the estimated proportion viewing the economy’s state as most urgent is: a. 0.0001. b. 0.0106. c. 0.0312. d. 0.4926. ANSWER: b 34. Each person in a random sample of 2000 “likely voters” (as defined by a professional polling organization) was questioned about her or his political views. Of those surveyed, 1308 felt that “the economy’s state” was the most urgent national concern. If we increase the number of likely voters sampled, what will happen to the standard error SE of the sample proportion? a. It will increase. b. It will decrease. c. It will stay the same. d. Not enough information is provided to be able to answer the question. ANSWER: b 35. Each person in a random sample of 2000 “likely voters” (as defined by a professional polling organization) was questioned about her or his political views. Of those surveyed, 1308 felt that “the economy’s state” was the most urgent national concern. Using the plus four confidence interval procedure, a 99% confidence interval for the proportion p of all likely voters who feel that the economy’s state is the most urgent national concern is given by: a. 0.624 to 0.663. b. 0.627 to 0.681. c. 0.615 to 0.672. d. 0.606 to 0.68. Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 22 ANSWER: b 36. If we want to estimate p, the population proportion of likely voters that believe the economy’s state is the most urgent national concern, with 99% confidence and a margin of error no greater than 3%, how many likely voters need to be surveyed? (Assume that you have no idea of the value of p.) a. 22 b. 56 c. 716 d. 1844 ANSWER: d 37. The American Veterinary Medical Association conducted a survey of veterinary clinics to estimate the proportion that do not treat large animals (such as cows and horses). The survey was mailed to a random sample of 120 veterinary clinics throughout the country and of these, 88 responded that they do not treat large animals. The standard error SE of the sample proportion of clinics that do not treat large animals is: a. 0.02. b. 0.03. c. 0.04. d. 0.05. ANSWER: c 38. The American Veterinary Medical Association conducted a survey of veterinary clinics to estimate the proportion that do not treat large animals (such as cows and horses). The survey was mailed to a random sample of 120 veterinary clinics throughout the country and of these, 88 responded that they do not treat large animals. A 95% confidence interval for p, the proportion of veterinary clinics that do treat large animals, is: a. 0.163 to 0.371. b. 0.188 to 0.346. c. 0.200 to 0.333. d. 0.629 to 0.837. ANSWER: b 39. A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. They randomly selected 850 residents in the community and contacted them by telephone. Of the 850 residents surveyed, 410 supported the property tax levy. Let p represent the proportion of residents in the community that support the property tax levy. A 90% confidence interval for p is: a. 0.4489 to 0.5159. b. 0.4543 to 0.5105. c. 0.4487 to 0.5161. d. 0.4463 to 0.5185. ANSWER: b 40. A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. They randomly selected 850 residents in the community and contacted them by Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 22 telephone. Of the 850 residents surveyed, 410 supported the property tax levy. Let p represent the proportion of residents in the community that support the property tax levy. How large a sample n would you need to estimate p with margin of error 0.04 with 95% confidence? (Assume that you don’t know anything about the value of p.) a. 256 b. 423 c. 601 d. 1037 ANSWER: c 41. According to the National Institute on Alcohol Abuse and Alcoholism, and the National Institutes of Health, 41% of college students nationwide engage in binge drinking behavior—having five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at their college that binge drinks is lower than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 162 admitted to having engaged in binge drinking. Based on the results of the test, a 95% confidence interval for the proportion of all students at this college that engages in binge drinking is: a. 0.308 to 0.394. b. 0.318 to 0.384. c. 0.321 to 0.381. d. 0.325 to 0.377. ANSWER: a 42. In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1472 U.S. adults (presumably selected randomly) during 2020 revealed that 677 had never smoked cigarettes. A 99% confidence interval for the proportion of U.S. adults in 2020 who have never smoked is: a. 0.461 to 0.56. b. 0.426 to 0.493. c. 0.481 to 0.54. d. 0.487 to 0.534. ANSWER: b 43. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects, prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion, p, is less than 0.1, the inspector will reject the shipment. The inspector selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Twelve of the potatoes sampled are found to have major defects. Using the plus four method, a 95% confidence interval for the true proportion of potatoes in the truck that have major defects is: a. 0.034 to 0.103. b. 0.009 to 0.111. c. 0.051 to 0.103. d. 0.027 to 0.093. ANSWER: a Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 22 44. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects, prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion, p, is less than 0.1, the inspector will reject the shipment. The inspector selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Twelve of the potatoes sampled are found to have major defects. How would you interpret the meaning of this confidence interval? a. You are 95% certain that the true population of defective potatoes lies somewhere between the lower bound and the upper bound of the confidence interval. b. You obtained the lower and upper bounds of the confidence interval using a method that provides correct results 95% of the time. c. Both option (a) and option (b) are correct. d. Neither option (a) nor option (b) is correct. ANSWER: c 45. A veterinarian investigating possible causes of stomach distress in horses suspects that feeding alfalfa may be to blame. The veterinarian wishes to estimate the proportion of horses with stomach distress who are fed at least two flakes of alfalfa per day. In a sample of 62 horses with stomach distress, it is found that 42 are fed two or more daily flakes of alfalfa. The estimated standard error is: a. 0.0594. b. 0.0035. c. 0.2185. d. 0.4675. ANSWER: a 46. A veterinarian investigating possible causes of stomach distress in horses suspects that feeding alfalfa may be to blame. The veterinarian wishes to estimate the proportion of horses with stomach distress who are fed at least two flakes of alfalfa per day. In a sample of 62 horses with stomach distress, 42 are fed two or more daily flakes of alfalfa. A 95% confidence interval is given by: a. (0.576, 0.744). b. (0.524, 0.83). c. (0.561, 0.794). d. (0.601, 0.754). ANSWER: c 47. A veterinarian investigating possible causes of stomach distress in horses suspects that feeding alfalfa may be to blame. The veterinarian wishes to estimate the proportion of horses with stomach distress who are fed at least two flakes of alfalfa per day. In a sample of 62 horses with stomach distress, 42 are fed two or more daily flakes of alfalfa. For a 99% confidence interval, the margin of error is: a. 0.0594. b. 2.575. c. 0.2181. d. 0.153. ANSWER: d Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 22 48. A veterinarian investigating possible causes of stomach distress in horses suspects that feeding alfalfa may be to blame. The veterinarian wishes to estimate the proportion of horses with stomach distress who are fed at least two flakes of alfalfa per day. In a sample of 62 horses with stomach distress, 42 are fed two or more daily flakes of alfalfa. The veterinarian wants to calculate a 95% confidence interval and decides to use the largesample method. This is: a. justified, because the sample size is larger than 30. b. justified, because and are at least 15. c. justified, because the majority of horses are fed at least two flakes per day. d. not justified, because the true proportion needs to be p = 0.5. ANSWER: b 49. A veterinarian investigating possible causes of stomach distress in horses suspects that feeding alfalfa may be to blame. The veterinarian wishes to estimate the proportion of horses with stomach distress who are fed at least two flakes of alfalfa per day. In a sample of 62 horses with stomach distress, 42 are fed two or more flakes of alfalfa. Using the large-sample method, the veterinarian obtains a 95% confidence interval of (0.561, 0.794). A statistician colleague tells the vet to use the plus four method for calculating a confidence interval. If the vet calculated the interval using that method, it would yield an interval with an upper endpoint: a. closer to 1 than 0.794. b. further from 1 than 0.794. c. that cannot be determined from the information given. d. closer to the point estimate than 0.794. ANSWER: b 50. A veterinarian investigating possible causes of enteroliths in horses suspects that feeding alfalfa may be to blame. The veterinarian wishes to estimate the proportion of horses with enteroliths who are fed at least two flakes of alfalfa per day. In a sample of 62 horses with enteroliths, 42 are fed two or more daily flakes of alfalfa. A 95% confidence interval is calculated to be (0.561, 0.794). That interval has a margin of error of m = 0.1165. The veterinarian believes that this is too large and decides to use the current data as a pilot study to plan a proper study with a smaller margin of error of m = 0.05. Using

= 0.678, the required sample size is calculated

to be: a. 336. b. 172. c. 17. d. 74. ANSWER: a 51. An instructor at a major research university occasionally teaches one of three sections of statistics during summer session. The instructor notices that there are often students repeating the class. On the first day of class, the instructor counts 105 students enrolled, 19 of whom are repeating the class. The university enrolls 15,000 students. The population proportion of students repeating the class over the summer is given by: a. 0.181. Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 22 b. 0.0013. c. 0.055. d. an unknown quantity; there is no information about other sections of this course over the summer. ANSWER: d 52. An instructor at a major research university occasionally teaches one of three sessions of statistics during summer session. The instructor notices that there are often students repeating the class. On the first day of class, the instructor counts 105 students enrolled, 19 of whom are repeating the class. The university enrolls 15,000 students. The sample proportion of students repeating the class over the summer is given by: a. 0.181. b. 0.0013. c. 0.007. d. an unknown quantity; there is no information on other sections that a student may take to repeat the class. ANSWER: a 53. An instructor at a major research university occasionally teaches one of three sessions of statistics during summer session. The instructor notices that there are often students repeating the class. On the first day of class, the instructor counts 105 students enrolled, 19 of whom are repeating the class. The university enrolls 15,000 students. An estimate of the population proportion repeating the class is given by: a. 0.0013. b. 0.007. c. 0.181. d. 0.046. ANSWER: c 54. An instructor at a major research university occasionally teaches one of three sessions of statistics during summer session. The instructor notices that there are often students repeating the class. On the first day of class, the instructor counts 105 students enrolled, 19 of whom are repeating the class. The university enrolls 15,000 students. The instructor wishes to estimate the proportion of students across campus who repeat a course during summer sessions and decides to do so on the basis of this class. Would you advise the instructor against this activity and why? a. Yes, because this class is too small. b. Yes, because this class is not a random sample of students. c. No, because it is completely arbitrary who takes this class. d. No, because 105 students is a pretty large class. ANSWER: b 55. An instructor at a major research university occasionally teaches one of three sessions of statistics during summer session. The instructor notices that there are often students repeating the class. On the first day of class, the instructor counts 105 students enrolled, 19 of whom are repeating the class. The university enrolls 15,000 students. The professor decides to estimate, with 95% confidence, the proportion of all students repeating the class. Besides ensuring that the sample is an SRS from the population, she needs to check whether the following Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 22 condition for inference is satisfied. a. The sample must have enough students who repeat the class (at least 15). b. The sample must have enough students who repeat the class and enough who do not (both at least 15). c. The sample must have enough students who do not repeat the class (at least 15). d. The sample size must be large, regardless of the number of students who repeat the class and the number who do not. ANSWER: b 56. An instructor at a major research university occasionally teaches one of three sessions of statistics during summer session. The instructor notices that there are often students repeating the class. On the first day of class, the instructor counts 105 students enrolled, 19 of whom are repeating the class. The university enrolls 15,000 students. The standard error for the estimated sample proportion is given by: a. 0.025. b. 0.0014. c. 0.0376. d. 0.005. ANSWER: c 57. An instructor at a major research university occasionally teaches one of three sessions of statistics during summer session. The instructor notices that there are often students repeating the class. Out of curiosity, the instructor designs a random sample of students enrolled in summer sessions and counts the number repeating a class. The instructor counts 105 students in the sample, 19 of whom are repeating the class. The university enrolls 15,000 students. A 95% confidence interval is given by: a. (0.345, 0.453). b. (0.107, 0.255). c. (0.15, 0.23). d. (0.09, 0.272). ANSWER: b 58. An instructor at a major research university occasionally teaches summer session and notices that there are often students repeating the class. Out of curiosity, the instructor designs a random sample of students enrolled in summer sessions and counts the number repeating a class. The instructor counts 105 students in the sample, 19 of whom are repeating a class. She decides a confidence interval provides a good estimate of the proportion of students repeating a class. The instructor wants a 95% confidence interval with a margin of error at most m = 0.025 and has no idea what the true proportion could be. How large a sample should be taken? a. 250 b. 1500 c. 1537 d. 400 ANSWER: c 59. An instructor at a major research university occasionally teaches summer session and notices that there are Copyright Macmillan Learning. Powered by Cognero.

Page 15

Name:

Class:

Date:

Chapter 22 often students repeating the class. Out of curiosity, the instructor designs a random sample of students enrolled in summer sessions and counts the number repeating a class. The instructor counts 105 students in the sample, 19 of whom are repeating a class. She decides a confidence interval provides a good estimate of the proportion of students repeating a class. The instructor wants a 95% confidence interval with a margin of error at most m = 0.025 and has no idea what the true proportion could be. How large a sample should she take if the sample that she has serves as a pilot sample to provide an estimate of p? a. 1537 b. 912 c. 911 d. 1536 ANSWER: c 60. An instructor at a major research university occasionally teaches summer session and notices that there are often students repeating the class. Out of curiosity, the instructor designs a random sample of students enrolled in summer sessions and counts the number repeating a class. The instructor counts 105 students in the sample, 19 of whom are repeating a class. The instructor hypothesizes that, in general, 10% of students repeat a course. The hypotheses to be tested are: a. . b.

ANSWER: b 61. An instructor at a major research university occasionally teaches summer session and notices that there are often students repeating the class. Out of curiosity, the instructor designs a random sample of students enrolled in summer sessions and counts the number repeating a class. The instructor counts 105 students in the sample, 19 of whom are repeating a class. The instructor hypothesizes that, in general, 10% of students repeat a course. The hypotheses to be tested are . The test statistic for this hypothesis is given by: a. 1.96. b. 2.332. c. 2.575. d. 2.765. ANSWER: d 62. An instructor at a major research university occasionally teaches summer session and notices that there are often students repeating the class. Out of curiosity, the instructor designs a random sample of students enrolled in summer sessions and counts the number repeating a class. The instructor counts 105 students in the sample, 19 of whom are repeating a class. The instructor hypothesizes that, in general, 10% of students repeat a course. The hypotheses to be tested are . The P-value for this test is: a. P > 0.05. Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 22 b. 0.05 > P > 0.01. c. 0.01 > P > 0.005. d. 0.005 > P. ANSWER: c 63. An instructor at a major research university occasionally teaches summer session and notices that there are often students repeating the class. Out of curiosity, the instructor designs a random sample of students enrolled in summer sessions and counts the number repeating a class. The instructor counts 105 students in the sample, 19 of whom are repeating a class. The instructor hypothesizes that, in general, 10% of students repeat a course. The hypotheses to be tested are H0 : p = 0.1 vs. Ha : p ≠ 0.1. The P-value for this test is calculated to be P < 0.01. Therefore: a. we have strong evidence that the proportion of students repeating a class during summer sessions is not 10%. b. we have strong evidence that the proportion of students repeating a class during summer sessions is 10%. c. we have convincing proof that the proportion of students repeating a class during summer sessions is not 10%. d. we have no doubt that the proportion of students repeating a class during summer sessions is not 10%. ANSWER: a 64. A nutrition study asked a small random sample of patients at a local clinic whether they eat three or more servings of fruit on a daily basis. Of the 50 subjects who participated, 10 answered Yes. The sample size in this study is: a. adequate for large-sample inference for a proportion, because n > 30. b. too small, because we need at least 40 subjects for large-sample inference. c. too small, because we need at least 15 subjects who do and 15 who do not eat three or more servings of fruit. d. None of the answer options is correct. ANSWER: c 65. A nutrition study asked a small random sample of patients at a local clinic whether they eat three or more servings of fruit on a daily basis. Of the 50 subjects who participated, 10 answered Yes. The sample size in this study is small, therefore: a. we wasted our time collecting data, because we cannot calculate a confidence interval. b. we need to collect more data so we can calculate the sample proportion and find a confidence interval. c. we must find a similar study and combine the data (there are plenty of nutrition studies). d. we will use the plus four method to adjust for the fact that we have a small sample. ANSWER: d 66. A nutrition study asked a small random sample of patients at a local clinic whether they eat three or more servings of fruit on a daily basis. Of the 50 subjects who participated, 10 answered Yes. The 95% confidence Copyright Macmillan Learning. Powered by Cognero.

Page 17

Name:

Class:

Date:

Chapter 22 interval for the true proportion of patients eating at least three or more servings of fruit a day is given by: a. (0.111, 0.334). b. (0.107, 0.293). c. (0.089, 0.311). d. (0.054, 0.346). ANSWER: c 67. A nutrition study asked a small random sample of patients at a local clinic whether they eat three or more servings of fruit on a daily basis. Of the 50 subjects who participated, 12 answered Yes. If the true proportion of patients who eat at least three servings of fruit a day is 20%, then the true standard deviation of the sample proportion in a sample of 50 patients is given by: a. 0.0016. b. 0.0566. c. 0.0032. d. 0.0604. ANSWER: b 68. A nutrition study asked a small random sample of patients at a local clinic whether they eat three or more servings of fruit on a daily basis. Of the 50 subjects who participated, 10 answered Yes. The nutritionists decided to obtain an 80% confidence interval, because the sample size is rather small. This is: a. a good idea, because a 95% confidence interval will be too wide. b. a good idea, because we can use the plus four method to account for the small sample size. c. a bad idea, because an 80% confidence interval does not have a good confidence level. d. a bad idea, because the plus four method should be used for confidence intervals of 90% or more. ANSWER: d

Page 18

Name:

Class:

Date:

Chapter 23 1. A candidate for one of Ohio’s two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, 1062 of whom support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, 900 of whom support the candidate. Using the large-sample estimate, we estimate that the proportion of registered adults in the northern half of the state who support this candidate is: a. 0.469. b. 0.531. c. 0.546. d. 0.825. ANSWER: b 2. A candidate for one of Ohio’s two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, 1062 of whom support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, 900 of whom support the candidate. Using the large-sample estimate, we estimate that the proportion of registered adults in the southern half of the state who support this candidate is: a. 0.183. b. 0.375. c. 0.45. d. 0.825. ANSWER: c 3. A candidate for one of Ohio’s two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, 1062 of whom support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, 900 of whom support the candidate. For purposes of comparing the two proportions, the sampling distribution for the difference in the sample proportions has an approximate standard error of: a. 0.3. b. 0.022. c. 0.016. d. 0.0002. ANSWER: c 4. A candidate for one of Ohio’s two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, 1062 of whom support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, 900 of whom support the candidate. A 95% confidence interval for the difference in the proportion of registered voters that support this candidate between the northern and southern halves of the state is: a. 0.05 to 0.112. b. 0.035 to 0.127. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 23 c. 0.04 to 0.122. d. 0.037 to 0.119. ANSWER: a 5. An educator is interested in the effect of active learning on student success in an introductory physics course. The professor ran two sections of the course, each with the same curriculum, but with one section receiving active learning engagement and the other not. Students were randomly assigned to sections, and there were 137 students in total in the study. At the end of the semester, of the 62 students in the active learning class, 42 students passed. Of the 75 students in the non-active learning class, 37 students passed the class. The estimated sample proportions are: a. Non Active (Control): 0.493 and Active (Treatment): 0.677 b. Non Active (Control): 0.677 and Active (Treatment): 0.493 c. Non Active (Control): 0.270 and Active (Treatment): 0.307 d. Non Active (Control): 0.307 and Active (Treatment): 0.270 ANSWER: a 6. An educator is interested in the effect of active learning on student success in an introductory physics course. The professor ran two sections of the course, each with the same curriculum, but with one section receiving active learning engagement and the other not. Students were randomly assigned to sections, and there were 137 students in total in the study. At the end of the semester, of the 62 students in the active learning class, 42 students passed. Of the 75 students in the non-active learning class, 37 students passed the class. The standard error for

equals:

a. 0.083. b. 0.0073. c. 0.0069. d. 0.0132. ANSWER: a 7. An educator is interested in the effect of active learning on student success in an introductory physics course. The professor ran two sections of the course, each with the same curriculum, but with one section receiving active learning engagement and the other not. Students were randomly assigned to sections, and there were 137 students in total in the study. At the end of the semester, of the 62 students in the active learning class, 42 students passed. Of the 75 students in the non-active learning class, 37 students passed the class. The professor calculates a 95% confidence interval for the difference in the proportion of passing students in the active learning class and the proportion of passing students in the non-active learning class as: a. (0.17, 0.20). b. (0.021, 0.34). c. (0.51, 0.84). d. (0.33, 0.66). ANSWER: b 8. An educator is interested in the effect of active learning on student success in an introductory physics course. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 23 The professor ran two sections of the course, each with the same curriculum, but with one section receiving active learning engagement and the other not. Students were randomly assigned to sections, and there were 137 students in total in the study. At the end of the semester, of the 62 students in the active learning class, 42 students passed. Of the 75 students in the non-active learning class, 37 students passed the class. The professor calculates a 95% confidence interval for the difference in the proportion of passing students in the active learning class and the proportion of passing students in the non-active learning class as (0.021, 0.34). Because this interval contains only positive values, a reasonable conclusion is that: a. there is evidence that the proportion of students in the active class who pass the class is the same as the proportion of students in the non-active class who pass, and that it is greater than 0. b. there is evidence that the proportion of students in the active class who pass is less than the proportion of students in the non-active class who pass. c. there is evidence that the proportion of students in the active class who pass is greater than the proportion of students in the non-active class who pass. d. there is no evidence that the proportion of students in the active class who pass is greater than the proportion of students in the non-active class who pass. ANSWER: c 9. A school has two kindergarten classes. There are 21 children in Ms. Toodle’s kindergarten class. Of these, 17 are “pre-readers,” or children on the verge of reading. There are 19 children in Mr. Grimace’s kindergarten class. Of these, 13 are pre-readers. Using the plus four confidence interval method, a 90% confidence interval for the difference in proportions of children in these classes who are pre-readers is −0.104 to 0.336. Which of the following statements is correct? a. This confidence interval is not reliable, because the samples are so small. b. This confidence interval is of no use, because it contains 0, which is the value of no difference between classes. c. This confidence interval is reasonable, because the sample sizes are both at least five. d. This confidence interval is not reliable, because these samples cannot be viewed as simple random samples taken from a larger population. ANSWER: d 10. An educator is interested in the effect of active learning on student success in an introductory physics course. The professor ran two sections of the course, each with the same curriculum, but with one section receiving active learning engagement and the other not. Students were randomly assigned to sections, and there were 137 students in total in the study. At the end of the semester, of the 62 students in the active learning class, 42 students passed. Of the 75 students in the non-active learning class, 37 students passed the class. To assess the conjecture that students in an active learning class are more likely to pass the class, the professor should test the following hypotheses: a. . b.

Page 3

Name:

Class:

Date:

Chapter 23 ANSWER: b 11. An educator is interested in the effect of active learning on student success in an introductory physics course. The professor ran two sections of the course, each with the same curriculum, but with one section receiving active learning engagement and the other not. Students were randomly assigned to sections, and there were 137 students in total in the study. At the end of the semester, of the 62 students in the active learning class, 42 students passed. Of the 75 students in the non-active learning class, 37 students passed the class. To assess the conjecture that students in an active learning class (called the case group) are more likely to pass the class than students in a non-active learning class (called the control group), she tested . The P-value for this test is less than 0.001. Which of the following is the most accurate conclusion statement? a. There is evidence that the proportion of students in an active learning class who pass is higher than the proportion of students in a non-active learning class who pass. b. The null hypothesis should be rejected in favor of the alternative hypothesis at = 0.01. c. There is no evidence that the proportion of students in an active learning class who pass is higher than the proportion of students in a non-active learning class who pass. d. There is evidence that the proportion of students in an active learning class who pass is less than the proportion of students in a non-active learning class who pass. ANSWER: a 12. An educator is interested in the effect of active learning on student success in an introductory physics course. The professor ran two sections of the course, each with the same curriculum, but with one section receiving active learning engagement and the other not. Students were randomly assigned to sections, and there were 137 students in total in the study. At the end of the semester, of the 62 students in the active learning class, 42 students passed. Of the 75 students in the non-active learning class, 37 students passed the class. The professor decided to base statistical procedures on pcase, the proportion of students in active learning classes who pass, and pcontrol, the proportion of students in non-active learning classes who pass. The professor is told by a statistician colleague that it is okay to proceed with a large-sample confidence interval for because: a. the two sample sizes combined (at 137) exceed 30. b. each sample (at ncase = 62 and ncontrol = 75) exceeds 30. c. the numbers of successes and failures exceed 10 in both samples. d. None of the answer options is correct; sample size does not matter for inference about proportions. ANSWER: c 13. An SRS of 100 flights of a large airline (Airline 1) showed that 64 flights were on time. An SRS of 100 flights of another large airline (Airline 2) showed that 80 were on time. Let p1 and p2 be the proportions of all flights that are on time for these two airlines. A 95% confidence interval for the difference is: a. −0.16 0.062. b. −0.16

0.122.

c. −0.16

0.103.

d. 0.16 0.062. Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 23 ANSWER: b 14. An SRS of 100 flights of a large airline (Airline 1) showed that 64 flights were on time. An SRS of 100 flights of another large airline (Airline 2) showed that 80 were on time. Let p1 and p2 be the proportions of all flights that are on time for these two airlines. Is there evidence of any difference between the on-time rates for the two airlines? To determine this, you test the following hypotheses: a. . b.

ANSWER: d 15. An SRS of 100 flights of a large airline (Airline 1) showed that 64 flights were on time. An SRS of 100 flights of another large airline (Airline 2) showed that 80 were on time. Let p1 and p2 be the proportions of all flights that are on time for these two airlines. Using the appropriate hypotheses from Question 14, the P-value of your test is: a. between 0.1 and 0.05. b. between 0.05 and 0.01. c. between 0.01 and 0.001. d. below 0.001. ANSWER: b 16. In the past decades, there have been intensive antismoking campaigns sponsored by both federal and private agencies. In one study of national smoking trends, two random samples of U.S. adults were selected in different years. The first sample, taken in 1995, involved 4276 adults, 1642of whom were smokers. The second sample, taken in 2020, involved 3908 adults, 1415 of whom were smokers. The samples are to be compared to determine whether the proportion of U.S. adults who smoked declined during the 25-year period between the samples. Let p1 be the proportion of all U.S. adults who smoked in 1995. Let p2 denote the proportion of all U.S. adults who smoked in 2020. The hypotheses to test in this problem are: a. . b.

ANSWER: b 17. In the past decades, there have been intensive antismoking campaigns sponsored by both federal and private agencies. In one study of national smoking trends, two random samples of U.S. adults were selected in different years. The first sample, taken in 1995, involved 4276 adults, 1642 of whom were smokers. The second sample, taken in 2020, involved 3908 adults, 1415 of whom were smokers. The samples are to be compared to determine whether the proportion of U.S. adults who smoked declined during the 25-year period between the samples. Let p1 be the proportion of all U.S. adults who smoked in 1995. Let p2 denote the proportion of all Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 23 U.S. adults who smoked in 2020. The value of the z statistic for testing equality of the proportions of smokers in 1995 and 2020 is: a. 1.39. b. 1.66. c. 2.05. d. 4.23. ANSWER: c 18. In the past decades, there have been intensive antismoking campaigns sponsored by both federal and private agencies. In one study of national smoking trends, two random samples of U.S. adults were selected in different years. The first sample, taken in 1995, involved 4276 adults, 1642 of whom were smokers. The second sample, taken in 2020, involved 3908 adults, 1415 of whom were smokers. The samples are to be compared to determine whether the proportion of U.S. adults who smoked declined during the 25-year period between the samples. Let p1 be the proportion of all U.S. adults who smoked in 1995. Let p2 denote the proportion of all U.S. adults who smoked in 2020. The P-value of the test for equality of the proportions of smokers in 1995 and 2010 is: a. greater than 0.1. b. between 0.05 and 0.1. c. between 0.01 and 0.05. d. below 0.01. ANSWER: c 19. To conduct a two-tailed test of significance for the difference between two proportions, you would choose the following hypotheses: a. . b.

c. Both option (a) and option (b) are appropriate. d. Neither option (a) nor option (b) is appropriate. ANSWER: c 20. A guidance counselor at a university is investigating demand for study abroad. The question is how engineering and humanities majors compare regarding interest in study abroad during the summer. Random samples of 20 engineering and humanities majors each were interviewed. Eight engineering majors and 12 humanities majors expressed interest in study abroad during the summer. The estimated difference in the proportions of engineering and humanities majors, , where pE is the proportion of engineering majors interested in study abroad and pH is the proportion for humanities majors, is given by: a. 0.2. b. −0.2. c. 0.4. d. 0.6. ANSWER: b Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 23 21. A guidance counselor at a university is investigating demand for study abroad. The question is how engineering and humanities majors compare regarding interest in study abroad during the summer. Random samples of 20 engineering and humanities majors each were interviewed. Eight engineering majors and 12 humanities majors expressed interest in study abroad during the summer. The estimated difference in the proportions of engineering and humanities majors, , where pE is the proportion of engineering majors interested in study abroad and pH is the proportion for humanities, has standard error: a. 0.48. b. 0.692. c. 0.24. d. 0.1549. ANSWER: d 22. A guidance counselor at a university is investigating demand for study abroad. The question is how engineering and humanities majors compare regarding interest in study abroad during the summer. Random samples of 20 engineering and humanities majors each were interviewed. Eight engineering majors and 12 humanities majors expressed interest in study abroad during the summer. The estimated difference in the proportions of engineering and humanities majors, , where pE is the proportion of engineering majors interested in study abroad and pH is the proportion for humanities, has sampling distribution: a. Normal with mean = 0.2 and standard deviation = 0.1549. b. Normal with mean = −0.2 and standard deviation = 0.1549. c. with mean = −0.2 and standard deviation = 0.1549; shape not known. d. with mean = 0.2 and standard deviation = 0.1549; shape not known. ANSWER: c 23. A guidance counselor at a university is investigating demand for study abroad. The question is how engineering and humanities majors compare regarding interest in study abroad during the summer. Random samples of 20 engineering and humanities majors each were interviewed. Eight engineering majors and 12 humanities majors expressed interest in study abroad during the summer. The estimated difference in the proportions of engineering and humanities majors, , where pE is the proportion of engineering majors interested in study abroad and pH is the proportion for humanities, has 95% confidence interval: a. (−0.472, 0.109). b. (−0.504, 0.104). c. (−0.104, 0.504). d. (−0.109, 0.472). ANSWER: b 24. A guidance counselor at a university is investigating demand for study abroad. The question is how engineering and humanities majors compare regarding interest in study abroad during the summer. Random samples of 20 engineering and humanities majors each were interviewed. Eight engineering majors and 12 humanities majors expressed interest in study abroad during the summer. The estimated difference in the proportions of engineering and humanities majors, , where pE is the proportion of engineering majors interested in study abroad and pH is the proportion of humanities majors, has which requirement for Normality? Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 23 a. n1

30 and n2

b. n1 + n2

c. x1, x2

30 and n1 − x1, n2 − x2

d. x1, x2

10 and n1 − x1, n2 − x2

ANSWER: d 25. A guidance counselor at a university is investigating demand for study abroad. The question is how engineering and humanities majors compare regarding interest in study abroad during the summer. Random samples of 40 engineering and humanities majors each were interviewed. Sixteen engineering majors and 24 humanities majors expressed interest in study abroad during the summer. The guidance counselor thinks that engineering majors are less interested in study abroad. The hypotheses to be tested, where pE is the proportion of engineering majors interested in study abroad and pH is the proportion of humanities majors, are: a. . b.

ANSWER: b 26. A guidance counselor at a university is investigating demand for study abroad. The question is how engineering and humanities majors compare regarding interest in study abroad during the summer. Random samples of 40 engineering and humanities majors each were interviewed. Sixteen engineering majors and 24 humanities majors expressed interest in study abroad during the summer. The hypotheses to be tested are , where pE is the proportion of engineering majors interested in study abroad and pH is the proportion of humanities majors. The test statistic has standard error: a. 0.0125. b. 0.1118. c. 0.012. d. 0.1095. ANSWER: b 27. A guidance counselor at a university is investigating demand for study abroad. The question is how engineering and humanities majors compare regarding interest in study abroad during the summer. Random samples of 40 engineering and humanities majors each were interviewed. Sixteen engineering majors and 24 humanities majors expressed interest in study abroad during the summer. The hypotheses to be tested are , where pE is the proportion of engineering majors interested in study abroad and pH is the proportion of humanities majors. The test statistic has the value: a. −0.17889. b. 0.17889. c. −0.18265. d. 0.18265. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 23 ANSWER: a 28. A guidance counselor at a university is investigating demand for study abroad. The question is how engineering and humanities majors compare regarding interest in study abroad during the summer. Random samples of 40 engineering and humanities majors each were interviewed. Sixteen engineering majors and 24 humanities majors expressed interest in study abroad during the summer. The hypotheses to be tested are , where pE is the proportion of engineering majors interested in study abroad and pH is the proportion for humanities majors, has p-value P = 0.0368. Therefore, the guidance counselor: a. has no evidence either way regarding proportions interested in study abroad. b. can be sure that engineering majors are as interested in study abroad as humanities majors. c. has moderate evidence that engineering majors are less likely to study abroad than humanities majors. d. can claim with certainty that engineering majors are less likely to study abroad than humanities majors. ANSWER: c 29. Inference for comparisons of two proportions requires that both samples have at least 10 successes and 10 failures. When it is not possible to get large samples, an alternative approach to finding a confidence interval of the difference in two proportions is to: a. add 2 to the number of successes in each sample, 2 to the number of failures, and 4 to the sample sizes. b. add 1 to the number of successes in each sample and 2 to each sample size. c. add 1 to the number of successes, 1 to the number of failures, and 4 to each sample size. d. add 2 to the number of successes in each sample and 4 to each sample size. ANSWER: b

Page 9

Name:

Class:

Date:

Chapter 25 1. In the United States, there has historically been a strong relationship between smoking and education, with well-educated people less likely to smoke. To examine whether this pattern has changed, a sample of 459 people was selected at random from those who had visited a health center for a routine check-up over the course of the past year. Education is classified into three categories corresponding to the highest level of education achieved, and smoking status is classified into four categories. Smoking Status Education Nonsmoker Former Moderate Heavy Total High School 56 54 41 36 187 College 37 43 27 32 139 Graduate School 53 28 36 16 133 Total 146 125 104 84 459 The proportion of people with a high school education who are current or former smokers is: a. 0.12. b. 0.3. c. 0.7. d. 0.78. ANSWER: c 2. In the United States, there has historically been a strong relationship between smoking and education, with well-educated people less likely to smoke. To examine whether this pattern has changed, a sample of 459 people was selected at random from those who had visited a health center for a routine check-up over the course of the past year. Education is classified into three categories corresponding to the highest level of education achieved, and smoking status is classified into four categories. Smoking Status Education Nonsmoker Former Moderate Heavy Total High School 56 54 41 36 187 College 37 43 27 32 139 Graduate School 53 28 36 16 133 Total 146 125 104 84 459 The proportion of former smokers with a college or graduate school education is: a. 0.15. b. 0.22. c. 0.34. d. 0.57. ANSWER: d 3. In the United States, there has historically been a strong relationship between smoking and education, with well-educated people less likely to smoke. To examine whether this pattern has changed, a sample of 459 people was selected at random from those who had visited a health center for a routine check-up over the course of the past year. Education is classified into three categories corresponding to the highest level of education achieved, and smoking status is classified into four categories. Smoking Status Education Nonsmoker Former Moderate Heavy Total High School 56 54 41 36 187 College 37 43 27 32 139 Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 25 Graduate School 53 28 36 Total 146 125 104 Given that this is an r c table, what is the value of c? a. 2 b. 3 c. 4 d. 6 ANSWER: c

16 84

133 459

4. In the United States, there has historically been a strong relationship between smoking and education, with well-educated people less likely to smoke. To examine whether this pattern has changed, a sample of 459 people was selected at random from those who had visited a health center for a routine check-up over the course of the past year. Education is classified into three categories corresponding to the highest level of education achieved, and smoking status is classified into four categories. Smoking Status Education Nonsmoker Former Moderate Heavy Total High School 56 54 41 36 187 College 37 43 27 32 139 Graduate School 53 28 36 16 133 Total 146 125 104 84 459 Suppose we wish to test the null hypothesis that there is no association between education level and smoking status. Under the null hypothesis, the expected number of nonsmokers with a high school education is: a. 42.37. b. 50.93. c. 59.48. d. 62.34. ANSWER: c 5. In the United States, there has historically been a strong relationship between smoking and education, with well-educated people less likely to smoke. To examine whether this pattern has changed, a sample of 459 people was selected at random from those who had visited a health center for a routine check-up over the course of the past year. Education is classified into three categories corresponding to the highest level of education achieved, and smoking status is classified into four categories. Smoking Status Education Nonsmoker Former Moderate Heavy Total High School 56 54 41 36 187 College 37 43 27 32 139 Graduate School 53 28 36 16 133 Total 146 125 104 84 459 The degrees of freedom for the chi-square test for this two-way table are: a. 2. b. 6. c. 7. d. 12. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 25 ANSWER: b 6. In the United States, there has historically been a strong relationship between smoking and education, with well-educated people less likely to smoke. To examine whether this pattern has changed, a sample of 459 people was selected at random from those who had visited a health center for a routine check-up over the course of the past year. Education is classified into three categories corresponding to the highest level of education achieved, and smoking status is classified into four categories. Smoking Status Education Nonsmoker Former Moderate Heavy Total High School 56 54 41 36 187 College 37 43 27 32 139 Graduate School 53 28 36 16 133 Total 146 125 104 84 459 Which hypotheses are being tested by the chi-square test? a. The null hypothesis is that the two categorical variables are dependent. The alternative is that they are independent. b. The null hypothesis is that there is a relationship between education level and smoking status. The alternative is that there is no such relationship. c. The null hypothesis is that there is no relationship between education level and smoking status. The alternative is that nonsmokers have higher education levels than smokers. d. The null hypothesis is that there is no relationship between education level and smoking status. The alternative is that there is such a relationship. ANSWER: d 7. A veterinary study of horses looked at the type of housing provided for the horse and the type of bedding. Bedding was classified as shavings or rubber mats, and housing was classified as stall, small paddock, large paddock, or pasture. The data from the study are provided in the table below. Housing Bedding Stall Small Paddock Large Paddock Pasture Total Shavings 20 23 29 12 84 Rubber Mats 3 5 33 21 62 Total 23 28 62 33 146 The proportion of horses housed in small or large paddocks is given by: a. 0.616. b. 0.458. c. 1.317. d. 1.379. ANSWER: a 8. A veterinary study of horses looked at the type of housing provided for the horse and the type of bedding. Bedding was classified as shavings or rubber mats, and housing was classified as stall, small paddock, large paddock, or pasture. The data from the study are provided in the table below. Housing Bedding Stall Small Paddock Large Paddock Pasture Total Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 25 Shavings 20 23 29 12 84 Rubber Mats 3 5 33 21 62 Total 23 28 62 33 146 The proportion of horses in small or large paddocks that have shavings for bedding is: a. 1.379. b. 0.703. c. 0.578. d. 0.845. ANSWER: c 9. A veterinary study of horses looked at the type of housing provided for the horse and the type of bedding. Bedding was classified as shavings or rubber mats, and housing was classified as stall, small paddock, large paddock, or pasture. The data from the study are provided in the table below. Housing Bedding Stall Small Paddock Large Paddock Pasture Total Shavings 20 23 29 12 84 Rubber Mats 3 5 33 21 62 Total 23 28 62 33 146 The data were obtained by taking a simple random sample of 136 horses and then classifying them by type of bedding and housing category. An appropriate chi-square test for association in the case is called: a. the test for concordance. b. the test for homogeneity. c. the test for independence. d. the test for agreement. ANSWER: c 10. A veterinary study of horses looked at the type of housing provided for the horse and the type of bedding. Bedding was classified as shavings or rubber mats, and housing was classified as stall, small paddock, large paddock, or pasture. The data from the study are provided in the table below. Housing Bedding Stall Small Paddock Large Paddock Pasture Total Shavings 20 23 29 12 84 Rubber Mats 3 5 33 21 62 Total 23 28 62 33 146 The investigators decide to do a chi-square test for independence, but this test should not be used here because: a. the observed counts in two of the eight cells are 5 or below. b. the expected counts in two of the eight cells are 5 or below. c. the expected counts need to be at least 10 in each cell. d. None of the answer options is correct. The chi-square test is appropriate here; all conditions are met. ANSWER: d 11. A veterinary study of horses looked at the type of housing provided for the horse and the type of bedding. Bedding was classified as shavings or rubber mats, and housing was classified as stall, small paddock, large paddock, or pasture. The data from the study are provided in the table below. Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 25 Housing Bedding Stall Small Paddock Large Paddock Pasture Total Shavings 20 23 29 12 84 Rubber Mats 3 5 33 21 62 Total 23 28 62 33 146 The investigators carried out a chi-square test for association and obtained the value statistic. The P-value for this statistic is obtained from a

as a test

table on:

a. 1 degree of freedom. b. 3 degrees of freedom. c. 4 degrees of freedom. d. 6 degrees of freedom. ANSWER: b 12. A veterinary study of horses looked at the type of housing provided for the horse and the type of bedding. Bedding was classified as shavings or rubber mats, and housing was classified as stall, small paddock, large paddock, or pasture. The data from the study are provided in the table below. Housing Bedding Stall Small Paddock Large Paddock Pasture Total Shavings 20 23 29 12 84 Rubber Mats 3 5 33 21 62 Total 23 28 62 33 146 A chi-square test for independence had P-value < 0.0001. Which of the following is the most appropriate conclusion? a. We have evidence that bedding and type of housing are not independent. b. We have evidence that bedding and type of housing are independent. c. We have evidence that stall housing is associated with shavings bedding. d. We have no evidence of a relationship between the two categorical variables. e. We reject the null hypothesis. f. We do not reject the null hypothesis. ANSWER: a 13. A veterinary study of horses looked at the type of housing provided for the horse and the type of bedding. Bedding was classified as shavings or rubber mats, and housing was classified as stall, small paddock, large paddock, or pasture. The data from the study are provided in the table below. Housing Bedding Stall Small Paddock Large Paddock Pasture Total Shavings 20 23 29 12 84 Rubber Mats 3 5 33 21 62 Total 23 28 62 33 146 A chi-square test for independence had P-value < 0.0001. Therefore, we conclude that bedding and type of housing are not independent. To determine which cells differ, we may: a. look at expected and observed cell counts. b. compare selected percent of shavings by type of housing. Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 25 c. look at which cells contribute large amounts to the chi-square statistic. d. All of the answer options are correct. ANSWER: d 14. A veterinary study of horses looked at water sources for horses, and the investigators found that horses received water from a well, from city water, or from a stream. The investigators wanted to know whether horses are equally likely to get water from each of those three sources. They collected data and observed the following values. Water Source Well City Water Stream Total Observed Count 62 43 31 136 To test the hypothesis that horses are equally likely to receive their water from a well, from city water, or from a stream, the investigators should use: a. a chi-square test for independence. b. a chi-square test for homogeneity. c. a chi-square goodness-of-fit test. d. None of the answer options is correct. ANSWER: c 15. A veterinary study of horses looked at water sources for horses, and the investigators found that horses received water from a well, from city water, or from a stream. The investigators wanted to know whether horses are equally likely to get water from each of those three sources. They collected data and observed the following values. Water Source Well City Water Stream Total Observed Count 62 43 31 136 The appropriate chi-square goodness-of-fit hypothesis is: a. H0: p1 = p2 = p3 = (1/3) vs. Ha: p1 p2 p3. b. H0: p1 = p2 = p3 = (1/3) vs. Ha: not all of p1, p2, p3 = (1/3). c. H0: p1 p2 p3 vs. Ha: p1 = p2 = p3. d. H0: p1

p3 vs. Ha: at least one of p1, p2, p3 = (1/3).

ANSWER: b 16. A veterinary study of horses looked at water sources for horses, and the investigators found that horses received water from a well, from city water, or from a stream. The investigators wanted to know whether horses are equally likely to get water from each of those three sources. They collected data and observed the following values. Water Source Well City Water Stream Total Observed Count 62 43 31 136 To test the hypothesis that horses are equally likely to get water from a well, from city water, or from a stream, the investigators conducted a chi-square goodness-of-fit test of the null hypothesis . The statistic they obtained was 10.78. The P-value for this statistic is 0.005. Therefore, they can conclude that: a. There is evidence that horses are more likely to have well water than to have either city water or water from streams. b. There is evidence that horses are more likely to have city water than well water. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 25 c. There is evidence that horses are not equally likely to have well water, city water, or water from streams. d. All of the answer options are correct. ANSWER: c 17. A veterinary study of horses looked at water sources for horses, and the investigators found that horses received water from a well, from city water, or from a stream. The investigators wanted to know whether horses are equally likely to get water from each of those three sources. They collected data and observed the following values. Water Source Well City Water Stream Total Observed Count 62 43 31 136 The chi-square goodness-of-fit test resulted in a chi-square statistic of 10.78 and a P-value of p = 0.005. The cell that contributed least to the chi-square goodness-of-fit statistic is: a. the city water cell, with (obs – exp)2/exp = 0.1201. b. the city water cell, with (obs – exp)2/exp = 1/3. c. the well water cell, with (obs – exp)2/exp = 6.13. d. the stream water cell, with (obs – exp)2/exp = 0.1201. ANSWER: a 18. Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 first years, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results are given in the following table. Strongly Opposed First Year Sophomore Junior Senior Yes 78 72 58 36 No 22 28 42 64 To compare the four classes (first year, sophomore, junior, and senior) with respect to their opinion regarding the proposed tuition increase (yes = opposed, no = not opposed), which distribution should we calculate? a. the joint distribution of year in school and opinion b. the marginal distribution of year in school c. the conditional distribution of opinion given year in school d. the conditional distribution of year in school given opinion ANSWER: c 19. Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 first years, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results are given in the following table. Strongly Opposed First Year Sophomore Junior Senior Yes 78 72 58 36 Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 25 No 22 28 42 64 Which hypotheses are being tested by the chi-square test? a. The null hypothesis is that the year in school and whether a student is strongly opposed are independent, and the alternative is that they are dependent. b. The null hypothesis is that the distributions of the number who are strongly opposed versus not strongly opposed are the same for a l l four years. The alternative is that these distributions are different. c. The null hypothesis is that the mean numbers of students who are strongly opposed are the same for each of the four years, and the alternative is that these means are different. d. The null hypothesis is that the distributions of the total number of students sampled in each of the four years are the same. The alternative is that these distributions are different. ANSWER: a 20. Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 first years, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results are given in the following table. Strongly Opposed First Year Sophomore Junior Senior Yes 78 72 58 36 No 22 28 42 64 Suppose we wish to test the null hypothesis that there is no association between student year in school and student opinion. Under the null hypothesis, what is the expected number of strongly opposed juniors? a. 58 b. 61 c. 75 d. 84 ANSWER: b 21. Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 first years, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results are given in the following table. Strongly Opposed First Year Sophomore Junior Senior Yes 78 72 58 36 No 22 28 42 64 What is the contribution to the chi-square statistic from the cell of strongly opposed juniors? a. 9 b. 0.1551 c. 3 d. 0.1475 Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 25 ANSWER: d 22. Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 first years, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results are given in the following table. Strongly Opposed First Year Sophomore Junior Senior Yes 78 72 58 36 No 22 28 42 64 The chi-square statistic for these data equals 43.9. The P-value is: a. greater than 0.10. b. between 0.05 and 0.10. c. less than 0.01. d. between 0.01 and 0.05. ANSWER: c 23. Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 first years, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results are given in the following table. Strongly Opposed First Year Sophomore Junior Senior Yes 78 72 58 36 No 22 28 42 64 The chi-square statistic for these data equals 43.9. What conclusion should be drawn from this chi-square test? a. There is strong evidence that year in school and opposition to the tuition increase are positively correlated. b. There is strong evidence that year in school and opposition to the tuition increase are dependent. c. There is some evidence that year in school and opposition to the tuition increase are positively correlated. d. There is no evidence that year in school and opposition to the tuition increase are related. ANSWER: b 24. A random sample of Ohio voters was asked about the number of cars or trucks they own (one, two, or at least three) and the type of community in which they live (rural, suburban, or urban). The two-way table follows. Community Type Number of Cars Rural Suburban Urban Total One 120 230 530 880 Two 470 620 390 1480 Three or More 335 420 85 840 Total 925 1270 1005 3200 Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 25 This is an r c table with dimensions: a. 3 3. b. 2 2. c. 2 3. d. 3 2. ANSWER: a 25. A random sample of Ohio voters was asked about the number of cars or trucks they own (one, two, or at least three) and the type of community in which they live (rural, suburban, or urban). The two-way table follows. Community Type Number of Cars Rural Suburban Urban Total One 120 230 530 880 Two 470 620 390 1480 Three or More 335 420 85 840 Total 925 1270 1005 3200 If community type and number of cars are independent, approximately how many urban residents would you expect to own at least three cars or trucks? a. 58 b. 85 c. 264 d. 335 ANSWER: c 26. A random sample of Ohio voters was asked about the number of cars or trucks they own (one, two, or at least three) and the type of community in which they live (rural, suburban, or urban). The two-way table follows. Community Type Number of Cars Rural Suburban Urban Total One 120 230 530 880 Two 470 620 390 1480 Three or More 335 420 85 840 Total 925 1270 1005 3200 The degrees of freedom for the chi-square test for this two-way table are: a. 2. b. 3. c. 4. d. 9. ANSWER: c 27. A random sample of Ohio voters was asked about the number of cars or trucks they own (one, two, or at least three) and the type of community in which they live (rural, suburban, or urban). The two-way table follows. Community Type Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 25 Number of Cars Rural Suburban Urban Total One 120 230 530 880 Two 470 620 390 1480 Three or More 335 420 85 840 Total 925 1270 1005 3200 Suppose we wish to test the null hypothesis that the distributions of car ownership a r e the same for a l l residence categories. Under the null hypothesis, the expected number of suburban residences with two cars is: a. 587.375. b. 651.445. c. 684.325. d. 710.765. ANSWER: a 28. A random sample of Ohio voters was asked about the number of cars or trucks they own (one, two, or at least three) and the type of community in which they live (rural, suburban, or urban). The two-way table follows. Community Type Number of Cars Rural Suburban Urban Total One 120 230 530 880 Two 470 620 390 1480 Three or More 335 420 85 840 Total 925 1270 1005 3200 The value of the chi-square statistic for testing the null hypothesis ( that there is no dependence between number of cars and type of community lived in) is 541.17. The P-value for the test is: a. greater than 0.10. b. between 0.05 and 0.10. c. between 0.01 and 0.05. d. less than 0.01. ANSWER: d 29. A random sample of Ohio voters was asked about the number of cars or trucks they own (one, two, or at least three) and the type of community in which they live (rural, suburban, or urban). The two-way table follows. Community Type Number of Cars Rural Suburban Urban Total One 120 230 530 880 Two 470 620 390 1480 Three or More 335 420 85 840 Total 925 1270 1005 3200 If the P-value is extremely small, what conclusion should be drawn from this chi-square test? a. There is strong evidence that number of cars and community type are positively correlated. b. There is strong evidence that number of cars and community type are dependent. c. There is some evidence that number of cars and community type are positively correlated. d. There is no evidence that number of cars and community type are related. Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 25 ANSWER: b 30. A random sample of Ohio voters was asked about the number of cars or trucks they own (one, two, or at least three) and the type of community in which they live (rural, suburban, or urban). The two-way table follows. Community Type Number of Cars Rural Suburban Urban Total One 120 230 530 880 Two 470 620 390 1480 Three or More 335 420 85 840 Total 925 1270 1005 3200 If the P-value is larger than 0.2, what conclusion should be drawn from this chi-square test? a. There is strong evidence that number of cars and community type are positively correlated. b. There is strong evidence that number of cars and community type are dependent. c. There is some evidence that number of cars and community type are positively correlated. d. There is no evidence that number of cars and community type are related. ANSWER: d 31. Do male and female primates treat female and male offspring differently? An observational study was conducted from 39 groups of three primates—one adult female, one adult male, and one toddler—in which the toddler was being carried. Recorded below is which adult (male or female) was carrying the toddler by the sex of the toddler. Sex of toddler

Sex of adult carrying toddler Male Female Male 8 17 Female 6 8 The proportion of times a male adult was carrying the toddler is: a. 0.32. b. 0.36. c. 0.57. d. 0.64. ANSWER: d 32. Do male and female primates treat female and male offspring differently? An observational study was conducted from 39 groups of three primates—one adult female, one adult male, and one toddler—in which the toddler was being carried. Recorded below is which adult (male or female) was carrying the toddler by the sex of the toddler. Sex of toddler

Sex of adult carrying toddler Male Female Male 8 17 Female 6 8 The proportion of all male toddlers that were carried by a male adult is: a. 0.32. b. 0.36. Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 25 c. 0.57. d. 0.64. ANSWER: c 33. Do male and female primates treat female and male offspring differently? An observational study was conducted from 39 groups of three primates—one adult female, one adult male, and one toddler—in which the toddler was being carried. Recorded below is which adult (male or female) was carrying the toddler by the sex of the toddler. Sex of toddler

Sex of adult carrying toddler Male Female Male 8 17 Female 6 8 Suppose we wish to test the null hypothesis that the proportion of male adults and the proportion of female adults carrying a toddler are the same, regardless of the sex of the toddler. Under the null hypothesis, the expected number of male adults who would be carrying a female toddler (according to the table) is: a. 8.97. b. 16.02. c. 18.97. d. 39. ANSWER: b 34. Do male and female primates treat female and male offspring differently? An observational study was conducted from 39 groups of three primates—one adult female, one adult male, and one toddler—in which the toddler was being carried. Recorded below is which adult (male or female) was carrying the toddler by the sex of the toddler. Sex of toddler

Sex of adult carrying toddler Male Female Male 8 17 Female 6 8 The numerical value of the chi-square statistic for testing independence of sex of the adult and sex of the toddler is: a. 0.46. b. 0.498. c. 3.94. d. 39.27. ANSWER: a 35. To study the export activity of manufacturing firms in Korea, questionnaires were mailed to an SRS of firms in each of three industries that export many of their products. The response rate was low, and to compare the industries, it is important that the response rates from the different industries be similar. Do the data in the Minitab output shown in the following table provide evidence of a difference in response rate among the four industries? The output includes the cell counts (O) and the expected cell counts (E), and the chi-square statistic is 4.754. Expected counts are below observed counts. Industry Responded Didn’t respond Total mailed Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 25 Machinery

O: 33 O: 94 E: 34.67 E: 92.33 Electrical equipment O: 21 O: 79 E: 27.30 E: 72.70 Precision instruments O: 41 O: 80 E: 33.03 E: 87.97 Given that this is an r c table, what are the values for r and c? a. 1 2 b. 2 3 c. 3 2 d. 3 3 ANSWER: c

127 100 121

36. To study the export activity of manufacturing firms in Korea, questionnaires were mailed to an SRS of firms in each of three industries that export many of their products. The response rate was low, and to compare the industries, it is important that the response rates from the different industries be similar. Do the data in the Minitab output shown in the following table provide evidence of a difference in response rate among the four industries? The output includes the cell counts (O) and the expected cell counts (E,) and the chi-square statistic is 4.754. Expected counts are below observed counts. Industry Responded Didn’t respond Total mailed Machinery O: 33 O: 94 127 E: 34.67 E: 92.33 Electrical equipment O: 21 O: 79 100 E: 27.30 E: 72.70 Precision instruments O: 41 O: 80 121 E: 33.03 E: 87.97 The appropriate number of degrees of freedom for the chi-square statistic is: a. 1. b. 2. c. 3. d. 4. ANSWER: b 37. To study the export activity of manufacturing firms in Korea, questionnaires were mailed to an SRS of firms in each of three industries that export many of their products. The response rate was low, and to compare the industries, it is important that the response rates from the different industries be similar. Do the data in the Minitab output shown in the following table provide evidence of a difference in response rate among the four industries? The output includes the cell counts (O) and the expected cell counts (E), and the chi-square statistic is 4.754. Expected counts are below observed counts. Industry Responded Didn’t respond Total mailed Machinery O: 33 O: 94 127 E: 34.67 E: 92.33 Electrical equipment O: 21 O: 79 100 Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 25 E: 27.30 E: 72.70 Precision instruments O: 41 O: 80 E: 33.03 E: 87.97 The overall response rate to the questionnaires was: a. 19%. b. 23%. c. 27%. d. 41%. ANSWER: c

121

38. To study the export activity of manufacturing firms in Korea, questionnaires were mailed to an SRS of firms in each of three industries that export many of their products. The response rate was low, and to compare the industries, it is important that the response rates from the different industries be similar. Do the data in the Minitab output shown in the following table provide evidence of a difference in response rate among the four industries? The output includes the cell counts (O) and the expected cell counts (E), and the chi-square statistic is 4.754. Expected counts are below observed counts. Industry Responded Didn’t respond Total mailed Machinery O: 33 O: 94 127 E: 34.67 E: 92.33 Electrical equipment O: 21 O: 79 100 E: 27.30 E: 72.70 Precision instruments O: 41 O: 80 121 E: 33.03 E: 87.97 Suppose we wish to test the null hypothesis that there is no association between industry and response rate. The P-value: a. is greater than 0.05. b. is between 0.025 and 0.05. c. is between 0.010 and 0.025. d. cannot be determined, because these are not the hypotheses being tested by the chi-square test. ANSWER: a 39. To study the export activity of manufacturing firms in Korea, questionnaires were mailed to an SRS of firms in each of three industries that export many of their products. The response rate was low, and to compare the industries, it is important that the response rates from the different industries be similar. Do the data in the Minitab output shown in the following table provide evidence of a difference in response rate among the four industries? The output includes the cell counts (O) and the expected cell counts (E), and the chi-square statistic is 4.754. Expected counts are below observed counts. Industry Responded Didn’t respond Total mailed Machinery O: 33 O: 94 127 E: 34.67 E: 92.33 Electrical equipment O: 21 O: 79 100 E: 27.30 E: 72.70 Precision instruments O: 41 O: 80 121 Copyright Macmillan Learning. Powered by Cognero.

Page 15

Name:

Class:

Date:

Chapter 25 E: 33.03 E: 87.97 Suppose we wish to test the null hypothesis that there is no association between industry and response rate. The P-value is greater than .1. What is the most appropriate conclusion? a. There is convincing evidence of no association between industry and response rate. b. There is convincing evidence of an association between industry and response rate. c. There is no convincing evidence of an association between industry and response rate. d. None of the above options is correct. ANSWER: c 40. Which of the following is required to conduct a chi-square test of independence? a. a contingency table containing observations made in terms of two categorical variables b. computations of the number of observations that would appear in each cell if the categorical variables were independent c. Both option (a) and option (b) are correct. d. Neither option (a) nor option (b) is correct. ANSWER: c 41. In 2013, there were many new studies published by psychology and neuroscience researchers on the science of happiness, meaning, and purpose. In one of those studies, a random sample of adults and a random sample of teens in northern California w e r e asked what they felt was the most important goal for them in life: to be happy, to live a meaningful life, or to know and pursue their life’s purpose. Results are presented in the following table. Teens Adults To be happy 192 590 To live a meaningful (but not necessarily happy) life 64 90 To know and pursue your purpose 188 80 Which hypotheses are being tested by the chi-square test? a. The null hypothesis is that the most important goal and age group are independent, and the alternative is that they are dependent. b. The null hypothesis is that the most important goal is the same for each age group, and the alternative is that the means differ. c. The distribution of most important goals is different for teens and adults. d. The distribution of age group is different for the three different goals. ANSWER: a 42. In 2013, there were many new studies published by psychology and neuroscience researchers on the science of happiness, meaning, and purpose. In one of those studies, a random sample of adults and a random sample of teens in northern California w e r e asked what they felt was the most important goal for them in life: to be happy, to live a meaningful life, or to know and pursue their life’s purpose. Results are presented in the following table. Teens Adults To be happy 192 590 To live a meaningful (but not necessarily happy) life 64 90 To know and pursue your purpose 188 80 Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 25 The data are going to be summarized by the researchers computing the conditional distributions of personal goals for teens and adults. For what proportion of adults is it most important to be happy? a. 0.222 b. 0.432 c. 0.754 d. 0.776 ANSWER: d 43. In 2013, there were many new studies published by psychology and neuroscience researchers on the science of happiness, meaning, and purpose. In one of those studies, a random sample of adults and a random sample of teens in northern California w e r e asked what they felt was the most important goal for them in life: to be happy, to live a meaningful life, or to know and pursue their life’s purpose. Results are presented in the following table. Teens Adults To be happy 192 590 To live a meaningful (but not necessarily happy) life 64 90 To know and pursue your purpose 188 80 The numerical value of the chi-square statistic for this table is: a. 7.76. b. 11.98. c. 32.21. d. 179.93. ANSWER: d 44. In 2013, there were many new studies published by psychology and neuroscience researchers on the science of happiness, meaning, and purpose. In one of those studies, a random sample of adults and a random sample of teens in northern California w e r e asked what they felt was the most important goal for them in life: to be happy, to live a meaningful life, or to know and pursue their life’s purpose. Results are presented in the following table. Teens Adults To be happy 192 590 To live a meaningful (but not necessarily happy) life 64 90 To know and pursue your purpose 188 80 The numerical value of the chi-square statistic for this table is 179.93. What is the most appropriate conclusion based on this? a. There is definitely a relationship between most important goal and age group. b. There is strong evidence of a relationship between most important goal and age group. c. There is no evidence of a relationship between most important goal and age group. d. There is evidence that adults are more concerned than teens with the goal “to be happy.” e. We reject the null hypothesis. f. We fail to reject the null hypothesis. ANSWER: b 45. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. Copyright Macmillan Learning. Powered by Cognero.

Page 17

Name:

Class:

Date:

Chapter 25 Accompanying parents were asked to classify a national brand of “fruit drink” (that contains less than 10% fruit juice) as 100% fruit juice, fruit juice mix, or no fruit juice at all. The investigators asked 150 parents, some of whom were new parents (meaning they had only one child) and some of whom were experienced parents (meaning they had at least two children). The table below contains the results. Juice ExperiencedNew Total Content Parent Parent 100% 15 15 30 1%–99% 55 25 80 0% 30 10 40 100 50 150 We are interested in comparing the responses of new and experienced parents. The number of conditional distributions we have is: a. two. b. three. c. four. d. six. ANSWER: a 46. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. Accompanying parents were asked to classify a national brand of “fruit drink” (that contains less than 10% fruit juice) as 100% fruit juice, fruit juice mix, or no fruit juice at all. The investigators asked 150 parents, some of whom were new parents (meaning they had only one child) and some of whom were experienced parents (meaning they had at least two children). The table below contains the results. Juice ExperiencedNew Total Content Parent Parent 100% 15 15 30 1%–99% 55 25 80 0% 30 10 40 100 50 150 The null hypothesis tests whether new parents and experienced parents have the same conditional distributions regarding classifying juice content. We ask whether the conditional probabilities classifying the drinks as 100% juice, 10% to 99% juice, or less than 10% juice are the same or different. The alternative tests whether they are different. Such an alternative: a. is one-sided. b. is two-sided. c. is many-sided. d. cannot be determined from the information given. ANSWER: c 47. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. Accompanying parents were asked to classify a national brand of “fruit drink” (that contains less than 10% fruit juice) as 100% fruit juice, fruit juice mix, or no fruit juice at all. The investigators asked 150 parents, some of whom were new parents (meaning they had only one child) and some of whom were experienced parents (meaning they had at least two children). The table below contains the results. Copyright Macmillan Learning. Powered by Cognero.

Page 18

Name:

Class:

Date:

Chapter 25 Juice Content 100% 1%–99% 0%

ExperiencedNew Total Parent Parent 15 15 30 55 25 80 30 10 40 100 50 150 The null hypothesis that the distribution of classifying the drink according to the three categories of juice content is the same for new and experienced parents is a test of: a. homogeneity. b. independence. c. concordance. d. discordance. ANSWER: b 48. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. Accompanying parents were asked to classify a national brand of “fruit drink” (that contains less than 10% fruit juice) as 100% fruit juice, fruit juice mix, or no fruit juice at all. The investigators asked 150 parents, some of whom were new parents (meaning they had only one child) and some of whom were experienced parents (meaning they had at least two children). The table below contains the results. Juice ExperiencedNew Total Content Parent Parent 100% 15 15 30 1%–99% 55 25 80 0% 30 10 40 100 50 150 To carry out a chi-square test of independence, we need to calculate the table of expected cell counts. Under the null hypothesis of independence, the expected numbers of new and experienced classifying the juice content as less than 10% juice are, respectively: a. 30 and 10. b. 20 and 20. c. 13 and 26. d. 26.67 and 13.33. ANSWER: d 49. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. Accompanying parents were asked to classify a national brand of “fruit drink” (that contains less than 10% fruit juice) as 100% fruit juice, fruit juice mix, or no fruit juice at all. The investigators asked 150 parents, some of whom were new parents (meaning they had only one child) and some of whom were experienced parents (meaning they had at least two children). The table below contains the results. Juice ExperiencedNew Total Content Parent Parent 100% 15 15 30 1%–99% 55 25 80 0% 30 10 40 Copyright Macmillan Learning. Powered by Cognero.

Page 19

Name:

Class:

Date:

Chapter 25 100 50 150 The chi-square statistic for the null hypothesis of independence has: a. 2 degrees of freedom. b. 3 degrees of freedom. c. 4 degrees of freedom. d. 6 degrees of freedom. ANSWER: a 50. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. Accompanying parents were asked to classify a national brand of “fruit drink” (that contains less than 10% fruit juice) as 100% fruit juice, fruit juice mix, or no fruit juice at all. The investigators asked 150 parents, some of whom were new parents (meaning they had only one child) and some of whom were experienced parents (meaning they had at least two children). The table below contains the results. Juice ExperiencedNew Total Content Parent Parent 100% 15 15 30 1%–99% 55 25 80 0% 30 10 40 100 50 150 What is the value of the chi-square statistic for the test of independence for this table? a. 3.84 b. 5.156 c. 7.239 d. 1.645 ANSWER: b 51. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. Accompanying parents were asked to classify a national brand of “fruit drink” (that contains less than 10% fruit juice) as 100% fruit juice, fruit juice mix, or no fruit juice at all. The investigators asked 150 parents, some of whom were new parents (meaning they had only one child) and some of whom were experienced parents (meaning they had at least two children). The table below contains the results. Juice ExperiencedNew Total Content Parent Parent 100% 15 15 30 1%–99% 55 25 80 0% 30 10 40 100 50 150 The P-value for the test for independence is p = 0.0759. This test is significant at = 0.10. To examine the source of the departure from independence, we should: a. compare selected proportions of new and experienced parent answers. b. compare expected and observed counts. c. look at terms of the chi-square statistic. d. All of the answer options are correct. Copyright Macmillan Learning. Powered by Cognero.

Page 20

Name:

Class:

Date:

Chapter 25 ANSWER: d 52. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. An initial study identified a lack of knowledge about the nutritional value of fruit drinks, and the participating parents were randomly assigned to an educational program (intervention, n = 75) or given a short informational brochure (control, n = 75). At the end of the program, they were asked to rate the juice content of a national brand of fruit drink that contained about 5% juice. Juice Group Group Total Content InterventionControl 5 15 20 30 45 75 40 15 55 75 75 150 The hypothesis to assess whether the intervention is effective is called: a. a test of homogeneity. b. a test of independence. c. a test of improvement. d. None of the answer options is correct. ANSWER: a 53. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. An initial study identified a lack of knowledge about the nutritional value of fruit drinks, and the participating parents were randomly assigned to an educational program (intervention, n = 75) or given a short informational brochure (control, n = 75). At the end of the program, they were asked to rate the juice content of a national brand of fruit drink that contained about 5% juice. Juice Group Group Total Content Intervention Control 5 15 20 30 45 75 40 15 55 75 75 150 What is the null hypothesis assessing the effectiveness of the intervention? a. There is no association between receiving the intervention and rating the drink correctly. b. The probability of rating the fruit drink as 100% juice, 10% to 90% juice, or less than 10% juice is the same whether the subjects are given the intervention or an informational brochure. c. The intervention leads to higher probabilities of correctly identifying the juice content. d. The group randomized to intervention will be better than the control goup at identifying the correct juice content. ANSWER: b 54. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. An initial study identified a lack of knowledge about the nutritional value of fruit drinks, and the participating parents were randomly assigned to an educational program (intervention, n = 75) or given a short informational Copyright Macmillan Learning. Powered by Cognero.

Page 21

Name:

Class:

Date:

Chapter 25 brochure (control, n = 75). At the end of the program, they were asked to rate the juice content of a national brand of fruit drink that contained about 5% juice. Juice Content

Group Group Intervention Control 5 15 30 45 40 15 75 75 The P-value for the test of homogeneity is: a. > 0.05. b. 0.05> p> 0.01. c. 0.01> p> 0.001. d. 0.001> p. ANSWER: d

Total 20 75 55 150

55. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. An initial study identified a lack of knowledge about the nutritional value of fruit drinks, and the participating parents were randomly assigned to an educational program (intervention, n = 75) or given a short informational brochure (control, n = 75). At the end of the program, they were asked to rate the juice content of a national brand of fruit drink that contained about 5% juice. Juice Content

Group Group Total InterventionControl 5 15 20 30 45 75 40 15 55 75 75 150 It is appropriate to use a chi-square test of homogeneity here because: a. all observed counts are at least 5. b. all expected counts are at least 1. c. all expected counts are above 5, so the criterion of all expected counts above 1 and no more than 20% of expected counts below 5 is met. d. all observed counts are above 5, so the criterion of all observed counts above 1 and no more than 20% of observed counts below 5 is met. ANSWER: c 56. A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. An initial study identified a lack of knowledge about the nutritional value of fruit drinks, and the participating parents were randomly assigned to an educational program (intervention, n = 75) or given a short informational brochure (control, n = 25). At the end of the program, they were asked to rate the juice content of a national brand of fruit drink that contained about 5% juice. The intervention was found to be effective, and, generally, only 5% of participants would subsequently classify a fruit drink with less than 5% juice as 100% juice, only about 35% would classify it as having between 10% and 90% fruit juice, and 60% would correctly identify it as having less than 10% fruit juice. The intervention was given to a group of parents in another country, and the Copyright Macmillan Learning. Powered by Cognero.

Page 22

Name:

Class:

Date:

Chapter 25 question was whether the parents from a different country would correctly classify the fruit drink with these same probabilities. This type of test is called: a. a test of homogeneity. b. a test of independence. c. a test for goodness-of-fit. d. a test for concordance. ANSWER: c

Page 23

Name:

Class:

Date:

Chapter 26 1. You can visit the official website of any large restaurant chain to examine the nutritional data for menu items. For fast-food restaurants, many menu items are high in fat, so most of their calorie content comes from fat (rather than from carbohydrates or protein). Here we investigate the relationship between the amount of fat in a menu item (in grams) and the number of calories. To predict the number of calories in a menu item given its fat content, we use the simple linear regression model: (average calories) = α + β (fat), where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation σ. The explanatory variable in this study is: a. number of calories. b. fat content (grams of fat). c. the slope, β. d. 12.546. ANSWER: b 2. You can visit the official website of any large restaurant chain to examine the nutritional data for menu items. For fast-food restaurants, many menu items are high in fat, so most of their calorie content comes from fat (rather than from carbohydrates or protein). Here we investigate the relationship between the amount of fat in a menu item (in grams) and the number of calories. To predict the number of calories in a menu item given its fat content, we use the simple linear regression model: (average calories) = α + β (fat), where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation σ. At one major fast-food restaurant chain, there were 26 items listed under the heading of “Sandwiches” (which includes hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model to the data using the method of least squares. We treat these 26 menu items (which came from one restaurant) as a sample from the population of all sandwich items at all fast-food restaurants. This assumption is probably dubious. The following results were obtained from software: , s = 43.5747 Parameter

Parameter estimate

Std. err. of parameter est.

151.092 30.082 12.546 1.213 The quantity s = 43.5747 is an estimate of the standard deviation of the deviations in the simple linear regression model. The degrees of freedom for s are: a. 3. b. 12. c. 24. d. 26. ANSWER: c 3. You can visit the official website of any large restaurant chain to examine the nutritional data for menu items. For fast-food restaurants, many menu items are high in fat, so most of their calorie content comes from fat (rather than from carbohydrates or protein). Here we investigate the relationship between the amount of fat in a menu item (in grams) and the number of calories. To predict the number of calories in a menu item given its fat content, we use the simple linear regression model: , where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation . At one major fast-food restaurant chain, there were 26 items listed under the heading of “Sandwiches” (which includes hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model to the data using the method of least squares. We treat these 26 menu items (which came from one restaurant) as a sample Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 26 from the population of all sandwich items at all fast-food restaurants. This assumption is probably dubious. The following results were obtained from software. s = 43.5747 Parameter

Parameter estimate

Std. err. of parameter est.

151.092 30.082 12.546 1.213 The slope of the least-squares regression line is: a. 151.09. b. 12.546. c. 0.846. d. None of the answer options is correct. ANSWER: b 4. You can visit the official website of any large restaurant chain to examine the nutritional data for menu items. For fast-food restaurants, many menu items are high in fat, so most of their calorie content comes from fat (rather than from carbohydrates or protein). Here we investigate the relationship between the amount of fat in a menu item (in grams) and the number of calories. To predict the number of calories in a menu item given its fat content, we use the simple linear regression model: , where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation . At one major fast-food restaurant chain, there were 26 items listed under the heading of “Sandwiches” (which includes hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model to the data using the method of least squares. We treat these 26 menu items (which came from one restaurant) as a sample from the population of all sandwich items at all fast-food restaurants. This assumption is probably dubious. The following results were obtained from software: , s = 43.5747 Parameter

Parameter estimate

151.092 12.546 Suppose the researchers test the hypotheses

Std. err. of parameter est.

30.082 1.213 . The value of the t statistic for this test is:

a. 10.343. b. 5.023. c. −5.023. d. −10.343. ANSWER: a 5. You can visit the official website of any large restaurant chain to examine the nutritional data for menu items. For fast-food restaurants, many menu items are high in fat, so most of their calorie content comes from fat (rather than from carbohydrates or protein). Here we investigate the relationship between the amount of fat in a menu item (in grams) and the number of calories. To predict the number of calories in a menu item given its fat content, we use the simple linear regression model: , where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation . At one major fast-food restaurant chain, there were 26 items listed under the heading of “Sandwiches” (which includes Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 26 hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model to the data using the method of least squares. We treat these 26 menu items (which came from one restaurant) as a sample from the population of all sandwich items at all fast-food restaurants. This assumption is probably dubious. Suppose the researchers test the hypotheses . The value of the t statistic for this test is greater than 5. The P-value corresponding to the test of the hypotheses is: a. more than 0.02. b. between 0.001 and 0.02. c. between 0.0005 and 0.001. d. less than 0.0005. ANSWER: d 6. To predict the number of calories in a menu item given its fat content, we use the simple linear regression model: , where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation . At one major fast-food restaurant chain, there were 26 items listed under the heading of “Sandwiches” (which includes hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model to the data using the method of least squares. We treat these 26 menu items (which came from one restaurant) as a sample from the population of all sandwich items at all fast-food restaurants. This assumption is probably dubious. The following results were obtained from software: , s = 43.5747 Parameter

Parameter estimate

Std. err. of parameter est.

151.092 30.082 12.546 1.213 A 95% confidence interval for the mean number of calories per gram of fat in sandwich menu items at fastfood restaurants is: a. 99.627 to 202.553. b. 89.007 to 213.172. c. 10.169 to 14.923. d. 10.042 to 15.05. ANSWER: d 7. To predict the number of calories in a menu item given its fat content, we use the simple linear regression model: , where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation . At one major fast-food restaurant chain, there were 26 items listed under the heading of “Sandwiches” (which includes hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model to the data using the method of least squares. We treat these 26 menu items (which came from one restaurant) as a sample from the population of all sandwich items at all fast-food restaurants. This assumption is probably dubious. The following results were obtained from software: , s = 43.5747 Parameter

Parameter estimate

Std. err. of parameter est.

151.092 30.082 12.546 1.213 The sample correlation between calories and fat in fast-food sandwich menu items is: Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 26 a. 0.716. b. 0.92. c. −0.92. d. −0.716. ANSWER: b 8. The following is a plot of the residuals versus fat for 26 menu items at a fast-food restaurant.

Which of the following statements is supported by this plot? a. A linear model is appropriate for explaining the relationship between the explanatory and response variables for this case. b. There is evidence that the deviations described by the model are not Normal in distribution. c. The abundance of outliers and influential observations in the plot means that the assumptions for regression are clearly violated. d. None of the answer options is correct. ANSWER: a 9. Frequent food questionnaires (FFQs) are often given to large groups of people to obtain information on their dietary habits. Study participants are asked about the frequency with which they consume certain goods. Another method to obtain information on foods consumed is a food diary. People are asked to record every type of food and amount consumed for a few days. Food diaries are more difficult to obtain, and response rates are lower than for FFQs. A study was conducted to see how well FFQs predict food consumed based on food diaries. In this study, the explanatory variable is: a. the amount of food consumed. b. the amount of food consumed according to the food diary. c. the amount of food consumed according to the FFQ. d. dependent on the response. ANSWER: c Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 26 10. Frequent food questionnaires (FFQs) are often given to large groups of people to obtain information on their dietary habits. Study participants are asked about the frequency with which they consume certain goods. Another method to obtain information on foods consumed is a food diary. People are asked to record every type of food and amount consumed for a few days. Food diaries are more difficult to obtain, and response rates are lower than for FFQs. A study was conducted to see how well frequent food questionnaires predict food consumed based on food diaries. The regression of alcohol consumption FFQ on an alcohol consumption food diary had an intercept of a = 2.96 and a slope of b = 0.67. The predicted number of drinks consumed in the food diary, if the FFQ states 5 drinks, is: a. 6.31. b. 0.67. c. 2.96. d. 5. ANSWER: a 11. Forced expiratory volume (FEV) is the volume of exhaled air, and it is related to lung size as well as to lung function. FEV is typically lower in persons with impaired lung function due to disease. The residual plots below are from two regressions: The first plot is from regressing height on FEV, and the second is from regressing height on log(FEV).

Page 5

Name:

Class:

Date:

Chapter 26

Page 6

Name:

Class:

Date:

Chapter 26

Based on these plots, which statement is correct? a. The residual plot for height on FEV shows a nonconstant variance. b. The residual plot for height regressed on FEV shows a nonlinear pattern. c. The residual plot for the regression of height on log(FEV) shows a linear pattern. d. All of the answer options are correct. ANSWER: d 12. Forced expiratory volume (FEV) is the volume of exhaled air, and it is related to lung size as well as to lung function. It is typically lower in persons with impaired lung function due to disease. A regression of height (in inches) on FEV (in liters) showed a nonlinear pattern. Therefore, height was regressed on log(FEV) (natural log), and the residual plot showed a much improved fit. The intercept a and slope b from the regression of height on log(FEV) are a = −2.2 and b = 0.06. A 5-foot-tall person is predicted to have a lung volume of: a. 1.4 liters. b. 4.1 liters. c. 2.2 liters. Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 26 d. 0.06 liters. ANSWER: b 13. Forced expiratory volume (FEV) is the volume of exhaled air, and it is related to lung size as well as to lung function. It is typically lower in persons with impaired lung function due to disease. A regression of height (in inches) on FEV (in liters) showed a nonlinear pattern. Therefore, height was regressed on log(FEV) (natural log), and the residual plot showed a much improved fit. The intercept a and slope b from the regression of height on log(FEV) are a = −2.2 and b = 0.06. The correlation for this regression is: a. positive. b. negative. c. zero. d. There is not enough information to determine the answer. ANSWER: a 14. The scatterplot below suggests a linear relationship between the age (in years) of an antique clock and its sale price (in euros) at auction. The data are age and sale price for 11 antique clocks sold at a recent auction.

We fit the least-squares regression line to the model:

, where the deviations are

assumed to be independent and Normally distributed, with mean 0 and standard deviation . A summary of the output is provided. , s = 33.1559 Parameter

Parameter estimate

Std. err. of parameter est.

27.73 1.893

34.84 0.267

The approximate intercept of the least-squares regression line is: a. 34.84. b. 1.893. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 26 c. 27.73 d. 0.267. ANSWER: c 15. The scatterplot below suggests a linear relationship between the age (in years) of an antique clock and its sale price (in euros) at auction. The data are age and sale price for 11 antique clocks sold at a recent auction.

We fit the least-squares regression line to the model:

, where the deviations are

assumed to be independent and Normally distributed, with mean 0 and standard deviation . A summary of the output is provided. , s = 33.1559 Parameter

Parameter estimate

Std. err. of parameter est.

27.73 1.893

34.84 0.267

An approximate 95% confidence interval for the slope in the simple linear regression model is: a. 1.289 to 2.497 euros. b. 1.289 to 2.497 euros per year. c. 1.289 to 2.497 years per euro. d. None of the answer options is correct. ANSWER: b 16. The scatterplot below suggests a linear relationship between the age (in years) of an antique clock and its sale price (in euros) at auction. The data are age and sale price for 11 antique clocks sold at a recent auction.

Page 9

Name:

Class:

Date:

Chapter 26

We fit the least-squares regression line to the model:

, where the deviations are

assumed to be independent and Normally distributed, with mean 0 and standard deviation . A summary of the output is provided. , s = 33.1559 Parameter

Parameter estimate

Std. err. of parameter est.

27.73 1.893

34.84 0.267

Suppose the researchers test the hypotheses

. The value of the t statistic for this test is:

a. −7.09. b. 1.893. c. 7.09. d. 0.796. ANSWER: c 17. The scatterplot below suggests a linear relationship between the age (in years) of an antique clock and its sale price (in euros) at auction. The data are age and sale price for 11 antique clocks sold at a recent auction.

Page 10

Name:

Class:

Date:

Chapter 26

We fit the least-squares regression line to the model price =

, where the deviations are assumed to be

independent and Normally distributed, with mean 0 and standard deviation . A summary of the output is given. , s = 33.1559 Parameter

Parameter estimate

Std. err. of parameter est.

27.73 1.893

34.84 0.267

The correlation between the age of the antique clock and its auction price is: a. −0.921. b. 0.921. c. −0.719. d. 0.719. ANSWER: b 18. A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used: (mean profits) = , where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. , s = 466.2 Parameter Parameter est. Std. err. of parameter est. −176.644 61.16 0.092498 0.0075 The approximate slope of the least-squares regression line is: Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 26 a. 0.09. b. 0.0075. c. −176.64. d. 61.16. ANSWER: a 19. A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used: (mean profits) = , where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. , s = 466.2 Parameter Parameter est. Std. err. of parameter est. −176.644 61.16 0.092498 0.0075 An approximate 90% confidence interval for the slope in the simple linear regression model is: a. −176.66 to −176.63. b. 0.079 to 0.106. c. 0.071 to 0.114. d. None of the answer options is correct. ANSWER: b 20. A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used: (mean profits) = , where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. , s = 466.2 Parameter Parameter est. Std. err. of parameter est. −176.644 61.16 0.092498 0.0075 Suppose the researchers test the hypotheses . The P-value of the test is: a. greater than 0.10. b. between 0.10 and 0.05. c. between 0.05 and 0.01. d. less than 0.01. ANSWER: d 21. A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 26 (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used: profits = , where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. , s = 466.2 Parameter Parameter est. Std. err. of parameter est. −176.644 61.16 0.092498 0.0075 Is there evidence of a straight-line relationship between sales and profits? a. Yes, because the slope of the least-squares line is positive. b. Yes, because the P-value for testing whether the slope is 0 is quite large. c. Yes, because the P-value for testing whether the slope is 0 is quite small. d. It is impossible to say, because we are not given the actual value of the correlation. ANSWER: c 22. Suppose we wish to predict the profits (in hundreds of thousands of dollars) for companies that had sales (in hundreds of thousands of dollars) of 500 units. A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used: (mean profits) = , where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. , s = 466.2 Parameter Parameter est. Std. err. of parameter est. −176.644 61.16 0.092498 0.0075 A 95% confidence interval for the average profit of companies with 500 units of sales is: a. −1066.4 to 805.6. b. −248.5 to −12.3. c. −189.7 to −71.1. d. 400.7 to 559.3. ANSWER: b 23. Suppose we wish to predict the profits (in hundreds of thousands of dollars) for companies that had sales (in hundreds of thousands of dollars) of 500 units. A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used: (mean profits) = , where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. For a specific company, we predict the profits using statistical software to use our least-squares line to make a prediction and obtain the following output. Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 26 Sales Predict St. dev. mean predict 500 −130.4 59.3 A 95% interval for this prediction is: a. −1066.4 to 805.6. b. −248.5 to −12.3. c. −189.7 to −71.1. d. 400.7 to 559.3. ANSWER: a

95% C.I. (−248.5, −12.3)

95% P.I. (−1066.4, 805.6)

24. The following is a scatterplot of a company’s profits versus their sales (in dollars). Each point on the plot represents profits and sales during one of the months in the sample.

Which of the following statements is supported by the plot? a. There is no striking evidence that the assumptions for regression are violated, and there is a clear, straight-line trend. b. There are very influential observations suggesting that the least-squares regression line must be interpreted with extreme caution. c. The plot contains dramatic evidence that the standard deviation of the response about the true regression line is not even approximately the same everywhere. d. The plot contains many fewer points than are needed to fit the least-squares regression line; obviously, there is a major error present. ANSWER: b 25. The following is a scatterplot of a company’s profits versus their sales (in dollars). Each point on the plot Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 26 represents profits and sales during one of the months in the sample.

What should you do about the two points that represent profits for sales of $20K or more? a. The two points are clearly outliers and should be eliminated from the data set prior to analysis. b. The two points are clearly outliers, and the point in the far upper right should be eliminated from the data set prior to analysis, because it is such an extreme outlier. c. The two points may or may not be outliers, but they are definitely influential points. Prior to analysis, the data should be inspected (if possible) to validate that these points are accurate and are not the result of faulty data entry or other issues. d. There is no need to do anything prior to analysis—all data points are equally valid and cannot simply be eliminated. ANSWER: c 26. The following is a scatterplot of a company’s profits versus their sales (in dollars). Each point on the plot represents profits and sales during one of the months in the sample.

Page 15

Name:

Class:

Date:

Chapter 26

Assume that the point in the far upper right was erroneous, resulting from inaccurate data entry. Which of the following statements will be correct once that point is removed from the regression analysis? a. The slope will decrease but will remain positive. b. The slope will decrease and may become negative. c. There will still be a clear linear trend, because the points are randomly scattered above and below the zero line. d. The assumptions for regression will be violated and there can be no definitive, straight-line trend. ANSWER: a 27. A study of obesity risk in children in a Head Start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 130 children. The researchers used a linear regression model for the prediction of BMI percentile. Which of the following is not a condition for linear regression? a. BMI percentile varies according to a Normal distribution for a fixed food score. b. The variation of BMI percentile around the regression line is the same for all food scores. c. Mean BMI percentile increases for all children over the 18-month period. d. Mean BMI percentile varies linearly with the food score. ANSWER: c 28. A study of obesity risk in children in a Head Start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 130 children. The researchers used a linear regression model for the prediction of BMI percentile. The food scores ranged from 45 to 245. Fifteen children had a food score of 170. A boxplot of those Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 26 15 children showed BMI percentile to be very skewed. This information is: a. irrelevant, because the relationship between food score and BMI percentile is being studied, not the BMI percentile values themselves. b. important, because one requirement for the validity of inference is that BMI percentile be Normally distributed at each value of the food score. c. irrelevant, as long as variation about the regression line is constant. d. probably due to some outlier and should simply be ignored. ANSWER: b 29. A study of obesity risk in children in a Head Start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 20 children. The researchers used a linear regression model for the prediction of BMI percentile. The food scores ranged from 45 to 245.

What is important to determine if a linear regression model can be used? a. scatter of points around a straight line b. even spread at each value of food score c. correlation between BMI percentiles for subjects with similar food scores Copyright Macmillan Learning. Powered by Cognero.

Page 17

Name:

Class:

Date:

Chapter 26 d. scatter of points around a straight line AND even spread at each value of food score ANSWER: d 30. A study of obesity risk in children in a Head Start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 20 children. The researchers used a linear regression model for the prediction of BMI percentile. The food scores ranged from 45 to 245. The regression line that is calculated by standard regression programs or by hand is called the least-squares line because it: a. minimizes the distances of actual BMI percentiles from the regression line. b. minimizes the squared distances of the actual BMI percentiles from the regression line. c. minimizes sum of the squared distances of the actual BMI percentiles from the regression line. d. minimizes the sum of the distances of the actual BMI percentiles from the regression line. ANSWER: c 31. A study of obesity risk in children in a Head Start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 20 children. The researchers used a linear regression model for the prediction of BMI percentile. The food scores ranged from 45 to 245. The appropriate regression model has: a. one unknown parameter to be estimated. b. two unknown parameters to be estimated. c. three unknown parameters to be estimated. d. four unknown parameters to be estimated. ANSWER: c 32. A study of obesity risk in children in a Head Start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 20 children. The researchers used a linear regression model for the prediction of BMI percentile with food scores ranging between 45 and 245. The least-squares estimates were slope = 0.29 and intercept = 18.3. If Child A has a food score of 145 and Child B has a food score of 180, then the difference in predicted BMI percentile between Child B and Child A is: a. 10.15. b. 0.29. c. 18.3. d. 28.45. ANSWER: a 33. A study of obesity risk in children in a Head Start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 20 children. The researchers used a linear regression model for the prediction of BMI percentile. The food scores ranged from 45 to 245. The linear regression had slope = 0.29 and intercept = 18.3. The average BMI percentile for a child with food score 150 equals 61.8. According to our model, an individual child with food score 150 will be predicted to have a BMI percentile of: a. 18.3. Copyright Macmillan Learning. Powered by Cognero.

Page 18

Name:

Class:

Date:

Chapter 26 b. 61.8. c. 80.1. d. 43.5. ANSWER: b 34. A study of obesity risk in children in a Head Start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 20 children. The researchers used a linear regression model for the prediction of BMI percentile. The food scores ranged from 45 to 245. Two computer programs were used to obtain their regression model and related calculations. The programs also provided two intervals for a child with food score 150. Interval I1 = (56.13, 67.35) and interval I2 = (36.35, 87.13). These intervals, respectively, are called: a. the regression and residual intervals. b. the mean interval and the regression interval. c. the interval for prediction of value and the interval for regression. d. the interval for mean BMI and the prediction interval for a child with food score 150. ANSWER: d 35. A study of obesity risk in children in a Head Start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 20 children. The researchers used a linear regression model for the prediction of BMI percentile. The food scores ranged from 45 to 245. The least-squares estimate for the slope was 0.29 with standard error SE = 0.046. The t statistic for the hypothesis is given by: a. 1.96. b. 6.3. c. 2.39. d. 4.62. ANSWER: b 36. A study of obesity risk in children in a head start program used a food score calculated from a 45-question food survey to predict body mass index (BMI) percentile in these children 18 months after the initial survey. The study enrolled 20 children. The researchers used a linear regression model for the prediction of BMI percentile. The food scores ranged from 45 to 245. The residual plot below was obtained by the researchers.

Page 19

Name:

Class:

Date:

Chapter 26

The plot does not show any obvious model violations because: a. there is no pattern in the plot. b. the residuals are spread evenly around the horizontal line through zero. c. there are no obvious outliers. d. All of the answer options are correct. ANSWER: d

Page 20

Name:

Class:

Date:

Chapter 27 1. Investigators gave caffeine to fruit flies to see whether it affected their rest. The four treatments were: a control, a low caffeine dose, a medium caffeine dose, and a higher caffeine dose. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest for each fly over a 24-hour period were recorded. Assume the data that follow are four independent SRSs (one from each of the four populations of caffeine levels) and that the distribution of the minutes of rest is Normal. Treatment Minutes of rest Minutes of rest Minutes of rest (Fly (Fly 1) (Fly 2) 3) Control 450 413 418 Low dose 466 422 435 Medium dose 421 453 419 High dose 364 330 389 The numerator degrees of freedom for the ANOVA F test are: a. 2. b. 3. c. 8. d. 11. ANSWER: b 2. Investigators gave caffeine to fruit flies to see whether it affected their rest. The four treatments were: a control, a low caffeine dose, a medium caffeine dose, and a higher caffeine dose. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest for each fly over a 24-hour period were recorded. Assume the data that follow are four independent SRSs (one from each of the four populations of caffeine levels) and that the distribution of the minutes of rest is Normal. Treatment Minutes of rest Minutes of rest Minutes of rest (Fly (Fly 1) (Fly 2) 3) Control 450 413 418 Low dose 466 422 435 Medium dose 421 453 419 High dose 364 330 389 The denominator degrees of freedom for the ANOVA F test are: a. 2. b. 3. c. 8. d. 11. ANSWER: c 3. Investigators gave caffeine to fruit flies to see whether it affected their rest. The four treatments were: a control, a low caffeine dose, a medium caffeine dose, and a higher caffeine dose. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest for each fly over a 24-hour period were recorded. Assume the data that follow are four independent SRSs (one from each of the four populations of caffeine levels) and that the distribution of the minutes of rest is Normal. Treatment Minutes of rest Minutes of rest Minutes of rest (Fly (Fly 1) (Fly 2) 3) Control 450 413 418 Low dose 466 422 435 Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 27 Medium dose 421 453 419 High dose 364 330 389 A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups. One-way ANOVA: Rest versus Caffeine Source D SS MS F P Caffeine 11976 Error 538.75 Total Level N Mean StDev Control 3 427.00 20.07 Low 3 441.00 22.61 Medium 3 431.00 19.08 High 3 361.00 29.61 For this example, we notice that: a. this is an observational study. b. the data show evidence of a violation of the assumption that the four populations have the same standard deviation. c. an ANOVA F test can be used on these data because the sample sizes are equal. d. None of the answer options is correct. ANSWER: d 4. Investigators gave caffeine to fruit flies to see whether it affected their rest. The four treatments were: a control, a low caffeine dose, a medium caffeine dose, and a higher caffeine dose. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest for each fly over a 24-hour period were recorded. Assume the data that follow are four independent SRSs (one from each of the four populations of caffeine levels) and that the distribution of the minutes of rest is Normal. The appropriate null hypothesis for the ANOVA F test is that: a. the population mean rest is the same for all four levels of caffeine. b. the population mean rest is increasing as the caffeine level gets larger. c. the population mean rest is decreasing as the caffeine level gets larger. d. the population mean rest is largest for the high level of caffeine. ANSWER: a 5. Investigators gave caffeine to fruit flies to see whether affected their rest. The four treatments were: a control, a low caffeine dose, a medium caffeine dose, and a higher caffeine dose. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest for each fly over a 24-hour period were recorded. Assume the data that follow are four independent SRSs (one from each of the four populations of caffeine levels) and that the distribution of the minutes of rest is Normal. A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups. One-way ANOVA: Rest versus Caffeine Source D SS MS F P Caffeine 11976 Error 538.75 Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 27 Total Level N Mean StDev Control 3 427.00 20.07 Low 3 441.00 22.61 Medium 3 431.00 19.08 High 3 361.00 29.61 The pooled standard deviation is: a. 22.84. b. 23.21. c. 91.37. d. 2154.82. ANSWER: b 6. Investigators gave caffeine to fruit flies to see whether it affected their rest. The four treatments were: a control, a low caffeine dose, a medium caffeine dose, and a higher caffeine dose. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest for each fly over a 24-hour period were recorded. Assume the data that follow are four independent SRSs (one from each of the four populations of caffeine levels) and that the distribution of the minutes of rest is Normal. Treatment Minutes of rest Minutes of rest Minutes of rest (Fly (Fly 1) (Fly 2) 3) Control 450 413 418 Low dose 466 422 435 Medium dose 421 453 419 High dose 364 330 389 A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups. One-way ANOVA: Rest versus Caffeine Source D SS MS F P Caffeine 11976 Error 538.75 Total Level N Mean StDev Control 3 427.00 20.07 Low 3 441.00 22.61 Medium 3 431.00 19.08 High 3 361.00 29.61 The value of the ANOVA F statistic for testing equality of the population means of the average rest time for the four caffeine levels is: a. 2.78. b. 4.73. c. 4.82. d. 7.41. ANSWER: d 7. Investigators gave caffeine to fruit flies to see whether it affected their rest. The four treatments were: a Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 27 control, a low caffeine dose, a medium caffeine dose, and a higher caffeine dose. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest for each fly over a 24-hour period were recorded. Assume the data that follow are four independent SRSs (one from each of the four populations of caffeine levels) and that the distribution of the minutes of rest is Normal. Treatment Minutes of rest Minutes of rest Minutes of rest (Fly (Fly 1) (Fly 2) 3) Control 450 413 418 Low dose 466 422 435 Medium dose 421 453 419 High dose 364 330 389 A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups. One-way ANOVA: Rest versus Caffeine Source D SS MS F P Caffeine 11976 Error 538.75 Total Level N Mean StDev Control 3 427.00 20.07 Low 3 441.00 22.61 Medium 3 431.00 19.08 High 3 361.00 29.61 The P-value of this test is: a. greater than 0.1. b. between 0.05 and 0.1. c. less than 0.05. d. It is not possible to determine the P-value from the information provided. ANSWER: c 8. Investigators gave caffeine to fruit flies to see whether it affected their rest. The four treatments were: a control, a low caffeine dose, a medium caffeine dose, and a higher caffeine dose. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest for each fly over a 24-hour period were recorded. Assume the data that follow are four independent SRSs (one from each of the four populations of caffeine levels) and that the distribution of the minutes of rest is Normal. Treatment Minutes of rest Minutes of rest Minutes of rest (Fly (Fly 1) (Fly 2) 3) Control 450 413 418 Low dose 466 422 435 Medium dose 421 453 419 High dose 364 330 389 A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups. One-way ANOVA: Rest versus Caffeine Source D SS MS F P Caffeine 11976 Error 538.75 Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 27 Total Level N Mean StDev Control 3 427.00 20.07 Low 3 441.00 22.61 Medium 3 431.00 19.08 High 3 361.00 29.61 What conclusion would you draw from this test? a. There is evidence that all of the groups have the same mean. b. There is no evidence to suggest that the groups have different means. c. There is evidence that all of the group means are different. d. There is evidence that at least one of the groups has a mean that is different. ANSWER: d 9. A traffic engineer wanted to study the delays in traffic movement at three traffic signal locations, as measured by the number of seconds before the first car clears the intersection. The engineer selected three locations randomly from all the signals with a similar amount of traffic and number of lanes, and similar turn and signal patterns. The engineer collected the following data on eight randomly chosen days. Location Mean Std. dev. n Site 1 39.30 17.05 8 Site 2 11.38 10.14 8 Site 3 27.45 5.44 8 The engineer obtains a statistics book and, after investigating, decides that analysis of variance is the appropriate method for this problem. Which of these hypotheses should be used to investigate whether mean delay times are the same at all three locations? a. b. c. d. None of the answer options is correct. ANSWER: d 10. A traffic engineer wanted to study the delays in traffic movement at three traffic signal locations, as measured by the number of seconds before the first car clears the intersection. The engineer selected three locations randomly from all the signals with a similar amount of traffic and number of lanes, and similar turn and signal patterns. The engineer collected the following data on eight randomly chosen days. Location Mean Std. dev. n Site 1 39.30 17.05 8 Site 2 11.38 10.14 8 Site 3 27.45 5.44 8 The engineer obtains a statistics book and, after investigating, decides that analysis of variance is the appropriate method for this problem. What conditions have to hold for analysis of variance to be valid? a. b. c. s1 = s2 = s3 Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 27 d. s1 > 2s2 > 2s3 ANSWER: a 11. A traffic engineer wanted to study the delays in traffic movement at three traffic signal locations, as measured by the number of seconds before the first car clears the intersection. The engineer selected three locations randomly from all the signals with a similar amount of traffic and number of lanes, and similar turn and signal patterns. The engineer collected the following data on eight randomly chosen days. Location Mean Std. dev. n Site 1 39.30 17.05 8 Site 2 11.38 10.14 8 Site 3 27.45 5.44 8 The engineer obtains a statistics book and, after investigating, decides that analysis of variance is the appropriate method for this problem. The pooled standard deviation for this problem is: a. 1571.5. b. 141. c. 11.88. d. 10.88. ANSWER: c 12. A traffic engineer wanted to study the delays in traffic movement at three traffic signal locations, as measured by the number of seconds before the first car clears the intersection. The engineer selected three locations randomly from all the signals with a similar amount of traffic and number of lanes, and similar turn and signal patterns. The engineer collected the following data on eight randomly chosen days. Location Mean Std. dev. n Site 1 39.30 17.05 8 Site 2 11.38 10.14 8 Site 3 27.45 5.44 8 The engineer obtains a statistics book and, after investigating, decides that analysis of variance is the appropriate method for this problem. Using technology, the engineer obtains a P-value = 0.001. This tells the engineer that: a. there is evidence that the mean delays at all three sites are different. b. there is evidence that the mean delay at Site 2 is the smallest and the mean delays at Sites 1 and 3 are the same. c. there is evidence that at least one site has a mean delay that is different. d. there is evidence that the mean delays at all three sites are the same, because it is rare to have different delay times. ANSWER: c 13. At what age do babies learn to crawl? Does it depend on the time of year that the babies were born? Data were collected from parents who brought their babies to the University of Denver’s Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of four feet within one minute. The resulting data were grouped by month of birth: January, May, and September. Crawling age is given in weeks. Assume that the data can be considered as three independent random samples (one from each of the populations composed of babies born in that particular month) and that the populations of crawling ages have Normal Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 27 distributions. Birth month Mean Std. dev. n January 29.84 7.08 32 May 28.58 8.07 27 September 33.83 6.93 38 The numerator degrees of freedom for the ANOVA F test are: a. 2. b. 3. c. 94. d. 96. ANSWER: a 14. At what age do babies learn to crawl? Does it depend on the time of year that the babies were born? Data were collected from parents who brought their babies to the University of Denver’s Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of four feet within one minute. The resulting data were grouped by month of birth: January, May, and September. Crawling age is given in weeks. Assume that the data can be considered as three independent random samples (one from each of the populations composed of babies born in that particular month) and that the populations of crawling ages have Normal distributions. Birth month Mean Std. dev. n January 29.84 7.08 32 May 28.58 8.07 27 September 33.83 6.93 38 The denominator degrees of freedom for the ANOVA F test are: a. 2. b. 3. c. 94. d. 96. ANSWER: c 15. At what age do babies learn to crawl? Does it depend on the time of year that the babies were born? Data were collected from parents who brought their babies to the University of Denver’s Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of four feet within one minute. The resulting data were grouped by month of birth: January, May, and September. Crawling age is given in weeks. Assume that the data can be considered as three independent random samples (one from each of the populations composed of babies born in that particular month) and that the populations of crawling ages have Normal distributions. The alternative hypothesis for the ANOVA F test is: a. The mean age at which babies learn to crawl is highest in September. b. The mean age at which babies learn to crawl is different for the three birth months. c. The mean age at which babies learn to crawl is the same for January and May. d. None of the answer options is correct. Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 27 ANSWER: b 16. At what age do babies learn to crawl? Does it depend on the time of year that the babies were born? Data were collected from parents who brought their babies to the University of Denver’s Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of four feet within one minute. The resulting data were grouped by month of birth: January, May, and September. Crawling age is given in weeks. Assume that the data can be considered as three independent random samples (one from each of the populations composed of babies born in that particular month) and that the populations of crawling ages have Normal distributions. Birth month Mean Std. dev. n January 29.84 7.08 32 May 28.58 8.07 27 September 33.83 6.93 38 An ANOVA F test was run on the data. The following shows a portion of the results. Source df Sums of Mean square F ratio squares Group 505.26 Error 53.45 Total The mean square for groups is: a. 5.38. b. 252.63. c. 1010.52. d. 1515.78. ANSWER: b 17. At what age do babies learn to crawl? Does it depend on the time of the year that the babies were born? Data were collected from parents who brought their babies to the University of Denver’s Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of four feet within one minute. The resulting data were grouped by month of birth: January, May, and September. Crawling age is given in weeks. Assume that the data can be considered as three independent random samples (one from each of the populations composed of babies born in that particular month) and that the populations of crawling ages have Normal distributions. Birth month Mean Std. dev. n January 29.84 7.08 32 May 28.58 8.07 27 September 33.83 6.93 38 An ANOVA F test was run on the data. The following shows a portion of the results. Source df Sums of Mean square F ratio squares Group 505.26 Error 53.45 Total Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 27 The value of the ANOVA F statistic is: a. 3.15. b. 4.73. c. 6.3. d. 9.45. ANSWER: b 18. Which of the following is a true statement about the analysis of variance F test? a. The null hypothesis test states that all population means are the same. b. The alternative hypothesis does not tell us which groups might have different means. c. The F test assesses evidence for some differences among the population means . d. All of the answer options are correct. ANSWER: d 19. A company conducted an experiment to investigate the effects of three different processes on the strength of its steel. The investigators randomly divided the production of 120 batches of steel, using 40 batches for each process. The steel was rated on a scale of 0 to 100 for its strength. The following sample means and standard deviations were obtained. Process

A 72.08 20.81 B 51.00 23.72 C 63.15 21.55 The mean square error for these data is: a. 486.7. b. 22.06. c. 56946. d. None of the answer options is correct. ANSWER: a 20. A company conducted an experiment to investigate the effects of three different processes on the strength of its steel. The investigators randomly divided the production of 120 batches of steel, using 40 batches for each process. The steel was rated on a scale of 0 to 100 for its strength. The following sample means and standard deviations were obtained. Process

A 72.08 20.81 B 51.00 23.72 C 63.15 21.55 The degrees of freedom for the ANOVA F test are: a. 3, 117. b. 3, 120. c. 2, 40. Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 27 d. 2, 117. ANSWER: d 21. A company conducted an experiment to investigate the effects of three different processes on the strength of its steel. The investigators randomly divided the production of 120 batches of steel, using 40 batches for each process. The steel was rated on a scale of 0 to 100 for its strength. The following sample means and standard deviations were obtained. Process

A 72.08 20.81 B 51.00 23.72 C 63.15 21.55 The sum of squares for groups for this experiment is given by 8952, and the sum of squares for error is given by 56946. The F statistic is: a. 0.1572. b. 9.2. c. 3.03. d. 6.288. ANSWER: b 22. A company runs a three-day workshop on strategies for working effectively in teams. On each day, a different strategy is presented. Forty-eight employees of the company attend the workshop. At the outset, all 48 are divided into 12 teams of four. The teams remain the same for the entire workshop. Strategies are presented in the morning. In the afternoon, the teams are presented with a series of small tasks. The number of these tasks completed successfully, using the strategy taught that morning, is recorded for each team. The mean number of tasks completed successfully by all teams each day and the standard deviation are computed. The results follow. Day (strategy) Mean Std. dev. 1 17.25 7.10 2 17.64 14.14 3 17.25 14.03 The degrees of freedom in the numerator for the ANOVA F test are: a. 36. b. 33. c. 2. d. 1. ANSWER: c 23. A company runs a three-day workshop on strategies for working effectively in teams. On each day, a different strategy is presented. Forty-eight employees of the company attend the workshop. At the outset, all 48 are divided into 12 teams of four. The teams remain the same for the entire workshop. Strategies are presented in the morning. In the afternoon, the teams are presented with a series of small tasks. The number of these tasks completed successfully, using the strategy taught that morning, is recorded for each team. The degrees of freedom in the denominator of the F test are: Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 27 a. 33. b. 12. c. 3. d. 2. ANSWER: a 24. A company runs a three-day workshop on strategies for working effectively in teams. On each day, a different strategy is presented. Forty-eight employees of the company attend the workshop. At the outset, all 48 are divided into 12 teams of four. The teams remain the same for the entire workshop. Strategies are presented in the morning. In the afternoon, the teams are presented with a series of small tasks. The number of these tasks completed successfully, using the strategy taught that morning, is recorded for each team. The mean number of tasks completed successfully by all teams each day and the standard deviation are computed. The results follow. Day (strategy) Mean Std. dev. 1 17.25 7.10 2 17.64 14.14 3 17.25 14.03 The researchers did an ANOVA F test of the data and obtained the following results. Source Sum of squares Mean square F ratio Day 1.36 0.68 0.0045 Error 5321.71 152.05 Total 5323.08 In this example, we notice that: a. there is clear evidence of bias in the results. This is undoubtedly due to the lack of blinding on the part of the subjects. b. the data show very strong evidence of a violation of the assumption that the three populations have the same standard deviation. c. an ANOVA F test cannot be used on these data, because the sample sizes are less than 20. d. the assumption that the data are independent for the three days is unreasonable, because the same teams were observed each day. ANSWER: d 25. A company runs a three-day workshop on strategies for working effectively in teams. On each day, a different strategy is presented. Forty-eight employees of the company attend the workshop. At the outset, all 48 are divided into 12 teams of four. The teams remain the same for the entire workshop. Strategies are presented in the morning. In the afternoon, the teams are presented with a series of small tasks. The number of these tasks completed successfully, using the strategy taught that morning, is recorded for each team. The mean number of tasks completed successfully by all teams each day and the standard deviation are computed. The results follow. Day (strategy) Mean Std. dev. 1 17.25 7.10 2 17.64 14.14 3 17.25 14.03 The researchers did an ANOVA F test of the data and obtained the following results. Source Sum of squares Mean square F ratio Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 27 Day 1.36 0.68 0.0045 Error 5321.71 152.05 Total 5323.08 Which of the following conclusions is most reasonable? a. There is moderate evidence that the strategies taught are effective in increasing the number of tasks completed successfully for the first two days, but the effect appears to wear off. b. An ANOVA F test is not appropriate for these data. Instead, the company should have done several tests to see whether the number of tasks completed successfully differed for the three days. This analysis would have shown that the treatment was effective. c. The data provide strong evidence that the mean number of tasks completed successfully differs for the three strategies taught. d. The data appear to provide little or no evidence that the strategies taught differ in their effectiveness in helping teams complete tasks successfully. ANSWER: d 26. The alternative hypothesis for the one-way analysis of variance states that: a. some of the means are statistically significant, but others are not. b. only one mean is different from all of the others. c. there is no difference between any of the means being considered. d. at least one of the means is different from all of the other means. ANSWER: d 27. The test statistic F used in one-way analysis of variance is: a. a ratio of the P-values that are computed for each pairwise comparison. b. a ratio of the variation between the sample means to the variation within the samples. c. a ratio of the variation within the sample means to the variation between the sample means. d. the sum of the variations between the sample means. ANSWER: b 28. Which of the following is not a condition that must be met for one-way analysis of variance to be valid? a. All of the populations must have the same population size. b. All of the populations must be Normally distributed. c. All of the populations must have the same standard deviation. d. All of the populations must have the same variance. ANSWER: a 29. Many Americans complain about being sleep deprived. A team of psychologists researched the reasons for this sleep deprivation. After determining that one reason was poor time management, they devised a program to help people manage their time better. They recruited a random sample of 30 people at a major shopping center and randomly split them into three groups of size 10. Group 1 (the controls) received a logbook asking them to record the number of hours slept for a week, but nothing else. Group 2 (the informed group) was shown a video to help improve time management. Group 3 (the intervention group) participated in a two-day training course on improving time management. Groups 2 and 3 were also asked to keep records for one week on the number of Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 27 hours slept. The psychologists were interested in learning whether providing information or an intervention affects sleep time. The analysis of this type of study is called: a. a many-means comparison study. b. a multiple intervention comparison study. c. a one-way analysis of variance. d. None of the answer options is correct. ANSWER: c 30. Many Americans complain about being sleep deprived. A team of psychologists researched the reasons for this sleep deprivation. After determining that one reason was poor time management, they devised a program to help people manage their time better. They recruited a random sample of 30 people at a major shopping center and randomly split them into three groups of size 10. Group 1 (the controls) received a logbook asking them to record the number of hours slept for a week but nothing else. Group 2 (the informed group) was shown a video to help improve time management. Group 3 (the intervention group) participated in a two-day training course on improving time management. Groups 2 and 3 were also asked to keep records for one week on the number of hours slept. The psychologists were interested in learning whether providing information or an intervention affects sleep time. After consulting a statistics manual, they decided to use an ANOVA F test for analyzing the data. Which of the following assumptions is required for this statistical procedure to be valid? a. equality of standard deviations for the three comparison populations b. equality of means for the three comparison populations c. matching of the study participants in the three groups to make sure they have similar habits prior to intervention d. nothing; the psychologists randomized, and the total sample size is 30 ANSWER: a 31. Many Americans complain about being sleep deprived. A team of psychologists researched the reasons for this sleep deprivation. After determining that one reason was poor time management, they devised a program to help people manage their time better. They recruited a random sample of 30 people at a major shopping center and randomly split them into three groups of size 10. Group 1 (the controls) received a logbook asking them to record the number of hours slept for a week but nothing else. Group 2 (the informed group) was shown a video to help improve time management. Group 3 (the intervention group) participated in a two-day training course on improving time management. Groups 2 and 3 were also asked to keep records for one week on the number of hours slept. The psychologists were interested in learning whether providing information or an intervention affects sleep time. Let mean sleep time for the control group, mean sleep time for the information group, and mean sleep time for the intervention group. The null hypothesis the psychologists wished to test is given by: a. . b. c.

. .

ANSWER: d Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 27 32. Many Americans complain about being sleep deprived. A team of psychologists researched the reasons for this sleep deprivation. After determining that one reason was poor time management, they devised a program to help people manage their time better. They recruited a random sample of 30 people at a major shopping center and randomly split them into three groups of size 10. Group 1 (the controls) received a logbook asking them to record the number of hours slept for a week but nothing else. Group 2 (the informed group) was shown a video to help improve time management. Group 3 (the intervention group) participated in a two-day training course on improving time management. Groups 2 and 3 were also asked to keep records for one week on the number of hours slept. The psychologists were interested in learning whether providing information or an intervention affects sleep time. Let mean sleep time for the control group, mean sleep time for the information group, and mean sleep time for the intervention group. With the null the appropriate alternative hypothesis is: a. . b. c.

. .

ANSWER: d 33. Many Americans complain about being sleep deprived. A team of psychologists researched the reasons for this sleep deprivation. After determining that one reason was poor time management, they devised a program to help people manage their time better. They recruited a random sample of 30 people at a major shopping center and randomly split them into three groups of size 10. Group 1 (the controls) received a logbook asking them to record the number of hours slept for a week but nothing else. Group 2 (the informed group) was shown a video to help improve time management. Group 3 (the intervention group) participated in a two-day training course on improving time management. Groups 2 and 3 were also asked to keep records for one week on the number of hours slept. The psychologists were interested in learning whether providing information or an intervention affects sleep time. Let mean sleep time for the control group, mean sleep time for the information group, and mean sleep time for the intervention group. The psychologists decide to use an ANOVA F test to test the null hypothesis . The F test for their hypothesis has numerator degrees of freedom: a. 1. b. 2. c. 3. d. 4. ANSWER: b 34. Many Americans complain about being sleep deprived. A team of psychologists researched the reasons for this sleep deprivation. After determining that one reason was poor time management, they devised a program to help people manage their time better. They recruited a random sample of 30 people at a major shopping center and randomly split them into three groups of size 10. Group 1 (the controls) received a logbook asking them to record the number of hours slept for a week but nothing else. Group 2 (the informed group) was shown a video to help improve time management. Group 3 (the intervention group) participated in a two-day training course on improving time management. Groups 2 and 3 were also asked to keep records for one week on the number of Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 27 hours slept. The psychologists were interested in learning whether providing information or an intervention affects sleep time. Let mean sleep time for the control group, mean sleep time for the information group, and mean sleep time for the intervention group. The psychologists decide to use an ANOVA F test to test the null hypothesis . The F test for their hypothesis has denominator degrees of freedom: a. 2. b. 3. c. 27. d. 30. ANSWER: c 35. Many Americans complain about being sleep deprived. A team of psychologists researched the reasons for this sleep deprivation. After determining that one reason was poor time management, they devised a program to help people manage their time better. They recruited a random sample of 30 people at a major shopping center and randomly split them into three groups of size 10. Group 1 (the controls) received a logbook asking them to record the number of hours slept for a week but nothing else. Group 2 (the informed group) was shown a video to help improve time management. Group 3 (the intervention group) participated in a two-day training course on improving time management. Groups 2 and 3 were also asked to keep records for one week on the number of hours slept. The psychologists were interested in learning whether providing information or an intervention affects sleep time. The sum of squares for groups SSG = 30.494 and the sum of squares for error SSE = 112.22. The F statistic value is: a. 0.272. b. 3.67. c. 1.96. d. 3.84. ANSWER: b 36. Many Americans complain about being sleep deprived. A team of psychologists researched the reasons for this sleep deprivation. After determining that one reason was poor time management, they devised a program to help people manage their time better. They recruited a random sample of 30 people at a major shopping center and randomly split them into three groups of size 10. Group 1 (the controls) received a logbook asking them to record the number of hours slept for a week but nothing else. Group 2 (the informed group) was shown a video to help improve time management. Group 3 (the intervention group) participated in a two-day training course on improving time management. Groups 2 and 3 were also asked to keep records for one week on the number of hours slept. The psychologists were interested in learning whether providing information or an intervention affects sleep time. The F-value derived from their data was F = 3.67, with a P-value> 0.1. Therefore, we can conclude that: a. all means are the same. b. all means are different. c. at least one mean is different. d. there is evidence that all means are different. e. there is evidence that at least one mean is different. f. there is no evidence against the null hypothesis that all means are equal. Copyright Macmillan Learning. Powered by Cognero.

Page 15

Name:

Class:

Date:

Chapter 27 ANSWER: f 37. Many Americans complain about being sleep deprived. A team of psychologists researched the reasons for this sleep deprivation. After determining that one reason was poor time management, they devised a program to help people manage their time better. They recruited a random sample of 30 people at a major shopping center and randomly split them into three groups of size 10. Group 1 (the control group, C) received a logbook asking them to record the number of hours slept for a week but nothing else. Group 2 (the informed group, IG) was shown a video to help improve time management. Group 3 (the intervention group, IV) participated in a twoday training course on improving time management. Groups 2 and 3 were also asked to keep records for one week on the number of hours slept. The psychologists were interested in learning whether providing information or an intervention affects sleep time. Below are 95% Tukey simultaneous confidence intervals for the pairwise comparisons of all three pairs of means. Diff Lower Upper IG – C –2.0845010 2.122018 IV – C 0.2257909 4.432310 IV – IG 0.2070324 4.413551 Based on these results, which of the following statements is true? a. Clearly, all three means are the same, because all confidence intervals include zero or nearly do so. b. We can be 95% confident that the intervention mean is different from both the control mean and the information mean, and that the control mean and the intervention mean are not different. c. There is evidence that the intervention group is different from the control and information groups, and that the information group is not different from the control group. d. We have evidence that the intervention mean is different from the control mean and the information mean, whereas the control mean and the information mean are not different, but we do not know the confidence level. ANSWER: c

Page 16

Name:

Class:

Date:

Chapter 28 1. The use of carpeting in hospitals, while having aesthetic value, raises an obvious question: Are carpeted floors sanitary? An experiment comparing airborne bacteria levels in carpeted rooms versus uncarpeted rooms was performed in an effort to answer this question. Specifically, for each of eight carpeted rooms and eight uncarpeted rooms in a hospital, the number of bacteria per cubic foot of air was measured. The data are given below. Assume that room sizes are equal and that the 16 rooms in this experiment were assigned randomly to the carpeted and uncarpeted groups. Group Bacteria per cubic foot Carpeted rooms 11.8 8.2 7.1 13.0 10.8 10.1 14.6 14.0 Uncarpeted rooms 12.1 8.3 3.8 7.2 12.0 11.1 10.1 13.7 In ranking the observations together, the bacteria counts of 10.1 should each be assigned the rank: a. 6. b. 6.5. c. 7. d. 7.5. ANSWER: b 2. The use of carpeting in hospitals, while having aesthetic value, raises an obvious question: Are carpeted floors sanitary? An experiment comparing airborne bacteria levels in carpeted rooms versus uncarpeted rooms was performed in an effort to answer this question. Specifically, for each of eight carpeted rooms and eight uncarpeted rooms in a hospital, the number of bacteria per cubic foot of air was measured. The data are given below. Assume that room sizes are equal and that the 16 rooms in this experiment were assigned randomly to the carpeted and uncarpeted groups. Group Bacteria per cubic foot Carpeted rooms 11.8 8.2 7.1 13.0 10.8 10.1 14.6 14.0 Uncarpeted rooms 12.1 8.3 3.8 7.2 12.0 11.1 10.1 13.7 In ranking all the observations together, the bacteria count ranked 12th is: a. 11.8. b. 12.0. c. 12.1. d. 13.0. ANSWER: c 3. The use of carpeting in hospitals, while having aesthetic value, raises an obvious question: Are carpeted floors sanitary? An experiment comparing airborne bacteria levels in carpeted rooms versus uncarpeted rooms was performed in an effort to answer this question. Specifically, for each of eight carpeted rooms and eight uncarpeted rooms in a hospital, the number of bacteria per cubic foot of air was measured. The data are given below. Assume that room sizes are equal and that the 16 rooms in this experiment were assigned randomly to the carpeted and uncarpeted groups. Group Bacteria per cubic foot Carpeted rooms 11.8 8.2 7.1 13.0 10.8 10.1 14.6 14.0 Uncarpeted rooms 12.1 8.3 3.8 7.2 12.0 11.1 10.1 13.7 If W, the Wilcoxon rank sum test statistic, is the sum of the ranks assigned to the carpeted group, then the value of W is: a. 18.5. b. 58.5. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 28 c. 62.5. d. 74.5. ANSWER: d 4. The use of carpeting in hospitals, while having aesthetic value, raises an obvious question: Are carpeted floors sanitary? An experiment comparing airborne bacteria levels in carpeted rooms versus uncarpeted rooms was performed in an effort to answer this question. Specifically, for each of eight carpeted rooms and eight uncarpeted rooms in a hospital, the number of bacteria per cubic foot of air was measured. The data are given below. Assume that room sizes are equal and that the 16 rooms in this experiment were assigned randomly to the carpeted and uncarpeted groups. Group Bacteria per cubic foot Carpeted rooms 11.8 8.2 7.1 13.0 10.8 10.1 14.6 14.0 Uncarpeted rooms 12.1 8.3 3.8 7.2 12.0 11.1 10.1 13.7 If W, the Wilcoxon rank sum test statistic, is the sum of the ranks assigned to the carpeted group, and if the two populations have the same continuous distribution, then the standard deviation of W is: a. 2.32. b. 8.51. c. 9.52. d. 90.67. ANSWER: c 5. The use of carpeting in hospitals, while having aesthetic value, raises an obvious question: Are carpeted floors sanitary? An experiment comparing airborne bacteria levels in carpeted rooms versus uncarpeted rooms was performed in an effort to answer this question. Specifically, for each of eight carpeted rooms and eight uncarpeted rooms in a hospital, the number of bacteria per cubic foot of air was measured. The data are given below. Assume that room sizes are equal and that the 16 rooms in this experiment were assigned randomly to the carpeted and uncarpeted groups. Group Bacteria per cubic foot Carpeted rooms 11.8 8.2 7.1 13.0 10.8 10.1 14.6 14.0 Uncarpeted rooms 12.1 8.3 3.8 7.2 12.0 11.1 10.1 13.7 If W, the Wilcoxon rank sum test statistic, is the sum of the ranks assigned to the carpeted group, then z, the standardized value of W, is: a. 0.37. b. 0.68. c. 1.68. d. 2.32. ANSWER: b 6. The use of carpeting in hospitals, while having aesthetic value, raises an obvious question: Are carpeted floors sanitary? An experiment comparing airborne bacteria levels in carpeted rooms versus uncarpeted rooms was performed in an effort to answer this question. Specifically, for each of eight carpeted rooms and eight uncarpeted rooms in a hospital, the number of bacteria per cubic foot of air was measured. The data are given below. Assume that room sizes are equal and that the 16 rooms in this experiment were assigned randomly to the carpeted and uncarpeted groups. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 28 Group Bacteria per cubic foot Carpeted rooms 11.8 8.2 Uncarpeted rooms 12.1 8.3 The researcher is interested in testing

7.1 13.0 10.8 10.1 14.6 14.0 3.8 7.2 12.0 11.1 10.1 13.7 no difference in distribution of bacteria counts for carpeted and

uncarpeted rooms, against the one-sided alternative

the carpeted group tends to have higher bacteria counts.

If W, the Wilcoxon rank sum test statistic, is the sum of the ranks assigned to the carpeted group, then the Pvalue for the test is: a. 0.046. b. 0.248. c. 0.496. d. 0.752. ANSWER: b 7. In a study to investigate the effect of regular exercise on HDL (good cholesterol) level, a random sample of five male subjects known to have low HDL levels had their HDL measured. After six months on a regular exercise schedule, it was measured again. The data are given in the following table. Subject 1 2 3 4 5 Initial HDL 31 36 32 28 37 HDL after six months 39 32 44 34 39 Difference 8 −4 12 6 2 How do you know that the data should be analyzed using the Wilcoxon signed rank test? a. There are three groups, and some of the observations are negative numbers. b. There are three groups, with one observation in each group matched to a subject. c. There are two groups, and some of the observations are negative numbers. d. There are two groups, with one observation in each group matched to a subject. ANSWER: d 8. In a study to investigate the effect of regular exercise on HDL (good cholesterol) level, a random sample of five male subjects known to have low HDL levels had their HDL measured. After six months on a regular exercise schedule, it was measured again. The data are given in the following table. Subject 1 2 3 4 5 Initial HDL 31 36 32 28 37 HDL after six months 39 32 44 34 39 Difference 8 −4 12 6 2 The data are to be analyzed using the Wilcoxon signed rank test. If the responses have a continuous distribution that is not affected by the different treatments, then W+ has mean: a. 6. b. 7.5 c. 13. d. 27.5. ANSWER: b 9. In a study to investigate the effect of regular exercise on HDL (good cholesterol) level, a random sample of Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 28 five male subjects known to have low HDL levels had their HDL measured. After six months on a regular exercise schedule, it was measured again. The data are given in the following table. Subject 1 2 3 4 5 Initial HDL 31 36 32 28 37 HDL after six months 39 32 44 34 39 Difference 8 −4 12 6 2 The value of the Wilcoxon signed rank test W+ is: a. 7.5. b. 13. c. 21. d. 34. ANSWER: b 10. In a study to investigate the effect of regular exercise on HDL (good cholesterol) level, a random sample of five male subjects known to have low HDL levels had their HDL measured. After six months on a regular exercise schedule, it was measured again. The data are given in the following table. Subject 1 2 3 4 5 Initial HDL 31 36 32 28 37 HDL after six months 39 32 44 34 39 Difference 8 −4 12 6 2 The standardized value z of the Wilcoxon signed rank test W+ is: a. 0.4. b. 0.95. c. 1.48. d. 3.51. ANSWER: c 11. In a study to investigate the effect of regular exercise on HDL (good cholesterol) level, a random sample of five male subjects known to have low HDL levels had their HDL measured. After six months on a regular exercise schedule, it was measured again. The data are given in the following table. Subject 1 2 3 4 5 Initial HDL 31 36 32 28 37 HDL after six months 39 32 44 34 39 Difference 8 −4 12 6 2 The researcher is interested in testing initial and final HDL measurements have the same distribution against the one-sided alternative

final HDL levels are systematically lower. The P-value for the Wilcoxon

signed rank test W+ is approximately: a. 0.0281. b. 0.0329. c. 0.0495. d. 0.0694. ANSWER: d Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 28 12. The Wilcoxon signed rank test is used for small samples when Normality cannot be established or is known not to hold for: a. more than two groups. b. two independent samples with unequal variances. c. paired data. d. All of the answer options are correct. ANSWER: c 13. The Wilcoxon rank sum test for comparing two independent samples tests which of the following hypotheses? a. median1 = median2 for two distributions having the same shape vs. median1 median2. b.

the two distributions are the same vs.

one distribution has values systematically larger than

the other. c. Both option (a) and option (b) are correct. d. None of the answer options is correct. ANSWER: c 14. A researcher decided to conduct an experiment to study the effect of caffeine by randomly dividing nine people into two groups. Group 1, consisting of five study subjects, had a cup of coffee to start the experiment. Group 2, consisting of four people, had a cup of decaffeinated coffee. The study subjects did not know which group they belonged to. All study subjects were then asked to tap their finger. The measurement taken was the number of finger taps per minute. This type of data is often skewed, and the researchers decided that they should not use a two-sample t test. They chose a Wilcoxon rank sum test and recorded the ranks of the subjects in the caffeine group. The mean of this test statistic is given by: a. 25. b. 45. c. 50. d. 90. ANSWER: a 15. A researcher decided to conduct an experiment to study the effect of caffeine by randomly dividing nine people into two groups. Group 1, consisting of five study subjects, had a cup of coffee to start the experiment. Group 2, consisting of four people, had a cup of decaffeinated coffee. The study subjects did not know which group they belonged to. All study subjects were then asked to tap their finger. The measurement taken was the number of finger taps per minute. This type of data is often skewed, and the researchers decided that they should not use a two-sample t test. They chose a Wilcoxon rank sum test and recorded the ranks of the subjects in the caffeine group. The standard deviation of this test statistic is given by: a. 16.67. b. 4.083. c. 22.5. d. None of the answer options is correct. ANSWER: b Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 28 16. A researcher decided to conduct an experiment to study the effect of caffeine by randomly dividing nine people into two groups. Group 1, consisting of five study subjects, had a cup of coffee to start the experiment. Group 2, consisting of four people, had a cup of decaffeinated coffee. The study subjects did not know which group they belonged to. All study subjects were then asked to tap their finger. The measurement taken was the number of finger taps per minute. This type of data is often skewed, and the researchers decided that they should not use a two-sample t test. They chose a Wilcoxon rank sum test and recorded the ranks of the subjects in the caffeine group. Every subject in the caffeine group had a higher frequency of taps than those in the noncaffeine group. The sum of the ranks for this problem is given by: a. 90. b. 25. c. 35. d. 55. ANSWER: c 17. A tool manufacturer tests three types of cutters used in a lathe operation. One type is a laminated steel cutter made of very hard high-carbon steel sandwiched between two softer steels. Another is a special highspeed steel cutter developed using powder metallurgy. The final type is made from cryogenically treated steel. Cutters of each type are tested to see how long they will last in continuous operation until they need to be sharpened. The times (in hours) are recorded for each cutter used in the study, and the results are given below. Type of cutter Time until sharpening is needed Laminated steel 24, 27, 31 High-speed steel 25, 26, 28 Cryogenically treated steel 32, 34, 37 The data are to be analyzed with the Kruskal-Wallis test. The null hypothesis is that the time until sharpening is needed has the same distribution in all groups. The alternative is: a. mean time until sharpening is needed is systematically higher in some groups than in others. b. not all three mean times until sharpening is needed are equal. c. the mean times until sharpening are different in all of the three groups of cutter types. d. the times until sharpening is needed are systematically longer for cryogenically treated steel cutters than for the other two types of cutters. ANSWER: a 18. A tool manufacturer tests three types of cutters used in a lathe operation. One type is a laminated steel cutter made of very hard high-carbon steel sandwiched between two softer steels. Another is a special highspeed steel cutter developed using powder metallurgy. The final type is made from cryogenically treated steel. Cutters of each type are tested to see how long they will last in continuous operation until they need to be sharpened. The times (in hours) are recorded for each cutter used in the study, and the results are given below. Type of cutter Time until sharpening is needed Laminated steel 24, 27, 31 High-speed steel 25, 26, 28 Cryogenically treated steel 32, 34, 37 The value of the Kruskal-Wallis statistic H for these data is: a. 2.75. b. 3.20. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 28 c. 4.76. d. 5.42. ANSWER: d 19. A tool manufacturer tests three types of cutters used in a lathe operation. One type is a laminated steel cutter made of very hard high-carbon steel sandwiched between two softer steels. Another is a special highspeed steel cutter developed using powder metallurgy. The final type is made from cryogenically treated steel. Cutters of each type are tested to see how long they will last in continuous operation until they need to be sharpened. The times (in hours) are recorded for each cutter used in the study, and the results are given below. Type of cutter Time until sharpening is needed Laminated steel 24, 27, 31 High-speed steel 25, 26, 28 Cryogenically treated steel 32, 34, 37 Under the null hypothesis that the three populations have the same continuous distribution: a. H has approximately a chi-square distribution, with 3 degrees of freedom. b. H has approximately an F(2, 6) distribution. c. H has approximately a chi-square distribution, with 2 degrees of freedom. d. H has a distribution that cannot be evaluated because the populations may not be Normal. ANSWER: c 20. A tool manufacturer tests three types of cutters used in a lathe operation. One type is a laminated steel cutter made of very hard high-carbon steel sandwiched between two softer steels. Another is a special highspeed steel cutter developed using powder metallurgy. The final type is made from cryogenically treated steel. Cutters of each type are tested to see how long they will last in continuous operation until they need to be sharpened. The times (in hours) are recorded for each cutter used in the study, and the results are given below. Type of cutter Time until sharpening is needed Laminated steel 24, 27, 31 High-speed steel 25, 26, 28 Cryogenically treated steel 32, 34, 37 The P-value of the Kruskal-Wallis statistic H for these data is: a. less than 0.025. b. between 0.025 and 0.05. c. between 0.05 and 0.1. d. greater than 0.1. ANSWER: c 21. The primary difference between the null hypothesis of the two-sample t test and the corresponding nonparametric Wilcoxon rank sum test is that: a. the Wilcoxon test presumes equality between the medians of the two samples. b. the Wilcoxon test presumes equality between the means of the two samples. c. the Wilcoxon test presumes equality between the medians of the two populations. d. the Wilcoxon test presumes equality between the means of the two populations. ANSWER: c Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 28 22. The mean and the standard deviation of W for the nonparametric Wilcoxon rank sum test: a. depend entirely on the characteristics of the two samples. b. depend entirely on the characteristics of the two populations. c. depend on the number of items that are being ranked, but not on the values themselves. d. depend on the number of items that are being ranked, as well as on the values themselves. ANSWER: c 23. The Wilcoxon signed rank test is best described as: a. a nonparametric alternative to one-way ANOVA that relaxes the Normality condition. b. a nonparametric alternative to the two-sample t test that relaxes the Normality condition. c. a nonparametric alternative to the paired t test that relaxes the Normality condition. d. None of the answer options is correct. ANSWER: c 24. The Kruskal-Wallis test is best described as: a. a nonparametric alternative to one-way ANOVA that relaxes the Normality condition. b. a nonparametric alternative to one-way ANOVA that relaxes the requirement of independent samples. c. a nonparametric alternative to the two-sample t test that relaxes the Normality condition. d. a nonparametric alternative to the two-sample t test that relaxes the requirement of independent samples. ANSWER: a 25. The alternative hypothesis for the Kruskal-Wallis test is typically: a. that not all median values from the populations are the same. b. that the response variables are systematically more different in some populations than in others. c. Both options (a) and (b)are correct; they express the same thing in different ways. d. Neither option (a) nor option (b) is correct. ANSWER: c 26. A study was conducted to assess the effects of caffeine on concentration. Fifteen subjects were recruited into the study and randomly divided into three groups of equal sample size. Group 1 was given an 8-ounce cup of coffee, Group 2 an 8-ounce cup of black tea, and Group 3 an 8-ounce cup of decaffeinated coffee. Each subject was shown a set of 20 numbers for one minute. The subjects were then asked to enter five of the numbers they had been shown, and the time this took was recorded. A statistician told the investigators they should use a nonparametric test, because their data were unlikely to be Normally distributed and their sample was small. The researchers consulted the literature on nonparametric tests and found several. An appropriate test to use here is: a. the Wilcoxon signed rank test. b. the Kruskal-Wallis test. c. the Wilcoxon rank sum test. d. the Mann-Whitney test. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 28 ANSWER: b 27. Which of the following is(are) part of the signed rank test? a. The absolute values of the differences of two measurements on each subject are ranked. b. The ranks of subjects in two samples are calculated, and the differences of all pairs of ranks are calculated. c. Subjects are given one of two treatments in random order. The responses under Treatment 1 are then ranked, and the same is done for Treatment 2. The differences in ranks are then computed. d. All of the answer options are correct. ANSWER: a 28. The Wilcoxon rank sum test comparing two populations tests the hypothesis

median1 = median2 when

which of the following conditions holds? a. The standard deviations and are equal. b. The means

and

are equal.

c. Both populations are symmetric. d. The shapes of both populations are the same. ANSWER: d 29. Which of the following statements is false? a. As the sample sizes n1, n2 increase, the distribution of the Wilcoxon rank sum test can be approximated by the Normal distribution. b. There is a direct algebraic link between the Mann-Whitney test and the Wilcoxon rank sum test. c. The Kruskal-Wallis test is used for paired data. d. Zero differences in the Wilcoxon signed rank test do not contribute to the test statistic. ANSWER: c 30. The Kruskal-Wallis test is the nonparametric equivalent of the analysis of variance comparison of three or more means. It is performed by combining the samples, obtaining the ranks in the combined sample, and carrying out an analysis of variance on the ranks. However, unlike traditional analysis of variance, it is not necessary to calculate both SSG and SSE because: a. the total sum of the ranks is a fixed number and is the same for all studies with the same total number of observations. b. the SSE is fixed and is the same for all studies with the same number of observations. c. the sum of the ranks is an approximate chi-square statistic, and no standard error is needed. d. All of the answer options are correct. ANSWER: a 31. Ten stores were selected to test the effects on sales of two different designs for packaging a tablet. Five stores were randomly assigned to Design 1, and the other five stores were assigned to Design 2. The data below provide the sales over a one-week period. Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 28 Design 1: 11 17 16 14 15 Design 2: 12 20 13 19 18 The mean of the Wilcoxon rank sum statistic is: a. 55. b. 27.5. c. 16.4. d. 14.6. ANSWER: b 32. Ten stores were selected to test the effects on sales of two different designs for packaging a tablet. Five stores were randomly assigned to Design 1, and the other five stores were assigned to Design 2. The data below provide the sales over a one-week period. Design 1: 11 17 16 14 15 Design 2: 12 20 13 19 18 The standard deviation of the Wilcoxon rank sum test is: a. 4.787. b. 22.92. c. 3.05. d. 9.3025. ANSWER: a 33. Ten stores were selected to test the effects on sales of two different designs for packaging a tablet. Five stores were randomly assigned to Design 1, and the other five stores were assigned to Design 2. The data below provide the sales over a one-week period. Design 1: 11 17 16 14 15 Design 2: 12 20 13 19 18 Design 2 was the newer design, and it was suspected that it would produce higher sales. The sum of the ranks for Design 2 is: a. 55. b. 32. c. 23. d. 27. ANSWER: b 34. A cosmetics company wanted to market a new suntan lotion. The developers recruited 10 volunteers for their study to test the effectiveness of the new lotion. Each volunteer was given the old lotion on one randomly selected arm and the new lotion on the other arm. The volunteer was then asked to expose both arms to the sun. The time was measured until there was visible redness on one arm, which was then shielded from the sun. The experiment ended when the other arm showed signs of redness. Below are the times (in minutes) for both arms for each subject. Subject: 1 2 3 4 5 6 7 8 9 10 Old: 15 22 16 16 23 25 19 28 26 29 New: 18 24 26 23 28 21 20 19 34 18 This study design is called: Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 28 a. a left vs. right design. b. a same-subject design. c. a matched pairs design. d. a before-and-after design. ANSWER: c 35. A cosmetics company wanted to market a new suntan lotion. The developers recruited 10 volunteers for their study to test the effectiveness of the new lotion. Each volunteer was given the old lotion on one randomly selected arm and the new lotion on the other arm. The volunteer was then asked to expose both arms to the sun. The time was measured until there was visible redness on one arm, which was then shielded from the sun. The experiment ended when the other arm showed signs of redness. Below are the times (in minutes) for both arms for each subject. Subject: 1 2 3 4 5 6 7 8 9 10 Old: 15 22 16 16 23 25 19 28 26 29 New: 18 24 26 23 28 21 20 19 34 18 The Wilcoxon signed rank statistic for testing whether the new lotion provides longer protection, subtracting tanning times for the old lotion from those for the new lotion, has the value: a. 32. b. 34. c. 46. d. 29. ANSWER: b 36. Fifteen stores were selected to test the effects on sales of three different designs for packaging a tablet. Five stores each were randomly assigned to Design 1, 2, or 3. The data below provide the sales over a one-week period. Design 1: 11 17 16 14 15 Design 2: 12 20 13 19 18 Design 3: 9 21 22 23 24 The marketing team decided not to use ANOVA to test whether the three different designs had the same effect on sales or whether sales were increased by some designs over others. The hypotheses to be tested are: a. . b.

c. . d. None of the answer options is correct. ANSWER: c

Page 11

Name:

Class:

Date:

Chapter 29 1. Multiple regression differs from simple linear regression in that: a. it considers more than one explanatory variable to predict a single response variable. b. it considers more than one response variable to predict a single explanatory variable. c. it considers more than one explanatory variable to predict more than one response variable. d. it considers more than one response variable to predict more than one explanatory variable. ANSWER: a 2. The multiple correlation coefficient a. describes the square of the proportion of variability in the explanatory variable that is explained by the response variables. b. describes the square of the proportion of variability in the response variable that is explained by the explanatory variables. c. describes the proportion of variability in the explanatory variable that is explained by the response variables. d. describes the proportion of variability in the response variable that is explained by the explanatory variables. ANSWER: d 3. Which of the following statements is true about multiple regression? a. All explanatory and response variables must be quantitative. b. The response variable must be quantitative, but explanatory variables can be either quantitative or categorical. c. The response variable must be quantitative, but explanatory variables can be either quantitative or categorical, so long as the categorical variables are recoded into appropriate numerical values. d. None of the answer options is correct. ANSWER: c 4. You have explored several different multiple regression models to predict a response variable. All other factors being equal, which model should you choose? a. the model with the fewest explanatory variables and the smallest b. the model with the most explanatory variables and the smallest c. the model with the fewest explanatory variables and the largest d. the model with the most explanatory variables and the largest ANSWER: c 5. The magnitude of the effect of one explanatory variable changing as a function of another explanatory variable: a. is an interaction. b. is parallel. c. satisfies the condition of constant variance. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 29 d. is a quadratic relationship. ANSWER: a 6. A study was conducted on the effect of exercise and diet on blood pressure in a population of overweight adults with high blood pressure. Scientists recorded the number of minutes of vigorous exercise in the previous week (x1) and the number of calories from fat (x2) for each subject. They classified subjects as being on a lowfat diet (x2 = 1) if they consumed less than 20% of their daily calories from fat. Otherwise they were classified as being on a high-fat diet (x2 = 0). The researchers measured blood pressure twice: first at a baseline visit and again a week later. They calculated the change in blood pressure from baseline to the second visit (y). This means negative y-values indicate a reduction in blood pressure, and positive y-values indicate an increase. Here are some of their findings: • The average change in blood pressure was a drop of 0.1 mmHg for every minute of vigorous exercise in the preceding week. • For those who ate a low-fat diet, the average change in blood pressure was a drop of 0.2 mmHg for every minute of vigorous exercise in the preceding week. • For those who ate a low-fat diet, blood pressure generally was lower by 10 mmHg. • For those who did not exercise and were on a high-fat diet was 15 mmHg. The regression equation for the predicted drop in blood pressure was determined to be: a. . b.

ANSWER: a 7. A study is conducted on the effect of exercise and diet on blood pressure in a population of overweight adults with high blood pressure. Scientists recorded the number of minutes of vigorous exercise in the previous week (x1) and the number of calories from fat (x2) for each subject. They classified subjects as being on a low-fat diet (x2 = 1) if they consumed less than 20% of their daily calories from fat. Otherwise they were classified as being on a high-fat diet (x2 = 0). The researchers measured blood pressure twice: first at a baseline visit and again a week later. They calculated the change in blood pressure from baseline to the second visit (y). This means negative y-values indicate a reduction in blood pressure, and positive y-values indicate an increase. Here are some of their findings: • The average change in blood pressure was a drop of 0.1 mmHg for every minute of vigorous exercise in the preceding week. • For those who ate a low-fat diet, the average change in blood pressure was a drop of 0.2 mmHg for every minute of vigorous exercise in the preceding week. • For those who ate a low-fat diet, blood pressure generally was lower by 10 mmHg. • For those who did not exercise and were on a high-fat diet was 15 mmHg. The effect of exercise on blood pressure is: a. the same for those who are on a high-fat diet and those who are on a low-fat diet. b. a larger average reduction in blood pressure for those with a low-fat diet. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 29 c. a smaller average reduction in blood pressure for those with a low-fat diet. d. The answer cannot be determined from the information provided. ANSWER: b 8. A study is conducted on the effect of exercise and diet on blood pressure in a population of overweight adults with high blood pressure. Scientists recorded the number of minutes of vigorous exercise in the previous week (x1) and the number of calories from fat (x2) for each subject. They classified subjects as being on a low-fat diet (x2 = 1) if they consumed less than 20% of their daily calories from fat. Otherwise they were classified as being on a high-fat diet (x2 = 0). The researchers measured blood pressure twice: first at a baseline visit and again a week later. They calculated the change in blood pressure from baseline to the second visit (y). This means negative y-values indicate a reduction in blood pressure, and positive y-values indicate an increase. The estimated regression is given by interaction and found that

. The researchers also fit the model without the

dropped from

= 0.84 to

= 0.835. Based on this result, they decided that:

a. a model without interaction fit much worse than a model with interaction. b. a model without interaction fit much better than a model with interaction. c. a model without interaction fit almost as well as a model with interaction. d. the two models cannot be compared in terms of fit by looking at . ANSWER: c 9. A study is conducted on the effect of exercise and diet on blood pressure in a population of overweight adults with high blood pressure. Scientists recorded the number of minutes of vigorous exercise in the previous week (x1) and the number of calories from fat (x2) for each subject. They classified subjects as being on a low-fat diet (x2 = 1) if they consumed less than 20% of their daily calories from fat. Otherwise they were classified as being on a high-fat diet (x2 = 0). The researchers measured blood pressure twice: first at a baseline visit and again a week later. They calculated the change in blood pressure from baseline to the second visit (y). This means negative y-values indicate a reduction in blood pressure, and positive y-values indicate an increase. The estimated regression is given by

, where

, and

. The researchers questioned whether a model without the interaction was acceptable. They found that the t statistic for the hypothesis

versus

was t = 2.52, and the number of study subjects was

n = 20. The P-value for this test is: a. 0.0059. b. 0.0104. c. 0.0102. d. 0.0114. ANSWER: d 10. Which of the following is not part of a regression analysis? a. a residual plot b. a scatterplot of each explanatory variable against the response variable y Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 29 c. a chi-square goodness-of-fit statistic d. an ANOVA table containing the sum of squares regression and the sum of squares residual ANSWER: c 11. A regression was conducted to assess the effect of height and smoking on lung volume as measured by FEV (in liters).

This residual plot shows: a. a violation of constant variance. b. a nonlinearity pattern. c. Both of the answer options are correct. ANSWER: c 12. The regression of height (in inches) and smoking on lung volume (FEV) had the following ANOVA table. The variable NoSmoke = 1 if an individual is not a smoker, and 0 otherwise. Source DF Adj SS Adj MS F-Value P-Value Regression 2 372.479 186.239 1023.65 0.000 Hgt 1 351.155 351.155 1930.09 0.000 NoSmoke 1 2.493 2.493 13.70 0.000 Error 651 118.441 0.182 Total 653 490.920 S R-sq R-sq(adj) 0.426541 75.87% 75.80% Coefficients Term Coef SE Coef T-Value P-Value Constant −5.390 0.180 −29.93 0.000 Hgt 0.13023 0.00296 43.93 0.000 Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 29 NoSmoke 0.1251 0.0338 The F-value for the hypotheses

3.70 versus

0.000 at least one of

does not equal zero is given by:

a. 1023.65. b. 1930.09. c. 13.7. d. 859.8. ANSWER: a 13. The regression of height (in inches) and smoking on lung volume (FEV) had the following ANOVA table. The variable NoSmoke = 1 if an individual is not a smoker, and 0 otherwise. Source DF Adj SS Adj MS F-Value P-Value Regression 2 372.479 186.239 1023.65 0.000 Hgt 1 351.155 351.155 1930.09 0.000 NoSmoke 1 2.493 2.493 13.70 0.000 Error 651 118.441 0.182 Total 653 490.920 S R-sq R-sq(adj) 0.426541 75.87% 75.80% Coefficients Term Coef SE Coef T-Value P-Value Constant −5.390 0.180 −29.93 0.000 Hgt 0.13023 0.00296 43.93 0.000 NoSmoke 0.1251 0.0338 3.70 0.000 The predicted value for someone who does smoke and who is 66.5 inches tall is: a. 3.56 liters. b. 3.27 liters. c. 3.395 liters. d. 3.145 liters. ANSWER: c 14. Has the number of home runs hit by Major League Baseball teams been changing over time? For 51 years, from 1960 to 2010, the average number of home runs hit per game per team for each season was computed, to assess any change over time. Initially, to study the trend in home runs over this period, simple linear regression was performed by using year to predict the average number of home runs per game per team in that year. However, it was pointed out that the manufacturer of major league baseballs was changed from Spalding to Rawlings after the 1976 season. Because the change in the type of baseball used might have affected the number of home runs (for example, the production of a livelier ball by Rawlings would likely lead to more home runs), it was decided to include an additional variable: Type = 0, if before 1976 (that is, the Spalding baseball was used) Type = 1, if after 1976 (that is, the Rawlings baseball was used). A multiple regression analysis for average home runs per game was performed using the model . The following results were obtained. Analysis of Variance Copyright Macmillan Learning. Powered by Cognero.

Parameter Estimates Page 5

Name:

Class:

Date:

Chapter 29 Source Model Error

df 2 48

Sum of squares 0.744384 2.53933

Variable Estimate SE Intercept –27.91 12.89 Year 0.042 0.0065 Type –0.11 0.16 What proportion of the variability in the response variable is explained by this model? a. 5.1% b. 22.7% c. 27.2% d. 74.4% ANSWER: b 15. Has the number of home runs hit by Major League Baseball teams been changing over time? For 51 years, from 1960 to 2010, the average number of home runs hit per game per team for each season was computed, to assess any change over time. Initially, to study the trend in home runs over this period, simple linear regression was performed by using year to predict the average number of home runs per game per team in that year. However, it was pointed out that the manufacturer of major league baseballs was changed from Spalding to Rawlings after the 1976 season. Because the change in the type of baseball used might have affected the number of home runs (for example, the production of a livelier ball by Rawlings would likely lead to more home runs), it was decided to include an additional variable: Type = 0, if before 1976 (that is, the Spalding baseball was used) Type = 1, if after 1976 (that is, the Rawlings baseball was used). A multiple regression analysis for average home runs per game was performed using the model . The following results were obtained. Analysis of Variance Source df Model 2 Error 48

Parameter Estimates Sum of squares Variable Estimate SE 0.744384 Intercept –27.91 12.89 2.53933 Year 0.042 0.0065 Type –0.11 0.16 You are interested in determining whether the change in manufacturer had any effect on the average number of home runs hit per game per team. You decide to test the hypotheses and . Using the estimates obtained from our statistical software, the P-value for this test is: a. greater than 0.05. b. between 0.05 and 0.01. c. between 0.01 and 0.005. d. below 0.005. ANSWER: a 16. Has the number of home runs hit by Major League Baseball teams been changing over time? For 51 years, from 1960 to 2010, the average number of home runs hit per game per team for each season was computed, to assess any change over time. Initially, to study the trend in home runs over this period, simple linear regression was performed by using year to predict the average number of home runs per game per team in that year. However, it was pointed out that the manufacturer of major league baseballs was changed from Spalding to Rawlings after the 1976 season. Because the change in the type of baseball used might have affected the number of home runs (for example, the production of a livelier ball by Rawlings would likely lead to more Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 29 home runs), it was decided to include an additional variable: Type = 0, if before 1976 (that is, the Spalding baseball was used) Type = 1, if after 1976 (that is, the Rawlings baseball was used). A multiple regression analysis for average home runs per game was performed using the model . The following results were obtained. Analysis of Variance Source df Model 2 Error 48

Sum of squares 0.744384 2.53933

Parameter Estimates Variable Estimate Intercept –27.91 Year 0.042 Type –0.11

SE 12.89 0.0065 0.16

From the results obtained, the value of MSE is: a. 0.0529. b. 0.3722. c. 0.7444. d. 2.5393. ANSWER: a 17. Has the number of home runs hit by Major League Baseball teams been changing over time? For 51 years, from 1960 to 2010, the average number of home runs hit per game per team for each season was computed, to assess any change over time. Initially, to study the trend in home runs over this period, simple linear regression was performed by using year to predict the average number of home runs per game per team in that year. However, it was pointed out that the manufacturer of major league baseballs was changed from Spalding to Rawlings after the 1976 season. Because the change in the type of baseball used might have affected the number of home runs (for example, the production of a livelier ball by Rawlings would likely lead to more home runs), it was decided to include an additional variable: Type = 0, if before 1976 (that is, the Spalding baseball was used) Type = 1, if after 1976 (that is, the Rawlings baseball was used). A multiple regression analysis for average home runs per game was performed using the model . The following results were obtained. Analysis of Variance Source df Model 2 Error 48

Sum of squares 0.744384 2.53933

Suppose we wish to test the hypotheses

Parameter Estimates Variable Estimate Intercept –27.91 Year 0.042 Type –0.11 and at least one of the

SE 12.89 0.0065 0.16 is not zero. Using the

ANOVA F test, the value of the F statistic is: a. 0.06. b. 0.29. c. 5.34. d. 7.04. ANSWER: d 18. Has the number of home runs hit by Major League Baseball teams been changing over time? For 51 years, Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 29 from 1960 to 2010, the average number of home runs hit per game per team for each season was computed, to assess any change over time. Initially, to study the trend in home runs over this period, simple linear regression was performed by using year to predict the average number of home runs per game per team in that year. However, it was pointed out that the manufacturer of major league baseballs was changed from Spalding to Rawlings after the 1976 season. Because the change in the type of baseball used might have affected the number of home runs (for example, the production of a livelier ball by Rawlings would likely lead to more home runs), it was decided to include an additional variable: Type = 0, if before 1976 (that is, the Spalding baseball was used) Type = 1, if after 1976 (that is, the Rawlings baseball was used). A multiple regression analysis for average home runs per game was performed using the model . The following results were obtained. Analysis of Variance Source df Model 2 Error 48

Sum of squares 0.744384 2.53933

Parameter Estimates Variable Estimate Intercept –27.91 Year 0.042 Type –0.11

SE 12.89 0.0065 0.16

If the value of the F statistic is 7.04, the conclusion to be drawn from this test is: a. to accept the null hypothesis. b. to fail to reject the null hypothesis (P > 0.05). c. to reject the null hypothesis, because there is some evidence (0.05 < P < 0.01) that at least one of the multiple regression coefficients is not zero. d. to reject the null hypothesis, because there is strong evidence (P < 0.01) that at least one of the multiple regression coefficients is not zero. ANSWER: d 19. Has the number of home runs hit by Major League Baseball teams been changing over time? For 51 years, from 1960 to 2010, the average number of home runs hit per game per team for each season was computed, to assess any change over time. Initially, to study the trend in home runs over this period, simple linear regression was performed by using year to predict the average number of home runs per game per team in that year. However, it was pointed out that the manufacturer of major league baseballs was changed from Spalding to Rawlings after the 1976 season. Because the change in the type of baseball used might have affected the number of home runs (for example, the production of a livelier ball by Rawlings would likely lead to more home runs), it was decided to include an additional variable: Type = 0, if before 1976 (that is, the Spalding baseball was used) Type = 1, if after 1976 (that is, the Rawlings baseball was used). A multiple regression analysis for average home runs per game was performed using the model . The following results were obtained. Analysis of Variance Source df Model 2 Error 48

Parameter Estimates Variable Estimate SE Intercept –27.91 12.89 Year 0.042 0.0065 Type –0.11 0.16 If the P-value is very large, it would be reasonable to conclude that: a. the model fits moderately well, and also, because we have examined a substantial fraction of the Sum of squares 0.744384 2.53933

Page 8

Name:

Class:

Date:

Chapter 29 time that Major League Baseball has been in existence, we can be fairly sure of the validity of the multiple linear regression model. b. the model fits fairly well, and the observed average number of home runs per game per team in the data can be predicted with moderate accuracy from a model using both year and manufacturer. c. both option (a) and option (b) are correct. In addition, the negative sign of the parameter estimate for manufacturer indicates that the baseballs by Rawlings are less lively (yield fewer home runs) than those by Spalding. d. None of the answer options is correct. ANSWER: d 20. An auctioneer of antique grandfather clocks knows that the price received for a clock at auction increases with the clock’s age and with the number of bidders. The model proposed for predicting the price of a clock from its age and the number of bidders is: , where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to a sample of 32 clocks selected from records of recent auctions. The following results summarize the least-squares regression fit of this model. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4277160 Intercept –1336.72 173.36 Error 29 514034 Age 12.73 0.90 Number of 85.82 8.71 Bidders An approximate 99% confidence interval for (the coefficient of the variable number of bidders) is: a. 85.82

24.00.

b. 85.82

8.71.

c. 12.73

0.90.

d. 12.73

2.48.

ANSWER: a 21. An auctioneer of antique grandfather clocks knows that the price received for a clock at auction increases with the clock’s age and with the number of bidders. The model proposed for predicting the price of a clock from its age and the number of bidders is: , where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to a sample of 32 clocks selected from records of recent auctions. The following results summarize the least-squares regression fit of this model. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4277160 Intercept –1336.72 173.36 Error 29 514034 Age 12.73 0.90 Number of 85.82 8.71 Bidders Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 29 The multiple correlation coefficient

is:

a. 0.059. b. 0.12. c. 0.893. d. 0.945. ANSWER: c 22. An auctioneer of antique grandfather clocks knows that the price received for a clock at auction increases with the clock’s age and with the number of bidders. The model proposed for predicting the price of a clock from its age and the number of bidders is: , where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to a sample of 32 clocks selected from records of recent auctions. The following results summarize the least-squares regression fit of this model. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4277160 Intercept –1336.72 173.36 Error 29 514034 Age 12.73 0.90 Number of 85.82 8.71 Bidders The auctioneer also ran the multiple regression model with a term for the interaction between age of clock and number of bidders. The model is: , where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4572548 Intercept 322.75 293.33 Error 28 218646 Age 0.87 2.02 Number of –93.41 29.71 Bidders Interaction 1.30 0.21 The proportion of variability in the response variable explained by the regression model with the interaction term is: a. 0.059. b. 0.12. c. 0.893. d. 0.954. ANSWER: d 23. An auctioneer of antique grandfather clocks knows that the price received for a clock at auction increases with the clock’s age and with the number of bidders. The model proposed for predicting the price of a clock Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 29 from its age and the number of bidders is:

, where the

deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to a sample of 32 clocks selected from records of recent auctions. The following results summarize the least-squares regression fit of this model. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4277160 Intercept –1336.72 173.36 Error 29 514034 Age 12.73 .90 Number of 85.82 8.71 Bidders The auctioneer also ran the multiple regression model with a term for the interaction between age of clock and number of bidders. The model is: , where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4572548 Intercept 322.75 293.33 Error 28 218646 Age 0.87 2.02 Number of –93.41 29.71 Bidders Interaction 1.30 0.21 Which of the following statements is correct with respect to comparing these two models? a. Adding the interaction term increases and decreases s (the estimate of ). b. Adding the interaction term decreases

and decreases s (the estimate of ).

c. Adding the interaction term decreases

and increases s (the estimate of ).

d. None of the answer options is correct. ANSWER: a 24. An auctioneer of antique grandfather clocks knows that the price received for a clock at auction increases with the clock’s age and with the number of bidders. The model proposed for predicting the price of a clock from its age and the number of bidders is: , where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to a sample of 32 clocks selected from records of recent auctions. The following results summarize the least-squares regression fit of this model. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4277160 Intercept –1336.72 173.36 Error 29 514034 Age 12.73 .90 Number of 85.82 8.71 Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 29 Bidders The auctioneer also ran the multiple regression model with a term for the interaction between age of clock and number of bidders. The model is: , where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4572548 Intercept 322.75 293.33 Error 28 218646 Age 0.87 2.02 Number of –93.41 29.71 Bidders Interaction 1.30 0.21 Based on the analyses above, we conclude that: a. including an interaction term isn’t necessary or useful—the simpler model is best. b. including the interaction term is very useful—age of clock and number of bidders interact, and we should incorporate this into our regression model. c. it would be best to use the simple linear regression model with only age of clock. d. it would be best to use the simple linear regression model with only number of bidders. ANSWER: b 25. An auctioneer of antique grandfather clocks knows that the price received for a clock at auction increases with the clock’s age and with the number of bidders. The model proposed for predicting the price of a clock from its age and the number of bidders is: , where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to a sample of 32 clocks selected from records of recent auctions. The following results summarize the least-squares regression fit of this model. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4277160 Intercept –1336.72 173.36 Error 29 514034 Age 12.73 .90 Number of 85.82 8.71 Bidders The auctioneer also ran the multiple regression model with a term for the interaction between age of clock and number of bidders. The model is: , where the deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 4572548 Intercept 322.75 293.33 Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 29 Error

218646

Age Number of Bidders Interaction

0.87 –93.41

2.02 29.71

1.30

0.21

The statistical results in the analyses above are: a. very meaningful, because the results are based on a very large sample of antique clocks. b. meaningful, because for the multiple regression model is quite large, suggesting that the model fits well and that the assumptions about the model are reasonable. c. meaningful, if we also conduct an analysis of residuals and investigate whether the typical regression assumptions are reasonable. d. very precise, because this model will produce very accurate predictions of antique clock prices. ANSWER: c 26. Based on a sample of the salaries of professors at a major university, you have performed a multiple regression relating salary to years of service and tenure. The estimated multiple linear regression model is = 45,000 + 2000(years) + 4000(tenure) + $500(years)(tenure), where tenure = 1 if the professor has tenure, and tenure = 0 if the professor does not have tenure. The interaction term in this model is: a. 2000(years). b. 4000(tenure). c. 500(years)(tenure). d. not present; there is no interaction term in this model. ANSWER: c 27. Based on a sample of the salaries of professors at a major university, you have performed a multiple regression relating salary to years of service and tenure. The estimated multiple linear regression model is = 45,000 + 2000(years) + 4000(tenure) + $500(years)(tenure), where tenure = 1 if the professor has tenure, and tenure = 0 if the professor does not have tenure. Using the multiple linear regression equation, you would estimate the average difference in the salaries of a tenured professor with 10 years of service and a non-tenured professor with 10 years of service to be: a. $3000. b. $4000. c. $5000. d. $9000. ANSWER: d 28. Based on a sample of the salaries of professors at a major university, you have performed a multiple regression relating salary to years of service and tenure. The estimated multiple linear regression model is = 45,000 + 2000(years) + 4000(tenure) + $500(years)(tenure), where tenure = 1 if the professor has tenure, and tenure = 0 if the professor does not have tenure. Using the multiple linear regression equation, you would estimate the average salary of a t e n u r e d professor with 10 years of experience to be: a. $53,000. b. $54,000. Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 29 c. $69,000. d. $74,000. ANSWER: d 29. Executives for a retail chain want to project sales for the coming winter holiday. It seems reasonable to believe that sales for the winter holiday during the current year might depend on sales for the winter holiday during the previous year, as well as on sales in some recent month―say, August. Hence, in this problem we consider the model , where average sales for the current winter holiday, x1 = previous year’s winter holiday sales, and x2 = sales for August of current year. The deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to data for the 10 previous years using the method of least squares. All units are in thousands of dollars. The following results were obtained from statistical software. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 23100 Intercept 106.51 10.30 Error 7 3900 X1 0.94 0.54 X2 0.34 0.02 The value of the MSE is: a. 18.9. b. 557.14. c. 11,050. d. 2,500. ANSWER: b 30. Executives for a retail chain want to project sales for the coming winter holiday. It seems reasonable to believe that sales for the winter holiday during the current year might depend on sales for the winter holiday during the previous year, as well as on sales in some recent month―say, August. Hence, in this problem we consider the model , where average sales for the current winter holiday, x1 = previous year’s winter holiday sales, and x2 = sales for August of current year. The deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to data for the 10 previous years using the method of least squares. All units are in thousands of dollars. The following results were obtained from statistical software. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 23100 Intercept 106.51 10.30 Error 7 3900 X1 0.94 0.54 X2 0.34 0.02 The estimate of standard deviation of sales for the current winter holiday season, given both explanatory variables, is: a. 3.24. b. 7.16. c. 23.60. d. 105.12. Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 29 ANSWER: c 31. Executives for a retail chain want to project sales for the coming winter holiday. It seems reasonable to believe that sales for the winter holiday during the current year might depend on sales for the winter holiday during the previous year, as well as on sales in some recent month―say, August. Hence, in this problem we consider the model , where average sales for the current winter holiday, x1 = previous year’s winter holiday sales, and x2 = sales for August of current year. The deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to data for the 10 previous years using the method of least squares. All units are in thousands of dollars. The following results were obtained from statistical software. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 23100 Intercept 106.51 10.30 Error 7 3900 X1 0.94 0.54 X2 0.34 0.02 Suppose we wish to use the ANOVA F test to test the following: versus at least one of and is not zero. The value of the F statistic is: a. 0.032. b. 8.84. c. 20.731. d. 72.64. ANSWER: c 32. Executives for a retail chain want to project sales for the coming winter holiday. It seems reasonable to believe that sales for the winter holiday during the current year might depend on sales for the winter holiday during the previous year, as well as on sales in some recent month―say, August. Hence, in this problem we consider the model , where average sales for the current winter holiday, x1 = previous year’s winter holiday sales, and x2 = sales for August of current year. The deviations were assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to data for the 10 previous years using the method of least squares. All units are in thousands of dollars. The following results were obtained from statistical software. Analysis of Variance Parameter Estimates Source df Sum of squares Variable Estimate SE Model 2 23100 Intercept 106.51 10.30 Error 7 3900 X1 0.94 0.54 X2 0.34 0.02 A 95% confidence interval for (the coefficient of the variable sales for last year’s winter holiday season) is approximately: a. 0.94 2.174. b. 0.94

1.058.

c. 0.94

1.277.

Page 15

Name:

Class:

Date:

Chapter 29 d. 0.94

0.092.

ANSWER: c 33. In a multiple regression with three explanatory variables, the total sum of squares SST = 1500 and the mean error sum of squares MSE = 20. There are 15 observations. The value of is: a. 0.85. b. 0.65. c. 0.52. d. There is not enough information to determine

ANSWER: a 34. A nutrition study investigated how well a food behavior survey could predict body mass index (BMI) three years later. The survey questionnaire had 40 questions, each with scores between 1 (item is high-calorie) and 5 (item is low-calorie), about different types of food. These questions were added to form a continuous scale called a qscale. The other variables of interest were age and smoking status (1 = female and 0 = male). The nutritionists considered the following model: Model 1: Average BMI = After careful study of the model, the nutritionists add total calories consumed (obtained from a food log) to Model 1. As a result, the coefficient for qscale becomes negative, indicating that a higher consumption of bad foods (typically high-calorie foods) results in lower BMI. The most reasonable explanation for this is that: a. there is a mistake, and something must have changed in the qscale variable. b. the qscale variable and total calories are highly correlated, and the estimate of the qscale coefficient is affected by the presence of total calories consumed. c. the total calorie variable is wrong and needs to be carefully checked. d. All of the answer options are correct. ANSWER: b 35. A study of carbon monoxide (CO) concentration in smokers was conducted using “minutes since last cigarette smoked” as a predictor. A question also arose about whether cigarette type made a difference. Ultralight cigarettes were coded as “1” and all other types as “0.” A linear regression model was fit with those two variables. The table provides computer output from a regression program using R. Coefficients: Estimate Std. Error t-Value P-Value Intercept 299.74 12.4 24.181 P < 0.0001 Time elapsed −0.23 0.02661 −8.651 P < 0.0001 Type −2.91 16.06 −0.181 P = 0.856 Residual standard error: 119.5 on 221 degrees of freedom Multiple R-squared: 0.2549 F statistic: 37.8 on 2 and 221 DF P-value < 0.0001 We can conclude that CO concentration: a. increases with time elapsed since last cigarette smoked. b. decreases with time elapsed since last cigarette smoked. c. decreases only with ultralight with time elapsed. d. increases only with ultralight with time elapsed. Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 29 ANSWER: b 36. A study of carbon monoxide (CO) concentration in smokers was conducted using “minutes since last cigarette smoked” as a predictor. A question also arose about whether cigarette type made a difference. Ultralight cigarettes were coded as “1” and all other types as “0.” A linear regression model was fit with those two variables. The table provides computer output from a regression program using R. Coefficients: Estimate Std. Error t-Value P-Value Intercept 299.74 12.4 24.181 P < 0.0001 Time elapsed −0.23 0.02661 −8.651 P < 0.0001 Type −2.91 16.06 −0.181 P = 0.856 Residual standard error: 119.5 on 221 degrees of freedom Multiple R-squared: 0.2549 F statistic: 37.8 on 2 and 221 DF P-value < 0.0001 The computer output provides: a. strong evidence of an interaction between time elapsed and type. b. weak evidence of an interaction between time elapsed and type. c. no evidence of an interaction between time elapsed and type. d. a clear indication that there is no interaction, because the term does not even appear in the output. ANSWER: c 37. A study of carbon monoxide (CO) concentration in smokers was conducted using “minutes since last cigarette smoked” as a predictor. A question also arose about whether cigarette type made a difference. Ultralight cigarettes were coded as “1” and all other types as “0.” A linear regression model was fit with those two variables. The table provides computer output from a regression program using R. Coefficients: Estimate Std. Error t-Value P-Value Intercept 299.74 12.4 24.181 P < 0.0001 Time elapsed −0.23 0.02661 −8.651 P < 0.0001 Type −2.91 16.06 −0.181 P = 0.856 Residual standard error: 119.5 on 221 degrees of freedom Multiple R-squared: 0.2549 F statistic: 37.8 on 2 and 221 DF P-value < 0.0001 The procedure to assess whether there is an interaction between time elapsed and type is: a. fit a regression with a time elapsed/type interaction, and examine the t statistic for the interaction. b. fit a model with only the interaction, and look at the F statistic for this one-term regression model. c. fit a model with only the interaction, and study the residual plot. d. create a scatterplot with different symbols for males and females, and make a judgment call. ANSWER: a 38. A study of carbon monoxide (CO) concentration in smokers was conducted using “minutes since last cigarette smoked” as a predictor. A question also arose about whether cigarette type made a difference. Ultralight cigarettes were coded as “1” and all other types as “0.” A linear regression model was fit with those two variables. The table provides computer output from a regression program using R. Coefficients: Estimate Std. Error t-Value P-Value Intercept 299.74 12.4 24.181 P < 0.0001 Copyright Macmillan Learning. Powered by Cognero.

Page 17

Name:

Class:

Date:

Chapter 29 Time elapsed −0.23 0.02661 −8.651 P < 0.0001 Type −2.91 16.06 −0.181 P = 0.856 Residual standard error: 119.5 on 221 degrees of freedom Multiple R-squared: 0.2549 F statistic: 37.8 on 2 and 221 DF P-value < 0.0001 The multiple R-squared is the ratio of: a. the model mean square to the error mean square. b. the model sum of squares to the error sum of squares. c. the model sum of squares to the total sum of squares. d. the error sum of squares to the total sum of squares. ANSWER: c 39. A study of carbon monoxide (CO) concentration in smokers was conducted using “minutes since last cigarette smoked” as a predictor. A question also arose about whether cigarette type made a difference. Ultralight cigarettes were coded as “1” and all other types as “0.” A linear regression model was fit with those two variables. The table provides computer output from a regression program using R. Coefficients: Estimate Std. Error t-Value P-Value Intercept 299.74 12.4 24.181 P < 0.0001 Time elapsed −0.23 0.02661 −8.651 P < 0.0001 Type −2.91 16.06 −0.181 P = 0.856 Residual standard error: 119.5 on 221 degrees of freedom Multiple R-squared: 0.2549 F statistic: 37.8 on 2 and 221 DF P-value < 0.0001 The investigators also decided to add age and an age-type interaction. This means that in the new model, the total number of parameters to estimate (including the intercept) is: a. 3. b. 4. c. 5. d. 6. ANSWER: d

Page 18

Name:

Class:

Date:

Chapter 30 1. Which test should be used to determine whether there are differences between the means of several groups that can be segmented according to two different explanatory variables? a. a one-way ANOVA b. a two-way ANOVA c. multiple comparisons procedures (without contrasts) d. multiple comparisons procedures (with contrasts) ANSWER: b 2. Which test should be used to determine whether there are differences between the means of several groups that cannot be segmented according to two different explanatory variables? a. a one-way ANOVA b. a two-way ANOVA c. multiple comparisons procedures (without contrasts) d. multiple comparisons procedures (with contrasts) ANSWER: a 3. A marketing manager studied the effect of packaging on sales. Four designs were chosen: Design 1 had three colors, Design 2 had three colors and cartoons, Design 3 had five colors, and Design 4 had five colors and cartoons. The plot below provides means at all four levels of color and cartoon combinations.

Page 1

Name:

Class:

Date:

Chapter 30

Based on the plot, what can we conclude? a. The plot suggests that adding cartoons to three colors may not increase sales. b. The plot suggests that adding cartoons to five colors may increases sales. c. The plot suggests that going from three to five colors may increase sales. d. All of the answer options are correct. ANSWER: d 4. A marketing manager studied the effect of packaging on sales. Four designs were chosen: Design 1 had three colors, Design 2 had three colors and cartoons, Design 3 had five colors, and Design 4 had five colors and cartoons. The ANOVA table below analyzes the effects on sales of varying the number of colors and adding cartoons. This is an example of a two-factor factorial design. Source df SS MS F P Color 1 432.45 432.45 43.68 0.000 Cartoon 1 54.45 54.45 5.50 0.032 Color*Cartoon 1 101.25 101.25 10.23 0.006 Error 16 158.40 9.90 Total 19 746.55 Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 30 The estimate of the standard deviation a. 9.9. b. 3.15. c. 158.4. d. 10.23. ANSWER: b

is given by:

5. A marketing manager studied the effect of packaging on sales. Four designs were chosen: Design 1 three colors, Design 2 had three colors and cartoons, Design 3 had five colors, and Design 4 had five colors and cartoons. The ANOVA table below analyzes the effects on sales of varying the number of colors and adding cartoons. There were 20 stores where the boxes with the new designs were sold. Source df SS MS F P Color 1 432.45 432.45 43.68 0.000 Cartoon 1 54.45 54.45 5.50 0.032 Color*Cartoon 1 101.25 101.25 10.23 0.006 Error 16 158.40 9.90 Total 19 746.55 The F statistic for testing that there is no interaction is: a. 10.23. b. 5.5. c. 43.68. d. None of the answer options is correct. ANSWER: a 6. Instructors gave caffeine to fruit flies to see whether it affected their rest. The three treatments were a control, a low caffeine dose, and a higher caffeine dose. Fifteen fruit flies were assigned at random to three treatments, five to each treatment. The minutes of rest measured over a 12-hour period were recorded; the data follow. Minutes of Minutes of Minutes of Minutes of Minutes Treatment rest rest rest rest of rest Control 450 413 418 481 385 Low dose 466 420 435 370 401 High dose 265 330 389 349 311 Minitab was used to obtain 95% simultaneous confidence intervals for the differences in means among the three treatments using Tukey’s procedure; the results follow. Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of Group Individual confidence level = 97.94% Group = Control subtracted from: Group Lower Center Upper High -167.81 -100.60 -33.39 Low -78.21 -11.00 56.21 Group = High subtracted from: Group Lower Center Upper Low 22.39 89.60 156.81 Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 30 The average minutes of rest for the five fruit flies assigned to the low-dose group were: a. 11 minutes higher than the average for the five fruit flies assigned to the control dose. b. 89.6 minutes lower than the average for the five fruit flies assigned to the high dose. c. 89.6 minutes higher than the average for the five fruit flies assigned to the high dose. d. 56.21 minutes higher than the average for the five fruit flies assigned to the control dose. ANSWER: c 7. Instructors gave caffeine to fruit flies to see whether it affected their rest. The three treatments were a control, a low caffeine dose, and a higher caffeine dose. Fifteen fruit flies were assigned at random to three treatments, five to each treatment. The minutes of rest measured over a 12-hour period were recorded; the data follow. Minutes of Minutes of Minutes of Minutes of Minutes Treatment rest rest rest rest of rest Control 450 413 418 481 385 Low dose 466 420 435 370 401 High dose 265 330 389 349 311 Minitab was used to obtain 95% simultaneous confidence intervals for the differences in means among the three treatments using Tukey’s procedure; the results follow. Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of Group Individual confidence level = 97.94% Group = Control subtracted from: Group Lower Center Upper High -167.81 -100.60 -33.39 Low -78.21 -11.00 56.21 Group = High subtracted from: Group Lower Center Upper Low 22.39 89.60 156.81 From these intervals: a. there is not sufficient evidence to conclude that . b. there is sufficient evidence to conclude that c. there is sufficient evidence to conclude that

. .

d. All of the answer options are correct. ANSWER: d 8. A researcher wished to compare the effects of the rate of stepping on heart rate in a step-aerobics workout. Thirty adult volunteers, 15 females and 15 males, were selected from a local gym. The males were randomly divided into three groups of five subjects each. Each group did a standard step-aerobics workout, with Group 1 at a low rate of stepping, Group 2 at a medium rate of stepping, and Group 3 at a rapid rate. The females were also randomly divided into three groups of five subjects each. As with the males, each group did one of the three standard step-aerobics workouts. The mean heart rate at the end of the workout for all subjects was determined (in beats per minute). A partial ANOVA table for these data is given below. Analysis of variance for heart rate: Source df SS MS F P Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 30 Step rate 2 2553.2 1276.6 Sex 1 70.7 70.7 Group*Sex 2 231.7 115.9 Error 24 5762.0 240.1 Total 29 8617.6 Which test was used to explore this problem? a. a one-way ANOVA b. a two-way ANOVA c. multiple comparisons procedures (without contrasts) d. multiple comparisons procedures (with contrasts) ANSWER: b

5.32 0.29 0.48

0.012 0.595 0.623

9. A researcher wished to compare the effects of the rate of stepping on heart rate in a step-aerobics workout. Thirty adult volunteers, 15 females and 15 males, were selected from a local gym. The males were randomly divided into three groups of five subjects each. Each group did a standard step-aerobics workout, with Group 1 at a low rate of stepping, Group 2 at a medium rate of stepping, and Group 3 at a rapid rate. The females were also randomly divided into three groups of five subjects each. As with the males, each group did one of the three standard step-aerobics workouts. The mean heart rate at the end of the workout for all subjects was determined (in beats per minute). A partial ANOVA table for these data is given below. Source df SS MS F P Step rate 2 2553.2 1276.6 5.32 0.012 Sex 1 70.7 70.7 0.29 0.595 Group*Sex 2 231.7 115.9 0.48 0.623 Error 24 5762.0 240.1 Total 29 8617.6 The factors in the experiment are: a. rate of stepping and heart rate. b. rate of stepping and gender. c. heart rate and gender. d. gym membership and gender. ANSWER: b 10. A researcher wished to compare the effects of the rate of stepping on heart rate in a step-aerobics workout. Thirty adult volunteers, 15 females and 15 males, were selected from a local gym. The males were randomly divided into three groups of five subjects each. Each group did a standard step-aerobics workout, with Group 1 at a low rate of stepping, Group 2 at a medium rate of stepping, and Group 3 at a rapid rate. The females were also randomly divided into three groups of five subjects each. As with the males, each group did one of the three standard step-aerobics workouts. The mean heart rate at the end of the workout for all subjects was determined (in beats per minute). A partial ANOVA table for these data is given below. Analysis of variance for heart rate: Source df SS MS F P Step rate 2 2553.2 1276.6 5.32 0.012 Sex 1 70.7 70.7 0.29 0.595 Group*Sex 2 231.7 115.9 0.48 0.623 Error 24 5762.0 240.1 Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 30 Total 29 8617.6 The number of treatment groups in the experiment is: a. 3. b. 5. c. 6. d. 30. ANSWER: c 11. A researcher wished to compare the effects of the rate of stepping on heart rate in a step-aerobics workout. Thirty adult volunteers, 15 females and 15 males, were selected from a local gym. The males were randomly divided into three groups of five subjects each. Each group did a standard step-aerobics workout, with Group 1 at a low rate of stepping, Group 2 at a medium rate of stepping, and Group 3 at a rapid rate. The females were also randomly divided into three groups of five subjects each. As with the males, each group did one of the three standard step-aerobics workouts. The mean heart rate at the end of the workout for all subjects was determined (in beats per minute). A partial ANOVA table for these data is given below: Source df SS MS F P Step rate 2 2553.2 1276.6 5.32 0.012 Sex 1 70.7 70.7 0.29 0.595 Group*Sex 2 231.7 115.9 0.48 0.623 Error 24 5762.0 240.1 Total 29 8617.6 The pooled standard error is: a. 15.5. b. 75.9. c. 240.1. d. 5762. ANSWER: a 12. A researcher wished to compare the effects of the rate of stepping on heart rate in a step-aerobics workout. Thirty adult volunteers, 15 females and 15 males, was selected from a local gym. The males were randomly divided into three groups of five subjects each. Each group did a standard step-aerobics workout, with Group 1 at a low rate of stepping, Group 2 at a medium rate of stepping, and Group 3 at a rapid rate. The females were also randomly divided into three groups of five subjects each. As with the males, each group did one of the three standard step-aerobics workouts. The mean heart rate at the end of the workout for all subjects was determined (in beats per minute). A partial ANOVA table for these data is given below. Analysis of variance for heart rate: Source df SS MS F P Step rate 2 2553.2 1276.6 5.32 0.012 Sex 1 70.7 70.7 0.29 0.595 Group*Sex 2 231.7 115.9 0.48 0.623 Error 24 5762.0 240.1 Total 29 8617.6 The plots and the P-value for the test for interaction show little evidence of interaction, which means that: a. there is little difference in the heart rates of males and females. b. there is evidence that the change in heart rate due to the different stepping rates is similar for males Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 30 and females. c. there is evidence that changes in stepping rate are positively associated with heart rate. d. step exercise is equally beneficial to males and females. ANSWER: b 13. A researcher wished to compare the effects of the rate of stepping on heart rate in a step-aerobics workout. Thirty adult volunteers, 15 females and 15 males, were selected from a local gym. The males were randomly divided into three groups of five subjects each. Each group did a standard step-aerobics workout, with Group 1 at a low rate of stepping, Group 2 at a medium rate of stepping, and Group 3 at a rapid rate. The females were also randomly divided into three groups of five subjects each. As with the males, each group did one of the three standard step-aerobics workouts. The mean heart rate at the end of the workout for all subjects was determined (in beats per minute). A partial ANOVA table for these data is given below. Analysis of variance for heart rate: Source df SS MS F P Step rate 2 2553.2 1276.6 5.32 0.012 Sex 1 70.7 70.7 0.29 0.595 Group*Sex 2 231.7 115.9 0.48 0.623 Error 24 5762.0 240.1 Total 29 8617.6 Because there is little evidence of interaction and the main effect of stepping, what can we conclude? a. There is evidence that the population mean heart rate for the rapid-rate group is higher than that for the other two groups. b. There is evidence that the population mean heart rate for the low-rate group is lower than those for the other two groups. c. There is evidence that the population mean heart rate for the low-rate group is lower than that for the medium-rate group. d. None of the answer options is correct. ANSWER: d 14. A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: The first had greater visual appeal, and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: Source df SS MS F P Design 0.613 Size 7256 Size*Design 41707 Error 12262 Total 17 206664 Which statement best describes the type of experiment being run? a. This is a two-factor experiment—each factor is at three levels. Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 30 b. This is a six-level experiment—each level has three observations. c. This is a two-factor experiment—one factor is at two levels, and the other factor is at three levels. d. None of the answer options is correct. ANSWER: c 15. A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: The first had greater visual appeal, and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: Source df SS MS F P Design 0.613 Size 7256 Size*Design 41707 Error 12262 Total 17 206664 The sum of squares for size is: a. 7256. b. 14512. c. 21768. d. 206664. ANSWER: b 16. A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: The first had greater visual appeal, and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: Source df SS MS F P Design 0.613 Size 7256 Size*Design 41707 Error 12262 Total 17 206664 What are the degrees of freedom for the main effect size? a. 1. b. 2. c. 3. Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 30 d. 6. ANSWER: b 17. A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: The first had greater visual appeal, and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: Source df SS MS F P Design 0.613 Size 7256 Size*Design 41707 Error 12262 Total 17 206664 The numerical value of the F statistic used for testing for the main effect of size is: a. 0.59. b. 1.69. c. 3.4. d. 202.33. ANSWER: a 18. A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: The first had greater visual appeal, and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: Source df SS MS F P Design 0.613 Size 7256 Size*Design 41707 Error 12262 Total 17 206664 In the ANOVA table, the test for the main effect of design has a P-value of 0.613, which indicates that: a. sales probably vary considerably for the different designs. b. for about 61.3% of the samples, there was a difference in the effect of design. c. for about 61.3% of the samples, there was no difference in the effect of design. d. None of the answer options is correct. ANSWER: d Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 30 19. A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: The first had greater visual appeal, and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: Source df SS MS F P Design 0.613 Size 7256 Size*Design 41707 Error 12262 Total 17 206664 What conclusion should be drawn from this test? a. Fail to reject the null hypothesis. b. There is no evidence to suggest that design is either more or less likely to influence sales. c. There is some evidence that design influences sales. d. There is strong evidence that design influences sales. ANSWER: b 20. A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population. Purpose Short Distance Medium Long Distance Distance Business 400 700 1500 Vacation 200 400 700 The average price for short flights is: a. $400. b. $300. c. $200. d. None of the answer options is correct. ANSWER: b 21. A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population. Purpose Short Distance Medium Long Distance Distance Business 400 700 1500 Vacation 200 400 700 The average cost of a business flight is: a. $400. Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 30 b. $2600. c. $650. d. $866.67. ANSWER: d 22. A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population. Purpose Short Distance Medium Long Distance Distance Business 400 700 1500 Vacation 200 400 700 The difference between the cost of a business flight and the cost of a vacation flight: a. is constant across distance. b. differs by distance. c. depends on the time of day. d. cannot be determined with the information given. ANSWER: b 23. A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population. Purpose Short Distance Medium Long Distance Distance Business 400 700 1500 Vacation 200 400 700 A medium-distance business flight costs $300 more than a short-distance business flight. However, a mediumdistance vacation flights is only $200 more than a short-distance vacation flight. This difference between business and vacation flights is called: a. interference of effects. b. confusion of effects. c. difference of effects. d. interaction. ANSWER: d 24. A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population and shows the presence of interactions. Purpose Short Distance Medium Long Distance Distance Business 400 700 1500 Vacation 200 400 700 If a study is conducted and we think there may be interactions, we should: Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 30 a. find the F test for interaction first, and if the P-value is small enough to reject the null hypothesis of no interaction, assess the effects of distance separately for business and vacation flights. b. test for effects of distance first, and if there is no distance effect, ignore the interactions. c. find the F tests for distance effects and for type of trip, and if there is no effect for either, declare that all the means are the same. d. drop observations that cause the interaction, and repeat the analysis. ANSWER: a 25. A study compared dry matter intake (dmi) in mature cows (C) and heifers (H) receiving no treatment (control), Treatment A, or Treatment B. The two factors are type of animal and treatment. Each factor combination has eight animals.

The above plot of the means, which is derived from a two-factor analysis of variance, is called: a. an interaction plot. b. a parallel means plot. c. a nonparallel means plot. d. a crossover plot. Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 30 ANSWER: a 26. A study compared dry matter intake (dmi) in mature cows (C) and heifers (H) receiving no treatment (control), Treatment A, or Treatment B. The two factors are type of animal and treatment. Each factor combination had eight animals. The degrees of freedom for the interaction effect are: a. 6. b. 4. c. 2. d. 8. ANSWER: c 27. A study compared dry matter intake (dmi) in mature cows (C) and heifers (H) receiving no treatment (control), treatment A, or treatment B. The two factors are type of animal and treatment. Each factor combination had eight animals. A partial ANOVA table is given below. Source df SS F Type of animal 1 206.90 83.2 Treatment 2 4.20 Type of animal*Treatment 2 14.95 Residual 42 104.40 The F test for interaction is: a. 83.2. b. 20.3. c. 3.02. d. 0.85. ANSWER: c

Page 13

Name:

Class:

Date:

Chapter 31 1. A cause-and-effect (or “fishbone”) diagram: a. organizes the logical relationships between the inputs and stages of a process and an output. b. is a picture of the stages of a process. c. is a scatterplot that uses different plotting symbols for points that correspond to possibly different causes. d. is a bar graph in which the bars are ordered by height. ANSWER: a 2. A variable is measured periodically during a process. The variable is said to be in statistical control: a. if its behavior is non-random. b. if the pattern of variation remains stable over time. c. if there is no variation within the process. d. if predicting the values of the variable over time is easy. ANSWER: b 3. You eat dinner every day. The average number of calories you consume with dinner is 805, but the number of calories varies each day, so your calorie consumption can be considered a process. Which of the following is an example of a source of special cause variation? a. The amount of oil or fat you use preparing dinner varies daily. b. You indulge in a holiday feast, such as Thanksgiving dinner. c. You occasionally choose to eat dessert. d. None of the answer options is correct. ANSWER: b 4. A chart in which the sample means of samples taken at regular intervals are plotted against the time order in which the samples were taken is called a(an): a. s chart. b. chart. c. R chart. d. p chart. ANSWER: b 5. The distribution of sample means on an

chart can best be described as:

a. having the same distribution as each of the items within the samples. b. uniform, because each of the means has the same probability of being observed. c. Normal, because the sampling distribution of sample means is usually Normal. d. Normal, as long as the central limit theorem applies. ANSWER: d

Page 1

Name:

Class:

Date:

Chapter 31 6. Which of the following statements about

charts and s charts is true?

a. The s chart should be examined first, because the b. The

chart is valid only if s is in control.

chart should be examined first, because the s chart is valid only if

c. It is impossible to interpret

is in control.

charts and s charts individually, because they must be examined at the

same time. d. None of the answer options is correct. ANSWER: a 7. Statistical stability refers to which of the following conditions? a. The chart shows a consistent trend up or down. b. The s chart shows a consistent trend up or down. c. The pattern of variation of the process remains stable. d. The mean never changes. ANSWER: c 8. A process that is in control has: a. no variation. b. a constant mean. c. a sample mean that is within 3 standard deviations of the true mean. d. None of the answer options is correct. ANSWER: c 9. The term “runs signal” refers to: a. having nine consecutive samples above or below the mean. b. having the means exceed the UCL or LCL for at least two samples. c. having all means alternate between being above and below the centerline. d. having sample means that are smaller than the sample variances. ANSWER: a 10. To create control charts for process monitoring, a quality control team should: a. wait a while for the process to evolve, and then take simple random samples from the process. b. get a sample as soon as possible after the process starts, and then bootstrap for more samples. c. combine data from similar processes to get started. d. None of the answer options is correct. ANSWER: d 11. Process control in manufacturing is important, because a process that is in control: a. implies that product quality is guaranteed to be excellent. Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 31 b. tells us the state the process is in. c. tells us what type of special cause we might expect next. d. None of the answer options is correct. ANSWER: b 12. An airline has a special call center for its frequent flyers. The airline considers the frequent flyers to be its most valued customers and is interested in keeping wait times to a minimum. Although most calls occur during daylight hours, a certain number of calls come in at night, particularly from frequent flyers who find themselves with delayed or canceled flights needing to be rebooked. The airline has been monitoring the process and has obtained data on wait times from the past 20 weeks, during which 10 incoming calls were monitored for wait time one day a week. The s chart (bottom) and chart (top) are displayed in the graph below.

Based on the graph, we can conclude that: a. the s chart is in control, because all values are between the UCL and the LCL. b. the chart is not in control, because it does not have the same pattern as the s chart. c. the s chart is not in control, because it shows more variability than the

chart.

d. None of the answer options is correct. ANSWER: a 13. An airline has a special call center for its frequent flyers. The airline considers the frequent flyers to be its most valued customers and is interested in keeping wait times to a minimum. Although most calls occur during daylight hours, a certain number of calls come in at night, particularly from frequent flyers who find themselves Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 31 with delayed or canceled flights needing to be rebooked. The airline was interested in identifying any customer service representatives who took longer to complete a call than others. The airline recorded the average length of phone calls for each of the 10 customer service representatives over several nights. The averages were then plotted in a Pareto chart for each worker.

The Pareto chart shows that: a. Worker 3 deals with 25.6% of all calls. b. Worker 6 had the shortest average call times. c. all 10 workers finished 100% of their phone calls. d. None of the answer options is correct. ANSWER: b 14. An airline has a special call center for its frequent flyers. The airline considers the frequent flyers to be its most valued customers and is interested in keeping wait times to a minimum. Although most calls occur during daylight hours, a certain number of calls come in at night, particularly from frequent flyers who find themselves with delayed or canceled flights needing to be rebooked. The airline has been monitoring the process and has obtained data on wait times from the past 20 weeks, during which incoming calls were monitored for 10 customer service representatives one day a week. The mean was Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 31 determined to be

minutes with

minutes. Based on this finding, the UCL of the control chart is:

a. 5.2 minutes. b. 6.34 minutes. c. 8.8 minutes. d. 7.6 minutes. ANSWER: b 15. An airline has a special call center for its frequent flyers. The airline considers the frequent flyers to be its most valued customers and is interested in keeping wait times to a minimum. Although most calls occur during daylight hours, a certain number of calls come in at night, particularly from frequent flyers who find themselves with delayed or canceled flights needing to be rebooked. The airline has been monitoring the process and has obtained data on wait times from the past 20 weeks, during which incoming calls were monitored for 10 customer service representatives one day a week. The airline found that during one 20-week period, the mean wait time was 5.2 minutes with a standard deviation of 1.2 minutes, based on samples of size 10. After monitoring the wait times for another 10 weeks, the airline noticed that during the month of January the average wait times went to 6 minutes (Week 1), then 7.2 minutes (Week 2), and then 10 minutes (Weeks 3 and 4). Based on this information, the manager in charge of customer service concluded that: a. the process was in control for all of January. b. the process was in control at the end of January. c. the process was not in control for all of January. d. the process was in control during the first week of January and not in control during Weeks 2, 3, and 4. ANSWER: d 16. An airline has a special call center for its frequent flyers. The airline considers the frequent flyers to be its most valued customers and is interested in keeping wait times to a minimum. Although most calls occur during daylight hours, a certain number of calls come in at night, particularly from frequent flyers who find themselves with delayed or canceled flights needing to be rebooked. The airline found that during the previous year, the mean wait time was 5.2 minutes with a standard deviation of 1.2 minutes. The airline kept monitoring the process during the winter months and collected 10 daily samples of wait times. The monitors found the following average times for during the 15 days from January 1 to January 15. 5.7 5.3 5.7 5.9 5.4 5.9 5.9 6.1 6.3 6.2 6.2 6.1 7.1 7.3 7.5 Based on these results, we conclude that: a. the process was in control the whole time. b. the process was in control until Day 13 and then was out of control, because the sample mean exceeded UCL. c. the process was out of control by Day 9 because of a run of sample means above the previous year mean. d. the process was out of control during the whole 15-day period, because the wait times were just too long. ANSWER: c Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 31 17. Piston rings for an automotive engine are produced by a forging process. We wish to monitor the inside diameter (in mm = millimeters) of the rings manufactured by this process, using an and an s control chart. Samples of size eight are to be taken at regular intervals, and the sample means and standard deviations are computed and plotted on the charts in time order. The target values for the inside diameter are a mean of mm and a standard deviation of partially reproduced below. Sample size n 2 0.7979 3 0.8862 4 0.9213 5 0.9400 6 0.9515 7 0.9594 8 0.9650 9 0.9693 The center line for the three-sigma

mm. Table 31.3 from the text, containing control chart constants, is

2.606 2.276 2.088 1.964 0.029 1.874 0.113 1.806 0.179 1.751 0.232 1.707 control chart would be:

a. 60 mm. b. 60.01 mm. c. 60.03 mm. d. 60.09 mm. ANSWER: a 18. Piston rings for an automotive engine are produced by a forging process. We wish to monitor the inside diameter (in mm = millimeters) of the rings manufactured by this process, using an and an s control chart. Samples of size eight are to be taken at regular intervals, and the sample means and standard deviations are computed and plotted on the charts in time order. The target values for the inside diameter are a mean of mm and a standard deviation of

mm. Table 31.3 from the text, containing control chart constants, is

partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 8 0.9650 0.179 1.751 9 0.9693 0.232 1.707 The lower control limit for the control chart would be: a. 60 mm. b. 59.958 mm. Copyright Macmillan Learning. Powered by Cognero.

Page 6

Name:

Class:

Date:

Chapter 31 c. 58.859 mm. d. 58.589 mm. ANSWER: b 19. Piston rings for an automotive engine are produced by a forging process. We wish to monitor the inside diameter (in mm = millimeters) of the rings manufactured by this process, using an and an s control chart. Samples of size eight are to be taken at regular intervals, and the sample means and standard deviations are computed and plotted on the charts in time order. The target values for the inside diameter are a mean of mm and a standard deviation of

mm. Table 31.3 from the text, containing control chart constants, is

partially reproduced below. Sample size n 2 0.7979 3 0.8862 4 0.9213 5 0.9400 6 0.9515 0.029 7 0.9594 0.113 8 0.9650 0.179 9 0.9693 0.232 The center line for the three-sigma s chart would be: a. 0.04 mm. b. 0.0093 mm. c. 0.0386 mm. d. 0.0394 mm. ANSWER: c

2.606 2.276 2.088 1.964 1.874 1.806 1.751 1.707

20. Piston rings for an automotive engine are produced by a forging process. We wish to monitor the inside diameter (in mm = millimeters) of the rings manufactured by this process, using an and an s control chart. Samples of size eight are to be taken at regular intervals, and the sample means and standard deviations are computed and plotted on the charts in time order. The target values for the inside diameter are a mean of mm and a standard deviation of

mm. Table 31.3 from the text, containing control chart constants, is

partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 8 0.9650 0.179 1.751 9 0.9693 0.232 1.707 The upper control limit for the three-sigma s chart would be: Copyright Macmillan Learning. Powered by Cognero.

Page 7

Name:

Class:

Date:

Chapter 31 a. 0 mm. b. 0.00716 mm. c. 0.07004 mm d. 0.04 mm. ANSWER: c 21. Parts manufactured by an injection-molding process are subjected to a compressive strength test. We wish to monitor the compressive strength of the parts manufactured by this process, using an and an s control chart. Samples of size nine are to be taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The target values for the compressive strengths are a mean of psi and a standard deviation of psi. Table 31.3 from the text, containing control chart constants, is partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 8 0.9650 0.179 1.751 9 0.9693 0.232 1.707 The center line for the three-sigma control chart would be: a. 3 psi. b. 77 psi. c. 80 psi. d. None of the answer options is correct. ANSWER: c 22. Parts manufactured by an injection-molding process are subjected to a compressive strength test. We wish to monitor the compressive strength of the parts manufactured by this process, using an and an s control chart. Samples of size nine are to be taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The target values for the compressive strengths are a mean of psi and a standard deviation of psi. Table 31.3 from the text, containing control chart constants, is partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 Copyright Macmillan Learning. Powered by Cognero.

Page 8

Name:

Class:

Date:

Chapter 31 8 0.9650 0.179 1.751 9 0.9693 0.232 1.707 The lower control limit for the three-sigma control chart would be: a. 71 psi. b. 77 psi. c. 83 psi. d. 89 psi. ANSWER: b 23. Parts manufactured by an injection-molding process are subjected to a compressive strength test. We wish to monitor the compressive strength of the parts manufactured by this process, using an and an s control chart. Samples of size nine are to be taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The target values for the compressive strengths are a mean of psi and a standard deviation of psi. Table 31.3 from the text, containing control chart constants, is partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 8 0.9650 0.179 1.751 9 0.9693 0.232 1.707 Suppose, at the time of sample 10, we observe a mean of 75 psi. We should: a. declare the process out of control. b. continue sampling—the process is still in control. c. continue sampling but increase the sample size to 16—the process is barely in control. d. continue sampling but reduce the sample size to 4—the process is well in control. ANSWER: a 24. Parts manufactured by an injection-molding process are subjected to a compressive strength test. We wish to monitor the compressive strength of the parts manufactured by this process, using an and an s control chart. Samples of size nine are to be taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The target values for the compressive strengths are a mean of psi and a standard deviation of psi. Table 31.3 from the text, containing control chart constants, is partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 Copyright Macmillan Learning. Powered by Cognero.

Page 9

Name:

Class:

Date:

Chapter 31 5 0.9400 6 0.9515 0.029 7 0.9594 0.113 8 0.9650 0.179 9 0.9693 0.232 The center line for the three-sigma s chart is: a. 0.7 psi. b. 2.9 psi. c. 3 psi. d. 5.1 psi. ANSWER: b

1.964 1.874 1.806 1.751 1.707

25. Parts manufactured by an injection-molding process are subjected to a compressive strength test. We wish to monitor the compressive strength of the parts manufactured by this process, using an and an s control chart. Samples of size nine are to be taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The target values for the compressive strengths are a mean of psi and a standard deviation of psi. Table 31.3 from the text, containing control chart constants, is partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 8 0.9650 0.179 1.751 9 0.9693 0.232 1.707 The upper control limit for the three-sigma s chart is: a. 0.696 psi. b. 2.932 psi. c. 5.121 psi. d. 12 psi. ANSWER: c 26. In examining

and R charts, it is a good strategy to:

a. start with the

chart and examine the R chart only if a point is out of control.

b. start with the R chart and ignore the

chart, unless the R chart is in control or until any special

causes for lack of control in the R chart have been found and removed. c. examine both charts simultaneously and declare a point out of control only if it is outside the control limits on both charts. Copyright Macmillan Learning. Powered by Cognero.

Page 10

Name:

Class:

Date:

Chapter 31 d. examine both charts simultaneously and declare a point out of control only if it is outside the control limits of the chart but within the control limits of the R chart. ANSWER: b 27. An R chart is used to monitor: a. the spread of a process. b. the center of a process. c. both the center and the spread of a process. d. the correlation of a process. ANSWER: a 28. Consider the following s control chart.

Which of the following statements is true? a. There is no evidence that the process is out of control. b. There is weak evidence that the process is out of control, because several samples are unusually close to the center line. c. There is a run of several points on or above the center line, so the process is out of control. d. We cannot draw conclusions about whether the process is in control until we have observed at least 40 samples from the process. ANSWER: a 29. Parts manufactured by an injection-molding process are subjected to a compressive strength test. We Copyright Macmillan Learning. Powered by Cognero.

Page 11

Name:

Class:

Date:

Chapter 31 monitor the compressive strength of the parts manufactured by this process using an

and an s control chart.

Samples of size nine are taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The overall mean of the sample means is = 81.2 psi, and the mean of the sample standard deviations is = 2.9 psi. Table 31.3 from the text, containing control chart constants, is partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 8 0.9650 0.179 1.751 9 0.9693 0.232 1.707 10 0.9727 0.276 1.669 The center line for an control chart would be: a. 18.8 psi. b. 78.7 psi. c. 81.2 psi. d. 138.6 psi. ANSWER: c 30. Parts manufactured by an injection-molding process are subjected to a compressive strength test. We monitor the compressive strength of the parts manufactured by this process using an and an s control chart. Samples of size nine are taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The overall mean of the sample means is = 81.2 psi, and the mean of the sample standard deviations is = 2.9 psi. Table 31.3 from the text, containing control chart constants, is partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 8 0.9650 0.179 1.751 9 0.9693 0.232 1.707 10 0.9727 0.276 1.669 The upper control limit for an control chart would be: a. 0 psi. Copyright Macmillan Learning. Powered by Cognero.

Page 12

Name:

Class:

Date:

Chapter 31 b. 78.3 psi. c. 81.1 psi. d. 84.1 psi. ANSWER: d 31. Parts manufactured by an injection-molding process are subjected to a compressive strength test. We monitor the compressive strength of the parts manufactured by this process using an and an s control chart. Samples of size nine are taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The overall mean of the sample means is = 81.2 psi, and the mean of the sample standard deviations is = 2.9 psi. Table 31.3 from the textbook, containing control chart constants, is partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 8 0.9650 0.179 1.751 9 0.9693 0.232 1.707 10 0.9727 0.276 1.669 The center line for an s chart is: a. 2.8 psi. b. 2.9 psi. c. 3 psi. d. 5 psi. ANSWER: a 32. Parts manufactured by an injection-molding process are subjected to a compressive strength test. We monitor the compressive strength of the parts manufactured by this process using an and an s control chart. Samples of size nine are taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The overall mean of the sample means is = 81.2 psi, and the mean of the sample standard deviations is = 2.9 psi. Table 31.3 from the text, containing control chart constants, is partially reproduced below. Sample size n 2 0.7979 2.606 3 0.8862 2.276 4 0.9213 2.088 5 0.9400 1.964 6 0.9515 0.029 1.874 7 0.9594 0.113 1.806 8 0.9650 0.179 1.751 Copyright Macmillan Learning. Powered by Cognero.

Page 13

Name:

Class:

Date:

Chapter 31 9 0.9693 0.232 10 0.9727 0.276 The lower control limit for an s chart is: a. 0.7 psi. b. 2.9 psi. c. 4.9 psi. d. 12 psi. ANSWER: a

1.707 1.669

33. Rational subgroups are: a. those parts of a process that are identified as most likely to be special causes. b. samples chosen to reflect only item-to-item variation in a process. c. those samples in an s chart that are in control. d. the specific groups of charts that we use to monitor a process. ANSWER: b 34. The 68−95−99.7 rule tells us that if a process with mean and standard deviation varies according to a Normal distribution, then almost all measurements on individual products will lie in the range . The values

and

are called:

a. control limits. b. confidence limits. c. natural tolerances. d. capability limits. ANSWER: a 35. The ability of a process to meet or exceed the requirements placed on it is called: a. being in control. b. being within tolerances. c. stability. d. its capability. ANSWER: d 36. An automobile dealer checks on the quality of the Service Department by keeping a log of customer complaints and incidences of repeat service. Regular samples of 35 customers are taken, and, based on these data, the process proportion of customer complaints and incidences of repeat service is estimated to be = 0.114. The center line for a p chart of future samples of size 25 is: a. 0.003. b. 0.052. c. 0.114. d. 0.155. Copyright Macmillan Learning. Powered by Cognero.

Page 14

Name:

Class:

Date:

Chapter 31 ANSWER: c 37. An automobile dealer checks on the quality of the Service Department by keeping a log of customer complaints and incidences of repeat service. Regular samples of 35 customers are taken, and, based on these data, the process proportion of customer complaints and incidences of repeat service is estimated to be = 0.114. The upper control limit for a p chart of future samples of size 25 is: a. 0.08. b. 0.124. c. 0.155. d. 0.305. ANSWER: d 38. Because some customers have reported receiving products that they did not order, and others have reported not receiving products that they did order, a warehouse is attempting to improve its process for selecting and packaging the correct products into shipping boxes. Eighty packages are randomly inspected each day. The proportion of packages that have been improperly packed, estimated from data collected over a one-month period, is = 0.049. The center line for a p chart of future samples of size 80 is: a. 0.026. b. 0.016. c. 0.049. d. 0.056. ANSWER: c 39. Because some customers have reported receiving products that they did not order and others have reported not receiving products that they did order, a warehouse is attempting to improve its process for selecting the correct products and packaging them into shipping boxes. Eighty packages are randomly inspected each day. The proportion of packages that have been improperly packed, estimated from data collected over a one-month period, is = 0.049. The lower control limit for a p chart of future samples of size 80 is: a. 0. b. 0.016. c. 0.0016. d. −0.023. ANSWER: a 40. Because some customers have reported receiving products that they did not order, and others have reported not receiving products that they did order, a warehouse is attempting to improve its process for selecting the correct products and packaging them into shipping boxes. Eighty packages are randomly inspected each day. The proportion of packages that have been improperly packed, estimated from data collected over a one-month period, is = 0.049. The lower control limit for a p chart of future samples of size 500 is: a. 0. Copyright Macmillan Learning. Powered by Cognero.

Page 15

Name:

Class:

Date:

Chapter 31 b. 0.011. c. 0.02. d. not possible to determine because the data involve samples of size 500. ANSWER: c 41. Because some customers have reported receiving products that they did not order, and others have reported not receiving products that they did order, a warehouse is attempting to improve its process for selecting the correct products and packaging them into shipping boxes. Eighty packages are randomly inspected each day. The proportion of packages that have been improperly packed, estimated from data collected over a one-month period, is = 0.049. The upper control limit for a p chart of future samples of size 500 is: a. not possible to determine because the data involve samples of size 500. b. 0.078. c. 0.092. d. 1. ANSWER: b 42. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the restaurant. In statistical process control, a process is: a. a set of samples taken to measure the duration of an activity. b. a chain of activities that turns inputs into outputs. c. a set of statistical calculations that results in a confidence interval. d. None of the answer options is correct. ANSWER: b 43. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. One tool to help them understand possible aspects of poor performance is: a. the cause-and-effect diagram. b. the flowchart. c. the identification of a performance measure. d. All of the answer options are correct. ANSWER: d 44. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. To use process control, they need to gain an understanding of typical waiting times. In particular, they would Copyright Macmillan Learning. Powered by Cognero.

Page 16

Name:

Class:

Date:

Chapter 31 like waiting times to be consistent. The process is in control if: a. it is constant and the customer knows exactly how long the wait for service will be. b. the waiting times are the same for all customers, regardless of the size of the party. c. the pattern of variation remains stable, and there are no large fluctuations. d. waiting times never exceed a set amount of time. ANSWER: c 45. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. To obtain estimates of the parameters of the process, sampling is necessary. Inference is: a. possible only if the population distribution is Normal. b. possible only if the population distribution is symmetric. c. possible without too many assumptions on the population distribution. d. impossible unless the sample size is at least 30. ANSWER: c 46. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. The quality control team needs to decide on performance measures. A performance measure: a. describes the outputs of the process. b. describes the inputs of the process. c. modifies the inputs of the process. d. modifies the outputs of the process. ANSWER: a 47. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. To determine the state of the process, the owners should obtain charts and s charts. Which of the following is true for s charts? a. They measure process variability. b. They assess variability in waiting times due to specific waiters. c. They assess average waiting times. d. Both options (a) and (b) are correct. ANSWER: d 48. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. Copyright Macmillan Learning. Powered by Cognero.

Page 17

Name:

Class:

Date:

Chapter 31 The consultant has heard about a method called process control, which she believes can be used to help the restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. The owners were told they needed to obtain charts, where they will plot the average waiting time for each day. These charts are useful for monitoring: a. variability in waiting times. b. the causes of changes in waiting times (such as a new waiter). c. days on which the average waiting times exhibit large deviations. d. All of the answer options are correct. ANSWER: c 49. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. The owners first focus on a training method for waiters. Then they establish average waiting times and variability in waiting times. The mean waiting time is found to be = 5 minutes with a standard deviation of = 2 minutes. If they decide to sample n = 16 tables per evening and assume that only a long waiting time is an issue, the process will be out of control if the average waiting time exceeds: a. 6.5 minutes. b. 12 minutes. c. 5 minutes. d. 10 minutes. ANSWER: a 50. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. The owners first focus on a training method for waiters. Then they establish average waiting times and variability in waiting times. The mean waiting time is found to be = 5 minutes with a standard deviation of = 2 minutes. They decide to sample n = 16 tables per evening for the following month. They obtain the following data for Days 1 to 10 for average waiting times: 5.2 3.6 4.7 5.7 4.2 6.6 5.4 5.8 4.8 6.9 The system was out of control on which of the following days? a. Days 4, 6, and 10 b. Days 6 and 10 c. Days 6 through 10 d. None of the answer options is correct. ANSWER: b 51. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the Copyright Macmillan Learning. Powered by Cognero.

Page 18

Name:

Class:

Date:

Chapter 31 restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. After some time, the waiting process seems to run smoothly and is considered statistically in control. With a major holiday season approaching, the restaurant hires additional waiters. To assess the impact of a specific new hire on the waiting times, the best option would be: a. to use charts. b. to use R charts. c. to use s charts. d. to use v charts. ANSWER: c 52. A restaurant wants to improve customer satisfaction and has hired a consultant to help it achieve that goal. The consultant has heard about a method called process control, which she believes can be used to help the restaurant. After some discussion and a few surveys of customers, the restaurant owners decide that waiting time for service is one area of concern. The owners first focus on a training method for waiters. Then they establish average waiting times and variability in waiting times. With a major holiday season approaching, the restaurant decides to hire additional waiters. To assess the impact of the new hires on waiting times in general, the restaurant should: a. use charts. b. use R charts. c. use s charts. d. None of the answer options is correct. ANSWER: a 53. A restaurant wishing to improve customer satisfaction has implemented process control to assess daily operations, as well as the impact of hiring new personnel. Data are routinely collected on waiting times for tables. After some time, the average waiting time is determined to be = 8 minutes with standard deviation = 2 minutes. The restaurant decides to record waiting times for n = 6 tables for each two-hour period, beginning at noon and ending at midnight. The s chart should be centered at: a. 2. b. 8. c. 1.903. d. 7.612. ANSWER: c 54. A restaurant wishing to improve customer satisfaction has implemented process control to assess daily operations, as well as the impact of hiring new personnel. Data are routinely collected on waiting times for tables. After some time, the average waiting time is determined to be = 8 minutes with standard deviation = 2 minutes. The restaurant decides to record waiting times for n = 6 tables for each two-hour period, beginning at noon and ending at midnight. To assess the impact of individual waiters, s charts are used to monitor the process. The Copyright Macmillan Learning. Powered by Cognero.

Page 19

Name:

Class:

Date:

Chapter 31 process remains in control if variations in waiting times fall between: a. 6 and 12 minutes. b. 7 and 11 minutes. c. 0.058 and 3.748 minutes. d. 0.5 and 3.5 minutes. ANSWER: c 55. A restaurant wishing to improve customer satisfaction has implemented process control to assess daily operations, as well as the impact of hiring new personnel. Data are routinely collected on waiting times for tables. After some time, the average waiting time is determined to be = 8 minutes with standard deviation = 2 minutes. The restaurant decides to record waiting times for four successive tables during each shift for each new hire. The process is in control if the variability in service times stays between: a. 0 and 4.176 minutes. b. 2 and 4 minutes. c. 0.5 and 5.5 minutes. d. 1.5 and 6.5 minutes. ANSWER: a 56. Which of the following statements about process control is true? a. Process control, if implemented properly, guarantees a quality product. b. Process control, if implemented properly, leads to consistency in a product. c. Capability is the ability of the process to produce a superior product. d. All of the answer options are correct. ANSWER: b

Page 20

Name:

Class:

Date:

Chapter 32 1. In resampling techniques, we: a. use theories like the CLT to help us construct sampling distributions. b. use the population to create a sampling distribution that is used for confidence intervals and running tests. c. use the sample data to create a sampling distribution that is used for confidence intervals and running tests. d. use multiple samples from the population to create a sampling distribution that is used for confidence intervals and running tests. ANSWER: c 2. In a randomized control experiment, we: a. make the assumptions that our data are a random sample from a population and that we have an experiment with at least three groups. b. make the assumptions that we are comparing two or more treatments and that random assignment is used to assign subjects to groups. c. make the assumptions that our sample is random and that we control for confounding/lurking variables. d. make the assumptions that our sample is random, that we are comparing two or more treatments, and that random assignment is used to assign subjects to groups. ANSWER: b 3. One illness that affects many people is a sinus infection. A company is testing to see whether a particular antibiotic or a steroid spray provides relief from a sinus infection. To test this, nine people were randomly assigned (1) to receive a placebo spray, (2) to receive the antibiotic spray, or (3) to receive the steroid spray. Three people are assigned to each group, meaning that there are 84 possible ways that people can be assigned to treatment groups. What is the probability that the first three people will be assigned to the placebo, the next three will receive the antibiotic, and the final three will be assigned to the steroid spray? a. We cannot tell from the information given. b. 1/3 c. 1/9 d. 1/84 ANSWER: d 4. One illness that affects many people is a sinus infection. A company is testing to see whether a particular antibiotic or a steroid spray provides relief from a sinus infection. To test this, 9 people who were just diagnosed with a sinus infection were randomly assigned (1) to receive a placebo spray, (2) to receive the antibiotic spray, or (3) to receive the steroid spray. Three people are assigned to each group, meaning that there are 84 possible ways that people can be assigned to treatment groups. We measure the number of days it takes each person to stop having symptoms of a sinus infection. If there is no effect of either treatment, what should be true? a. For all patients, it should take the same number of days for symptoms to disappear. b. The average number of days until symptoms disappear should be the same for each of the three groups. Copyright Macmillan Learning. Powered by Cognero.

Page 1

Name:

Class:

Date:

Chapter 32 c. The average number of days until symptoms disappear should be the same for each of the two treatment groups, but it may be different for the control group. d. The average number of days until symptoms disappear should be higher for the treatment groups than for the control group. ANSWER: b 5. One illness that affects many people is a sinus infection. A company is testing to see whether a particular antibiotic or a steroid spray provides relief from a sinus infection. To test this, nine people who were just diagnosed with a sinus infection were randomly assigned (1) to receive a placebo spray, (2) to receive the antibiotic spray, or (3) to receive the steroid spray. Three people are assigned to each group, meaning that there are 84 possible ways that people can be assigned to treatment groups. We measure the number of days it takes each person to stop having symptoms of a sinus infection. We want to use an ANOVA test to assess whether there is an effect of the treatments on the number of days it takes symptoms to disappear. Is such a test appropriate for these data? a. Yes, because we can assume the three populations have the same standard deviation. b. Yes, because we have randomly assigned individuals to treatments. c. Yes, because we have randomly assigned individuals to treatments, and we are interested in determining whether there is an effect of the treatments. d. No, because we do not know whether these nine people were randomly sampled, and the sample size is too small. ANSWER: d 6. One illness that affects many people is a sinus infection. A company is testing to see whether a particular antibiotic or a steroid spray provides relief from a sinus infection. To test this, nine people who were just diagnosed with a sinus infection were randomly assigned (1) to receive a placebo spray, (2) to receive the antibiotic spray, or (3) to receive the steroid spray. Three people are assigned to each group, meaning that there are 84 possible ways that people can be assigned to treatment groups. We measure the number of days it takes each person to stop having symptoms of a sinus infection. We want to use a simple permutation test to assess whether there is an effect of the treatments on the number of days it takes symptoms to disappear. Is such a test appropriate for these data? a. Yes, because there are 84 possible ways in which we could have assigned individuals to treatments. b. Yes, because we have randomly assigned individuals to treatments. c. Yes, because we have randomly assigned individuals to treatments, and we are interested in determining whether there is an effect of the treatments. d. No, because we do not know whether these nine people were randomly sampled, and the sample size is too small. ANSWER: c 7. One illness that affects many people is a sinus infection. A company is testing to see whether a particular antibiotic or a steroid spray provides relief from a sinus infection. To test this, nine people who were just diagnosed with a sinus infection were randomly assigned (1) to receive a placebo spray, (2) to receive the antibiotic spray, or (3) to receive the steroid spray. Three people are assigned to each group. We measure the number of days it takes each person to stop having symptoms of a sinus infection. We want to use a simple permutation test to assess whether there is an effect of the antibiotic treatment on the number of days it takes Copyright Macmillan Learning. Powered by Cognero.

Page 2

Name:

Class:

Date:

Chapter 32 symptoms to disappear (we ignore the steroid treatment group for now). To do this, we arrange the data in each of the possible permutations (each of the 20 ways in which six people could have been assigned to the treatment and control groups). What do we compute then? a. For each permutation, we compute the difference in the average number of days it took symptoms to disappear in the control group versus the treatment group. b. For all patients, we compute the difference in the number of days it took for symptoms to disappear when the patient was in the treatment group versus the control group. c. For each permutation, we compute the average number of days it took for symptoms to disappear in each group. d. For each permutation, we compute the average number of days it took for symptoms to disappear in the treatment group. ANSWER: a 8. One illness that affects many people is a sinus infection. A company is testing to see whether a particular antibiotic or a steroid spray provides relief from a sinus infection. To test this, nine people who were just diagnosed with a sinus infection were randomly assigned (1) to receive a placebo spray, (2) to receive the antibiotic spray, or (3) to receive the steroid spray. Three people are assigned to each group. We measure the number of days it takes each person to stop having symptoms of a sinus infection. We want to use a simple permutation test to assess whether there is an effect of the antibiotic treatment on the number of days it takes symptoms to disappear (we ignore the steroid treatment group for now). To do this, we arrange the data in each of the possible permutations (each of the 20 ways in which six people could have been assigned to the treatment and control group) and compute the appropriate test statistic. We obtain the following differences: –2, –1, –1, – 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3. In our data, the sample statistic was 2.67. What is the P-value for our permutation test? a. 0.4 b. 0.45 c. 0.05 d. 0.1 ANSWER: c 9. One illness that affects many people is a sinus infection. A company is testing to see whether a particular antibiotic or a steroid spray provides relief from a sinus infection. To test this, nine people who were just diagnosed with a sinus infection were randomly assigned (1) to receive a placebo spray, (2) to receive the antibiotic spray, or (3) to receive the steroid spray. Three people are assigned to each group. We measure the number of days it takes each person to stop having symptoms of a sinus infection. We want to use a simple permutation test to assess whether there is an effect of the steroid treatment on the number of days it takes symptoms to disappear (we ignore the antibiotic treatment group for now). The P-value was 0.03. What does this mean? The steroid treatment is more effective than the antibiotic treatment at reducing the number of days until the symptoms of a sinus infection disappear. a. We are certain that the steroid reduces the number of days it takes for the symptoms of a sinus infection to disappear. b. Three percent of individuals in the sample had a reduction in the number of days until sinus infection symptoms disappeared as extreme as we observed in our sample data. Copyright Macmillan Learning. Powered by Cognero.

Page 3

Name:

Class:

Date:

Chapter 32 c. Three percent of the permutations yielded a difference in days until symptom disappearance between the control and treatment groups as extreme as the difference we observed in our sample data. d. Three percent of the means in the sampling distribution obtained from the CLT are more extreme than the difference between the control and treatment groups as extreme as our sample data. ANSWER: d 10. One illness that affects many people is a sinus infection. A company is testing to see whether a particular antibiotic or a steroid spray provides relief from a sinus infection. To test this, nine people who were just diagnosed with a sinus infection were randomly assigned (1) to receive a placebo spray, (2) to receive the antibiotic spray, or (3) to receive the steroid spray. Three people are assigned to each group. We measure the number of days it takes each person to stop having symptoms of a sinus infection. We want to use a simple permutation test to assess whether there is an effect of the steroid treatment on the number of days it takes symptoms to disappear (we ignore the antibiotic treatment group for now). The P-value was 0.03. What do we conclude? a. The steroid treatment is more effective than the antibiotic treatment at reducing the number of days until sinus infection symptoms disappear. b. We are certain that the steroid reduces the number of days it takes for symptoms of a sinus infection to disappear. c. We have evidence that the number of days until sinus infection symptoms disappear is lower when the steroid is used than when the antibiotic is used. d. We have evidence that the number of days until sinus infection symptoms disappear is lower when the steroid is used than when the placebo is used. ANSWER: d 11. We are interested in creating a confidence interval for the average number of calories in a Starbucks beverage. We have a random sample of 15 drinks, one of which is a high outlier. Which of the following methods should we use to create a confidence interval? a. A t confidence interval, because our sample is random and our sample size is small b. A z confidence interval, because our sample is random and we can assume the population distribution is Normal. c. A permutation confidence interval, because our sample is random and our sample size is small d. A bootstrap confidence interval, because our sample is random, our sample size is small, and we can easily resample from the population e. A bootstrap confidence interval, because our sample is random and our sample size is small ANSWER: e 12. We are interested in creating a confidence interval for the average number of calories in a Starbucks beverage. We have a random sample of 15 drinks, one of which is a high outlier. We create an appropriate 95% confidence interval by: a. computing our sample mean and then adding and subtracting 2.14 times the standard error, which is the sample standard deviation over the square root of 15. b. resampling from our original sample to create many samples of size 15, computing the sample mean of each sample, and finding the middle 95% of these sample means by removing the bottom 2.5% and the top 2.5%. Copyright Macmillan Learning. Powered by Cognero.

Page 4

Name:

Class:

Date:

Chapter 32 c. computing our sample mean and then adding and subtracting 1.96 times the standard error, which is the sample standard deviation over the square root of 15. d. computing every possible permutation of the 15 drinks, computing the sample mean for each, and then finding the middle 95% of these sample means by removing the bottom 2.5% and the top 2.5%. ANSWER: b 13. Suppose we have a sample with values 1, 4, 5, 14, and 30. Which of the following is(are) not a possible bootstrap sample(s)? a. 1, 4, 5, 5, 15 b. 1, 4, 5, 5, 5, 5, 5, 5 c. 5 , 5 , 5 , 5 , 5 d. 1 , 4 , 14 , 14, 14 e. Both option (a) and option (b) are correct. f. Both option (b) and option (c) are correct. g. Both option (c) and option (d) are correct. h. Both option (a) and option (c) are correct. ANSWER: e 14. Suppose we have a sample with values 1, 4, 5, 14, and 30, and we use this to create a bootstrap distribution. Which of the following statements is necessarily true? a. The bootstrap distribution is made up of sample statistics taken from many different samples in the population. b. The bootstrap distribution is made up of sample statistics taken from many samples created from this sample using resampling. c. The bootstrap distribution is symmetric. d. The bootstrap distribution is exactly the sampling distribution of the statistic. e. The bootstrap distribution is unimodal. ANSWER: b 15. The bootstrap standard error is: a. the standard deviation of the bootstrap distribution. b. the standard deviation of the bootstrap sample. c. the standard deviation of the sampling distribution. d. a measure of the variance in the individual data points in a bootstrap sample. ANSWER: a 16. Suppose we create 100 bootstrap samples from an original sample and compute the bootstrap standard error. We next create 1000 bootstrap samples from the original sample and then compute the bootstrap standard error. In general, the bootstrap standard error will be: a. smaller for the bootstrap distribution of 100 bootstrap samples. b. smaller for the bootstrap distribution of 1000 bootstrap samples. c. There will be no difference, because the bootstrap distribution does not rely on distribution Copyright Macmillan Learning. Powered by Cognero.

Page 5

Name:

Class:

Date:

Chapter 32 assumptions. d. We would need to know the size of the original sample in order to determine this, because standard error is related to sample size. ANSWER: b 17. True or False: The bootstrap method can be used to create confidence intervals for the median. a. True; the bootstrap method can be used to create confidence intervals for many kinds of statistics, including the median. b. True; the bootstrap method works equally well for all statistics. c. True; the bootstrap method can be used to create confidence intervals for many kinds of statistics, including the median, but you need a large number of bootstrap samples. d. False; the bootstrap method should be used for creating confidence intervals for means and ratios of means. e. False; we can use t confidence intervals to make confidence intervals for the median. ANSWER: c 18. What one of the following is not a reason why we might use a bootstrap percentile confidence interval instead of a z confidence interval or t confidence interval? a. It is generally faster and more accurate to use a bootstrap percentile confidence interval for any statistic of interest. b. The sampling distribution for the statistic of interest might be unknown. c. The conditions for the CLT might not apply, because the sample size is too small and the population distribution is highly skewed. d. The population distribution might be highly skewed. ANSWER: a 19. We are interested in exploring the number of calories in Starbucks coffees. We take a random sample of 50 coffees, and we find that the median number of calories is 200. We then create the following bootstrap distribution using 50 bootstrap samples.

Page 6

Name:

Class:

Date:

Chapter 32

Based on this, what is a 90% bootstrap percentile confidence interval for the population median? a. (180, 200) b. (180, 210) c. (180, 230) d. (190, 210) ANSWER: b 20. We are interested in exploring the number of calories in Starbucks coffees. We take a random sample of 50 coffees, and we find that the median number of calories is 200. We then create the following bootstrap distribution using 50 bootstrap samples.

Page 7

Name:

Class:

Date:

Chapter 32

What does each dot in the plot represent? a. A sample median from a different sample of size 50 from the population b. A sample median from a sample of size 50 created by sampling without replacement from our original sample c. The number of calories in one of the 50 coffees in our sample d. A sample median from a sample of size 50 created by sampling with replacement from our original sample ANSWER: d 21. We are interested in exploring the number of calories in Starbucks coffees. We take a random sample of 50 coffees, and we find that the median number of calories is 200. We then create the following bootstrap distribution using 50 bootstrap samples.

Page 8

Name:

Class:

Date:

Chapter 32

In practice, should we use this bootstrap distribution to create a confidence interval for the population median? a. No, we should create more bootstrap samples. b. No, we should use a t confidence interval. c. No, we need a bigger sample size. d. Yes, the bootstrap distribution is a good way of building a confidence interval for the population median. ANSWER: a

Page 9