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QNT 561 Week 2 Weekly Learning Assessments Chapter 5 Exercise 4
A large company must hire a new president. The Board of Directors prepares a list of five candidates, all of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to select the president by lottery. a. What is the probability one of the minority candidates is hired? (Round your answer to 1 decimal place.) b. Which concept of probability did you use to make this estimate? Chapter 5 Exercise 14 The chair of the board of directors says, "There is a 50% chance this company will earn a profit, a 30% chance it will break even, and a 20% chance it will lose money next quarter." a. Use an addition rule to find the probability the company will not lose money next quarter. (Round your answer to 2 decimal places.) b. Use the complement rule to find the probability it will not lose money next quarter. (Round your answer to 2 decimal places.)
Chapter 5 Exercise 22 A National Park Service survey of visitors to the Rocky Mountain region revealed that 50% visit Yellowstone Park, 40% visit the Tetons, and 35% visit both.
1
a. What is the probability a vacationer will visit at least one of these attractions? (Round your answer to 2 decimal places.) b. What is the probability .35 called? c. Are the events mutually exclusive?
Chapter 5 Exercise 34 P(A1) = .20, P(A2) = .40, and P(A3) = .40. P(B1|A1) = .25. P(B1|A2) = .05, and P(B1|A3) = .10. Use Bayes' theorem to determine P(A3|B1). (Round your answer to 4 decimal places.)
Chapter 5 Exercise 40 Solve the following: a. 20! 17! b. 9P3 c. 7C2
Chapter 6 Exercise 4 Which of these variables are discrete and which are continuous random variables? a. The number of new accounts established by a salesperson in a year. b. The time between customer arrivals to a bank ATM. c. The number of customers in Big Nick’s barber shop. d. The amount of fuel in your car’s gas tank. e. The number of minorities on a jury. 2
f. The outside temperature today. Chapter 6 Exercise 14 The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations. a. What is the probability that all six arrive within 2 days? (Round your answer to 4 decimal places.) b. What is the probability that exactly five arrive within 2 days? (Round your answer to 4 decimal places.) c. Find the mean number of letters that will arrive within 2 days. (Round your answer to 1 decimal place.) d-1. Compute the variance of the number that will arrive within 2 days. (Round your answer to 3 decimal places.) d-2. Compute the standard deviation of the number that will arrive within 2 days. (Round your answer to 4 decimal places.)
Chapter 6 Exercise 20 In a binomial distribution, n = 12 and π = .60. a. Find the probability for x = 5? (Round your answer to 3 decimal places.) b. Find the probability for x ≤ 5? (Round your answer to 3 decimal places.) c. Find the probability for x ≼ 6? (Round your answer to 3 decimal places.)
Chapter 6 Exercise 26 A population consists of 15 items, 10 of which are acceptable. 3
In a sample of four items, what is the probability that exactly three are acceptable? Assume the samples are drawn without replacement. (Round your answer to 4 decimal places.) Chapter 7 Exercise 4 According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts. a. What is the mean amount spent on insurance? b. What is the standard deviation of the amount spent? (Round your answer to 2 decimal places.) c. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? (Round your answer to 4 decimal places.) d. What is the probability a family spends more than $3,000 per year? (Round your answer to 4 decimal places.)
Chapter 7 Exercise 10 The mean of a normal probability distribution is 60; the standard deviation is 5. (Round your answers to 2 decimal places.) a. About what percent of the observations lie between 55 and 65? b. About what percent of the observations lie between 50 and 70? c. About what percent of the observations lie between 45 and 75? Chapter 7 Exercise 14 A normal population has a mean of 12.2 and a standard deviation of 2.5. a. Compute the z value associated with 14.3. (Round your answer to 2 decimal places.) 4
b. What proportion of the population is between 12.2 and 14.3? (Round your answer to 4 decimal places.) c. What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.)
Chapter 7 Exercise 18 A normal population has a mean of 80.0 and a standard deviation of 14.0. a. Compute the probability of a value between 75.0 and 90.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.) b. Compute the probability of a value of 75.0 or less. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.) c. Compute the probability of a value between 55.0 and 70.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)
Chapter 7 Exercise 28 For the most recent year available, the mean annual cost to attend a private university in the United States was $26,889. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500. Ninety-five percent of all students at private universities pay less than what amount? (Round z value to 2 decimal places and your final answer to the nearest whole number.) QNT 561 Week 3 Weekly Learning Assessments Chapter 8 Exercise 2 The following is a list of 29 hospitals in the Cincinnati (Ohio) and Northern Kentucky region. The hospitals are identified by numbering them 00 through 28. Also included is whether the hospital is a general medical/surgical hospital (M/S) or a specialty hospital (S). We are interested in estimating the average number of full- and part-time nurses employed in the area hospitals. 5
A sample of five hospitals is to be randomly selected. The random numbers are 09, 16, 00, 49, 54, 12, and 04. Which hospitals are included in the sample? (Select hospital names included in sample in numerical order.) A sample is to consist of every fifth location. We select 02 as the starting point. Which hospitals will be included in the sample? (Hint: Enter the ID number used to identify the hospitals) (Select hospital names included in sample in numerical order.)
Chapter 8 Exercise 8 A population consists of the following five values: 2, 2, 4, 5, 6. a. List all samples of size 3, and compute the mean of each sample. (Round sample means to 2 decimal places.) Sample
Values
1
2, 2, 4
2
2, 2, 5
3
2, 2, 6
4
2, 4, 5
5
2, 4, 6
6
2, 5, 6
7
2, 4, 5
8
2, 4, 6
9
2, 5, 6
10
Sum
Mean
4, 5, 6
b. Compute the mean of the distribution of sample means and the population mean. (Round your answers to 1 decimal place.) 6
Chapter 8 Exercise 12 Scrapper Elevator Caompany has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be the population values. 2
3
2 3
3 4
2 4
3 2
2 7
3
4 5
3 3
3 3
5
Click here for the Excel Data File b. Compute the mean of the population. (Round your answer to 1 decimal place.) Chapter 8 Exercise 16 A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Compute the probability the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places): a. Less than 74. b. Between 74 and 76. c. Between 76 and 77. d. Greater than 77.
Chapter 9 Exercise 4 Suppose you know Ďƒ and you want an 85% confidence level. What value would you use as z in formula of confidence interval for a population mean? (Round your answer to 2 decimal places.)
Chapter 9 Exercise 6 7
A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. They found the distribution of amounts spent per week followed the normal distribution with a population standard deviation of $5. A sample of 64 steady smokers revealed that . formula233.mml. a. What is the 95% confidence interval estimate of formula22.mml ? (Round your answers to 3 decimal places.)
Chapter 9 Exercise 10 Use Appendix B.5 to locate the value of t under the following conditions. (Round your answers to 3 decimal places.) a. The sample size is 15 and the level of confidence is 95%. b. The sample size is 24 and the level of confidence is 98%. c. The sample size is 12 and the level of confidence is 90%.
Chapter 9 Exercise 26 Past surveys reveal that 30% of tourists going to Las Vegas to gamble spend more than $1,000. The Visitor’s Bureau of Las Vegas wants to update this percentage. a. The new study is to use the 90% confidence level. The estimate is to be within 1% of the population proportion. What is the necessary sample size? (Round your answer to the next whole number.) b. The Bureau feels the sample size determined above is too large. What can be done to reduce the sample? Based on your suggestion, recalculate the sample size. (Hint: Use an allowable error in the range of 0.01 to 0.05) (Round your answer to the next whole number.)
Chapter 9 Exercise 28 8
Forty-nine items are randomly selected from a population of 500 items. The sample mean is 40 and the sample standard deviation 9. Develop a 99% confidence interval for the population mean. (Round your answers to 3 decimal places.) QNT 561 Week 4 Weekly Learning Assessments Chapter 10 Exercise 2 [The following information applies to the questions displayed below.] A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level H0: μ ≤ 10 H1: μ > 10 1. Award: 10 out of 10.00 points a. Is this a one- or two-tailed test? b. What is the decision rule? c. What is the value of the test statistic? d. What is your decision regarding H0? e. What is the p-value?
Chapter 10 Exercise 10 Given the following hypotheses: H0 : μ = 400 H1 : μ ≠ 400 9
A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level: a. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.) b. Compute the value of the test statistic. (Round your answer to 3 decimal places.) c. What is your decision regarding the null hypothesis?
Chapter 10 Exercise 12 The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster? a. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) b. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) c. What is your decision regarding H0?
Chapter 10 Exercise 16
Given the following hypotheses: H0 : Ο = 100 H1 : Ο ≠100 10
A random sample of six resulted in the following values: 118, 105, 112, 119, 105, and 111. Assume a normal population. a. Using the .05 significance level, determine the decision rule? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) b. Compute the value of the test statistic. (Round your answer to 2 decimal places.) c-1. What is your decision regarding the H0? c-2. Can we conclude the mean is different from 100? d. Estimate the p-value.
Chapter 11 Exercise 2 A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level. H0 : μ1 ≤ μ2 H1 : μ1 > μ2 a. This a -tailed test. b. State the decision rule. (Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.) c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) d. What is your decision regarding H0? e. What is the p-value? (Round your answer to 4 decimal places.)
11
Chapter 11 Exercise 8
The null and alternate hypotheses are: A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the .10 significance level, is there a difference in the population means? a. This is a -tailed test. b. The decision rule is to reject if (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) c. The test statistic is (Round your answer to 3 decimal places.) d. What is your decision regarding? e. The p-value is between and .
Chapter 11 Exercise 14
The null and alternate hypotheses are: H0: μ1 ≤ μ2 H1: μ1 > μ2 A random sample of 20 items from the first population showed a mean of 100 and a standard deviation of 15. A sample of 16 items for the second population showed a mean of 94 and a standard deviation of 8. Use the .05 significant level. a. Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.) 12
b. State the decision rule for .05 significance level. (Round your answer to 3 decimal places.) c. Compute the value of the test statistic. (Round your answer to 3 decimal places.) d. What is your decision regarding the null hypothesis? Use the .05 significance level.
Chapter 12 Exercise 8 The following are six observations collected from treatment 1, four observations collected from treatment 2, and five observations collected from treatment 3. Test the hypothesis at the 0.05 significance level that the treatment means are equal. Treatment1
Treatment 2
Treatment 3
9
13
10
7
20
9
11
14
15
9
13
14
12
15
10 a. State the null and the alternate hypothesis. Ho : H1 : Treatment means are all the same. b. What is the decision rule? (Round your answer to 2 decimal places.) c. Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.) d. Complete the ANOVA table. (Round SS, MS and F values to 2 decimal places.) e. State your decision regarding the null hypothesis. 13
Chapter 12 Exercise 14
A stock analyst wants to determine whether there is a difference in the mean rate of return for three types of stock: utility, retail, and banking stocks. The following output is obtained: a. Using the .05 level of significance, is there a difference in the mean rate of return among the three types of stock? b. Can the analyst conclude there is a difference between the mean rates of return for utility and retail stocks? For utility and banking stocks? For banking and retail stocks? Explain.
Chapter 12 Exercise 18 There are three hospitals in the Tulsa, Oklahoma, area. The following data show the number of outpatient surgeries performed on Monday, Tuesday, Wednesday, Thursday, and Friday at each hospital last week. At the 0.05 significance level, can we conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week? Number of Surgeries Performed Day St. Luke's St. Vincent Mercy Monday
14 18 14
24 Tuesday 20 24 14
Wednesday
16 22 14
Thursday 18 20 22
Friday
20 28 24
15
1.Set up the null hypothesis and the alternative hypothesis. For Treatment: Null hypothesis H0: µSt. Luke's = µSt. Vincent =
2. Alternative hypothesis H1: Not all means are
3. For blocks: Null hypothesis H0: µMon = µTue = µWed = µThu =
4. Alternative hypothesis H1: Not all means are
5. State the decision rule for .05 significance level. (Round your answers to 2 decimal places.)
For Treatment: Reject H0 if F> For blocks: Reject H0 if F>
16
6. Complete the ANOVA table. (Round SS, MS and F to 2 decimal places.) 7.What is your decision regarding the null hypothesis? The decision for the F value (Treatment) at 0.05 significance is: Do not Reject
8. The decision for the F value (Block) at 0.05 significance is: Do not Reject 9. Can we conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week? There is no in the mean number of surgeries performed by hospital or by day of the week. Chapter 13 Exercise 16 Mr. James Mc Whinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. Mc Whinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled. Number of Sales
Sales
Contacts, thousands),
($ thousands),
X Y
Number of
Y 14
Contacts,
($
X 24
30
17
23
12
14
48
20
28
50
16
30
55
46
80
50
90 85 120 110 a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round final answers to 2 decimal places.) b. Determine the estimated sales if 40 contacts are made.(Do not round intermediate calculations. Round final answers to 2 decimal places.) Chapter 13 Exercise 18 We are studying mutual bond funds for the purpose of investing in several funds. For this particular study, we want to focus on the assets of a fund and its five-year performance. The question is: Can the five-year rate of return be estimated based on the assets of the fund? Nine mutual funds were selected at random, and their assets and rates of return are shown below. Assets
Return
($ millions)
(%)
Assets
Return Fund millions)
Fund
($
(%)
AARP High Quality Bond 11.6
$622.20
10.8
MFS Bond A
Babson Bond L 9.5
160.4
11.3
Nichols Income
Compass Capital 18
$494.50 158.3
Fixed Income
275.7
11.4
T. Rowe Price Short-term
681
Thompson Income B
241.3
8.2 Galaxy Bond Retail 6.8
433.2
9.1
Keystone Custodian B-1
437.9
9.2
b-1. Compute the coefficient of correlation. (Round your answer to 3 decimal places. Negative amount should be indicated by a minus sign.) b-2. Compute the coefficient of determination. (Round your answer to 3 decimal places.) c. Give a description of the degree of association between the variables. d. Determine the regression equation. Use assets as the independent variable. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.) e. For a fund with $400.0 million in sales, determine the five-year rate of return (in percent). (Round your answer to 4 decimal places.)
Chapter 13 Exercise 30 On the first statistics exam, the coefficient of determination between the hours studied and the grade earned was 80%. The standard error of estimate was 10. There were 20 students in the class. Develop an ANOVA table for the regression analysis of hours studied as a predictor of the grade earned on the first statistics exam. Source
DF
SS
MS
Regression Error Total 19
QNT 561 Week 5 Weekly Learning Assessments Chapter 13 Exercise 6 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car
Age (years)
Selling Car
Age (years)
Selling Price ($000)
Price ($000) 1 7.6
9
8.1
7
8
2 8.0
7
6.0
8
11
3 8.0
11
3.6
9
10
4 6.0
12
4.0
10
12
5 8.6
8
5.0
11
6
6 8.0
7
10.0
12
6
a. If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable? b-1. Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) b-2. Determine the coefficient of determination. (Round your answer to 3 decimal places.) c. Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.) 20
Chapter 13 Exercise 12 The Student Government Association at Middle Carolina University wanted to demonstrate the relationship between the number of beers a student drinks and his or her blood alcohol content (BAC). A random sample of 18 students participated in a study in which each participating student was randomly assigned a number of 12-ounce cans of beer to drink. Thirty minutes after they consumed their assigned number of beers, a member of the local sheriff’s office measured their blood alcohol content. The sample information is reported below. Student BAC
Beers
BAC
Student
Beers
1 0.07
6
0.1
10
3
2 0.05
7
0.09
11
3
3 0.08
7
0.09
12
7
4 0.04
4
0.1
13
1
5 0.07
5
0.1
14
4
6 0.06
3
0.07
15
2
7 0.12
3
0.1
16
7
8 0.05
6
0.12
17
2
9 0.02
6
0.09
18
1
21
Use a statistical software package to answer the following questions. a-1. Choose a scatter diagram that best fits the data. Picture Picture Picture Picture
b. Fill in the blanks below. (Round your answers to 3 decimal places.) c. Determine the coefficient of correlation and coefficient of determination. (Round your answers to 3 decimal places.) c-1. State the decision rule for .01 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.)
c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.) c-3. What is the p-value? (Hint: use your analysis software) (Round p-value to 4 decimal places.) c-4. At the .01 significance level, is it reasonable to conclude that there is a positive relationship in the population between the number of beers consumed and the BAC?
Chapter 13 Exercise 14 The following sample observations were randomly selected. a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) 22
b. Determine the value of when X is 7. (Round your answer to 3 decimal places.) Chapter 13 Exercise 22 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car Age (years) Selling Price ($000)
Selling Price ($000)
Car
Age (years)
1 7.6
9
8.1
7
8
2 8
7
6
8
11
3 8
11
3.6
9
10
4 6
12
4
10
12
5 8.6
8
5
11
6
6 8
7
10
12
6
The regression equation is, the sample size is 12, and the standard error of the slope is 0.23. Use the .05 significance level. Can we conclude that the slope of the regression line is less than zero? Chapter 13 Exercise 26 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car
Age (years)
Selling Price ($000) 23
1
9
8.1
2
7
6.0
3
11
3.6
4
12
4.0
5
8
5.0
6
7
10.0
7
8
7.6
8
11
8.0
9
10
8.0
10
12
6.0
11
6
8.6
12
6
8.0
a. Determine the standard error of estimate. (Round your answer to 3 decimal places.) b. Determine the coefficient of determination. (Round your answer to 3 decimal places.) c. Interpret the coefficient of determination. (Round your answer to the nearest whole number.)
Chapter 14 Exercise 2 Thompson Photo Works purchased several new, highly sophisticated processing machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as an operator (in years) important? In order to explore further the factors needed to estimate performance on the new processing machines, four variables were listed: 24
X1 = Length of time an employee was in the industry X2 = Mechanical aptitude test score X3 = Prior on-the-job rating X4 = Age Performance on the new machine is designated y. Thirty employees were selected at random. Data were collected for each, and their performances on the new machines were recorded. A few results are: Mechanical
Performance Prior
on New On-the-Job Machine, Performance,
Length of Time in
Aptitude
Industry, Age,
Score,
Name X2
Y X3
X1
Mike Miraglia 121
112 52
12
Sue Trythall 123
113 27
2
X4
The equation is: Ĺś = 11.6 + 0.4X1 + 0.286X2 + 0.112X3 + 0.002X4 a. What is this equation called? b. How many dependent and independent variables are there? c. What is the number 0.286 called?
25
312 380
d. As age increases by one year, how much does estimated performance on the new machine increase? (Round your answer to 3 decimal places.) e. Carl Knox applied for a job at Photo Works. He has been in the business for 6 years and scored 280 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)
Chapter 14 Exercise 6 Consider the ANOVA table that follows. Analysis of Variance Source MS F Regression 742
DF
SS
5
3710
12.89
Residual Error 2647.38 57.55
46
Total 6357.38
51
a-1. Determine the standard error of estimate. (Round your answer to 2 decimal places.) a-2. About 95% of the residuals will be between what two values? (Round your answers to 2 decimal places.) b-1. Determine the coefficient of multiple determination. (Round your answer to 3 decimal places.) b-2. Determine the percentage variation for the independent variables. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) c. Determine the coefficient of multiple determination, adjusted for the degrees of freedom. (Round your answer to 3 decimal places.) 26
Chapter 14 Exercise 8 The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor
Co eff
SE Co eff
t
&n
QNT 561 Week 5 Weekly Learning Assessments Chapter 13 Exercise 6 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car
Age (years)
Selling Car
Age (years)
Selling Price ($000)
Price ($000) 1 7.6
9
8.1
7
8
2 8.0
7
6.0
8
11
3 8.0
11
3.6
9
10
4 6.0
12
4.0
10
12
5 8.6
8
5.0
11
6
6 8.0
7
10.0
12
6
a. If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable? 27
b-1. Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) b-2. Determine the coefficient of determination. (Round your answer to 3 decimal places.) c. Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.)
Chapter 13 Exercise 12 The Student Government Association at Middle Carolina University wanted to demonstrate the relationship between the number of beers a student drinks and his or her blood alcohol content (BAC). A random sample of 18 students participated in a study in which each participating student was randomly assigned a number of 12-ounce cans of beer to drink. Thirty minutes after they consumed their assigned number of beers, a member of the local sheriff’s office measured their blood alcohol content. The sample information is reported below. Student BAC
Beers
BAC
Student
Beers
1 0.07
6
0.1
10
3
2 0.05
7
0.09
11
3
3 0.08
7
0.09
12
7
4 0.04
4
0.1
13
1
5 0.07
5
0.1
14
4
28
6 0.06
3
0.07
15
2
7 0.12
3
0.1
16
7
8 0.05
6
0.12
17
2
9 0.02
6
0.09
18
1
Use a statistical software package to answer the following questions. a-1. Choose a scatter diagram that best fits the data.
Picture Picture Picture Picture b. Fill in the blanks below. (Round your answers to 3 decimal places.) c. Determine the coefficient of correlation and coefficient of determination. (Round your answers to 3 decimal places.) c-1. State the decision rule for .01 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.) c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.) c-3. What is the p-value? (Hint: use your analysis software) (Round p-value to 4 decimal places.)
29
c-4. At the .01 significance level, is it reasonable to conclude that there is a positive relationship in the population between the number of beers consumed and the BAC?
Chapter 13 Exercise 14 The following sample observations were randomly selected. a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
b. Determine the value of when X is 7. (Round your answer to 3 decimal places.
Chapter 13 Exercise 22
The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
Car Age (years) Selling Price ($000)
Selling Price ($000)
Car
Age (years)
1 7.6
9
8.1
7
8
2 8
7
6
8
11
3 8
11
3.6
30
9
10
4 6
12
4
10
12
5 8.6
8
5
11
6
6 8
7
10
12
6
The regression equation is, the sample size is 12, and the standard error of the slope is 0.23. Use the .05 significance level. Can we conclude that the slope of the regression line is less than zero?
Chapter 13 Exercise 26 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
Car
Age (years)
Selling Price ($000)
1
9
8.1
2
7
6.0
3
11
3.6
4
12
4.0
5
8
5.0
6
7
10.0
7
8
7.6
8
11
8.0
9
10
8.0 31
10
12
6.0
11
6
8.6
12
6
8.0
a. Determine the standard error of estimate. (Round your answer to 3 decimal places.) b. Determine the coefficient of determination. (Round your answer to 3 decimal places. c. Interpret the coefficient of determination. (Round your answer to the nearest whole number.)
Chapter 14 Exercise 2 Thompson Photo Works purchased several new, highly sophisticated processing machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as an operator (in years) important? In order to explore further the factors needed to estimate performance on the new processing machines, four variables were listed: X1 = Length of time an employee was in the industry X2 = Mechanical aptitude test score X3 = Prior on-the-job rating X4 = Age Performance on the new machine is designated y. Thirty employees were selected at random. Data were collected for each, and their performances on the new machines were recorded. A few results are: Mechanical
Performance Prior
Length of
32
on New On-the-Job Machine, Performance,
Time in
Aptitude
Industry, Age,
Score,
Name X2
Y X3
X1
Mike Miraglia 121
112 52
12
Sue Trythall 123
113 27
2
X4 312 380
The equation is: Ŷ = 11.6 + 0.4X1 + 0.286X2 + 0.112X3 + 0.002X4
a. What is this equation called? b. How many dependent and independent variables are there? c. What is the number 0.286 called? d. As age increases by one year, how much does estimated performance on the new machine increase? (Round your answer to 3 decimal places.)
e. Carl Knox applied for a job at Photo Works. He has been in the business for 6 years and scored 280 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)
33
Chapter 14 Exercise 6
Consider the ANOVA table that follows. Analysis of Variance Source MS F Regression 742
DF
SS
5
3710
12.89
Residual Error 2647.38 57.55
46
Total 6357.38
51
a-1. Determine the standard error of estimate. (Round your answer to 2 decimal places.) a-2. About 95% of the residuals will be between what two values? (Round your answers to 2 decimal places.) b-1. Determine the coefficient of multiple determination. (Round your answer to 3 decimal places.) b-2. Determine the percentage variation for the independent variables. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) c. Determine the coefficient of multiple determination, adjusted for the degrees of freedom. (Round your answer to 3 decimal places.)
Chapter 14 Exercise 8
The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. 34
Predictor
Co eff
SE Co eff
t
&n
QNT 561 Week 6 Weekly Learning Assessments Chapter 18 Exercise 2
Listed below is the number of movie tickets sold at the Library Cinema-Complex, in thousands, for the period from 2001 to 2013. Compute a five-year weighted moving average using weights of 0.15, 0.1, 0.2, 0.17, and 0.38, respectively. Describe the trend in yield. (Round your answers to 3 decimal places.) 2001
8.41
2002
8.14
2003
7.77
2004
6.59
2005
7.17
2006
6.78
2007
6.81
2008
6.51
2009
5.78
2010
5.57
2011
5.84
2012
5.59
2013
5.53
35
Chapter 18 Exercise 10 Appliance Center sells a variety of electronic equipment and home appliances. For the last 4 years, 2010 through 2013, the following quarterly sales (in $ millions) were reported. Year
I
II
III
IV
2010
5.3
4.1
6.8
6.7
2011
4.8
3.8
5.6
6.8
2012
4.3
3.8
5.7
6
2013
5.6
4.6
6.4
5.9
Determine a typical seasonal index (adjusted) for each of the four quarters. (Round your answers to 4 decimal places.)
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