Essentials of Modern Business Statistics with Microsoft Excel 8th Edition Test Bank by Ace Test Banks

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Chapter 09: Hypothesis Tests Multiple Choice 1. More evidence against H0 is indicated by _____. a. lower levels of significance b. smaller p-values c. smaller critical values d. lower probabilities of a Type II error ANSWER: b 2. Two approaches to drawing a conclusion in a hypothesis test are _____. a. p-value and critical value b. one-tailed and two-tailed c. Type I and Type II d. null and alternative ANSWER: a 3. As a general guideline, the research hypothesis should be stated as the _____. a. null hypothesis b. alternative hypothesis c. tentative assumption d. hypothesis the researcher wants to disprove ANSWER: b 4. A Type I error is committed when _____. a. a true alternative hypothesis is not accepted b. a true null hypothesis is rejected c. the critical value is greater than the value of the test statistic d. sample data contradict the null hypothesis ANSWER: b 5. Which of the following hypotheses is not a valid null hypothesis? a. H0: µ ≤ 0 b. H0: µ ≥ 0 c. H0: µ = 0 d. H0: µ < 0 ANSWER: d 6. The practice of concluding “do not reject H0” is preferred over “accept H0” when we _____. a. are conducting a one-tailed test b. are testing the validity of a claim c. have an insufficient sample size d. have not controlled for the Type II error Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests ANSWER: d 7. If the cost of a Type I error is high, a smaller value should be chosen for the _____. a. critical value b. confidence coefficient c. level of significance d. test statistic ANSWER: c 8. When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve _____. a. less than or equal to the critical value b. less than or equal to the test statistic c. greater than or equal to the critical value d. greater than or equal to the test statistic ANSWER: b 9. In tests about a population proportion, p0 represents the _____. a. hypothesized population proportion b. observed sample proportion c. observed p-value d. probability of ANSWER: a 10. Which of the following is an improper form of the null and alternative hypotheses? a.

and

ANSWER: c 11. For a two-tailed hypothesis test about μ, we can use any of the following approaches EXCEPT compare the _____ to the _____. a. confidence interval estimate of μ; hypothesized value of μ b. p-value; value of α c. value of the test statistic; critical value d. level of significance; confidence coefficient ANSWER: d 12. An example of statistical inference is _____. a. a population mean b. descriptive statistics Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests c. calculating the size of a sample d. hypothesis testing ANSWER: d 13. In hypothesis testing, the hypothesis tentatively assumed to be true is _____. a. the alternative hypothesis b. the null hypothesis c. either the null or the alternative hypothesis, depending on the sample size d. always proven to be true ANSWER: b 14. In hypothesis testing, the alternative hypothesis is _____. a. the hypothesis tentatively assumed true in the hypothesis-testing procedure b. the hypothesis concluded to be true if the null hypothesis is rejected c. the maximum probability of a Type I error d. the maximum probability of a Type II error ANSWER: b 15. Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is _____. a. H0: μ < 10.0% Ha: μ ≥ 10.0% b. H0: μ ≤ 10.0% Ha: μ > 10.0% c. H0: μ > 10.0% Ha: μ ≤ 10.0% d. H0: μ ≥ 10.0% Ha: μ < 10.0% ANSWER: d 16. A meteorologist stated that the average temperature during July in Chattanooga was 80 degrees. A sample of July temperatures over a 32-year period was taken. The correct set of hypotheses is _____. a. H0: μ < 80 Ha: μ ≤ 80 b. H0: μ ≤ 80 Ha: μ > 80 c. H0: μ ≠ 80 Ha: μ = 80 d. H0: μ = 80 Ha: μ ≠ 80 ANSWER: d 17. A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is _____. a. H0: μ < 85 Ha: μ ≥ 85 b. H0: μ ≤ 85 Ha: μ > 85 c. H0: μ ≥ 85 Ha: μ < 85 d. H0: μ > 85 Ha: μ ≤ 85 ANSWER: c Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests 18. The average life expectancy of tires produced by Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is _____. a. H0: μ < 40,000 Ha: μ ≥ 40,000 b. H0: μ ≤ 40,000 Ha: μ > 40,000 c. H0: μ > 40,000 Ha: μ ≤ 40,000 d. H0: μ ≥ 40,000 Ha: μ < 40,000 ANSWER: b 19. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any overfilling or underfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is _____. a. H0: μ < 12 Ha: μ ≤ 12 b. H0: μ ≤ 12 Ha: μ > 12 c. H0: μ ≠ 12 Ha: μ = 12 d. H0: μ = 12 Ha: μ ≠ 12 ANSWER: d 20. The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is _____. a. H0: μ < 5 Ha: μ ≤ 5 b. H0: μ ≤ 5 Ha: μ > 5 c. H0: μ > 5 Ha: μ ≤ 5 d. H0: μ ≥ 5 Ha: μ < 5 ANSWER: b 21. In hypothesis testing if the null hypothesis is rejected, _____. a. no conclusions can be drawn from the test b. the alternative hypothesis must also be rejected c. the data must have been collected incorrectly d. the evidence supports the alternative hypothesis ANSWER: d 22. If a hypothesis test leads to the rejection of the null hypothesis, a _____. a. Type II error must have been committed b. Type II error may have been committed c. Type I error must have been committed d. Type I error may have been committed ANSWER: d 23. The error of rejecting a true null hypothesis is _____. Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests a. a Type I error b. a Type II error c. committed when the sample size is too small d. committed when not enough information is available ANSWER: a 24. In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true, _____. a. a Type I error has been committed b. a Type II error has been committed c. the sample size is too small d. the correct decision has been made ANSWER: d 25. A Type II error is committed when _____. a. a true alternative hypothesis is mistakenly rejected b. a true null hypothesis is mistakenly rejected c. the sample size has been too small d. not enough information has been available ANSWER: a 26. The probability of making a Type I error is denoted by _____. a. α b. β c. 1 − α d. 1 − β ANSWER: a 27. The level of significance is the _____. a. maximum allowable probability of a Type II error b. maximum allowable probability of a Type I error c. same as the confidence coefficient d. same as the p-value ANSWER: b 28. The level of significance in hypothesis testing is the probability of _____. a. accepting a true null hypothesis b. accepting a false null hypothesis c. rejecting a true null hypothesis d. rejecting a false null hypothesis ANSWER: c 29. In the hypothesis testing procedure, α is _____. a. the level of significance b. the critical value Copyright Cengage Learning. Powered by Cognero.

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Chapter 10: Statistical Inferences About Means and Proportions with Two Populations newborns are low-birth-weight babies. The following information was accumulated from samples of new births selected from two counties: Sample size Number of low-birth-weight babies a. b.

Hamilton 150 18

Shelby 200 22

Develop a 95% confidence interval estimate for the difference between the proportions of low-birth-weight babies in the two counties. Is there conclusive evidence that one of the proportions is significantly more than the other? If yes, which county? Explain, using the results of part (a). Do not perform any test.

ANSWER: a. b.

–.0577 to .0777 Since the range of the interval is from negative to positive, there is no indication that one proportion is significantly different (at 95% confidence) from the other.

121. A poll was administered this year asking college students if they considered themselves overweight. A similar poll was administered five years ago. Results are summarized below. Has the proportion increased significantly? Let α = 0.05.

Present sample Previous sample

Sample Size 300 275

Number Considered Themselves Overweight 150 121

ANSWER: H0: p1 – p2 ≤ 0 Ha: p1 – p2 > 0 z = 1.44; p-value = 0.0749; do not reject H0. There is not sufficient evidence to conclude that the proportion of college students who consider themselves overweight has increased significantly. 122. A potential investor conducted a 144-day survey in each theater in order to determine the difference between the average daily attendance at the North Mall and South Mall theaters. The North Mall Theater averaged 630 patrons per day, while the South Mall Theater averaged 598 patrons per day. From past information, it is known that the variance for North Mall is 1,000, while the variance for the South Mall is 1,304. Develop a 95% confidence interval for the difference between the average daily attendances at the two theaters. ANSWER: 24.16 to 39.84 123. A comparative study of organic and conventionally grown produce was checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. coli in organic versus conventionally grown produce? Test at α = .10. Organic Conventional

Sample Size 200 500

E. Coli Prevalence 3 20

ANSWER: H0: p1 – p2 = 0 Ha: p1 – p2 ≠ 0 z = –1.68, p-value = .093; reject H0 and conclude that there is a significant difference in the proportion of E.coli in organic versus conventionally grown produce. Copyright Cengage Learning. Powered by Cognero.

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Chapter 10: Statistical Inferences About Means and Proportions with Two Populations 124. Starting annual salaries for business school graduates majoring in finance and management information systems (MIS) were collected in two independent random samples summarized below. Based on previous studies, the population standard deviations for finance and MIS salaries are estimated to be $2,100 and $2,600, respectively. Finance

MIS

n1 = 60

n2 = 50

1 = $43,200

2 = $46,500

a. Develop a 95% confidence interval estimate of the difference between the starting salaries for the two majors. b. Using α = .10, test to determine if the average starting salary for an MIS graduate is $4,000 more than the starting salary for a finance graduate. Use both the critical value and p-value approaches to hypothesis testing. (Hint: The null hypothesis is H0: μ1 – μ2 = $4,000, where μ1 is the average starting salary of MIS graduates.) ANSWER: a. MIS is higher by $2,404.62 to $4,195.38. b. z = –1.53 > –1.645; do not reject H0. There is not sufficient evidence to conclude that the average starting salary for an MIS graduate is $4,000 more than the starting salary for a finance graduate. 125. A manager is thinking of providing, on a regular basis, in-house training for employees preparing for an inventory management certification exam. In the past, some employees received the in-house training before taking the exam, while others did not. Independent random samples selected from the company’s records provided the following exam scores for 10 workers who did not receive in-house training and eight workers who did receive training. (The manager is confident that the distributions of both populations’ exam scores are approximately normal.) No Training 76 80 60 91 73 77 82 68 75 86

Training 80 66 71 79 94 74 83 78

a. Develop a 95% confidence interval estimate for the difference between the average test scores for the two populations of employees. b. Using α = .05, test for any difference between the average test scores for the two populations of employees. ANSWER: a. –10.02 to 7.37 (thus, μ1 – μ2 could be 0) b. t = –.325 > –2.131, p-value = .75 > .05; do not reject H0: μ1 – μ2 = 0. There is not sufficient evidence to conclude that there is a difference between the average test scores. 126. A survey was recently conducted to determine if consumers spend more on computer-related purchases via the Internet or store visits. Assume a random sample of eight respondents provided the following data on their computerrelated purchases during a 30-day period. Using a .05 level of significance, can we conclude that consumers spend more on computer-related purchases by way of the Internet than by visiting stores? Copyright Cengage Learning. Powered by Cognero.

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Chapter 10: Statistical Inferences About Means and Proportions with Two Populations Respondent 1 2 3 4 5 6 7 8

Expenditures (dollars) In-Store 132 90 119 16 85 248 64 49

Internet 225 24 95 55 13 105 57 0

ANSWER: t = 1.12 < 1.89, p-value = .15 > .05; do not reject H0: μd < 0. There is not sufficient evidence to conclude that consumers spend more on computer-related purchases by way of the Internet than by visiting stores. 127. A movie based on a best-selling novel was recently released. Six hundred viewers of the movie, 235 of whom had previously read the novel, were asked to rate the quality of the movie. The survey showed that 141 of the novel readers gave the movie a rating of excellent, while 248 of the non-readers gave the movie an excellent rating. a. Develop an interval estimate of the difference between the proportions of the two populations, using a .05 level of significance, as the basis for your decision. b. Can we conclude, on the basis of a hypothesis test about p1 – p2, that the proportion of the non-readers of the novel who thought the movie was excellent is greater than the proportion of readers of the novel who thought the movie was excellent? Use a 0.05 level of significance. (Hint: This is a one-tailed test.) ANSWER: a. .0118 to .1690 (note that 0 is not in the interval) b. H0: pNR – pR < 0; z = 2.274 > 1.645; p-value = 0.0115 < .05; reject H0 and conclude that the proportion of the non-readers of the novel who thought the movie was excellent is greater than the proportion of readers of the novel who thought the movie was excellent.

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Chapter 11: Inferences About Population Variances Multiple Choice 1. A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The χ2 values to be used for this interval estimation are _____. a. –1.96 and 1.96 b. 14.573 and 43.195 c. 16.151 and 40.113 d. 15.308 and 44.461 ANSWER: b 2. We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is _____. a. H0: σ2 < 1.44 b. H0: s2 ≥ 1.44 c. H0: σ ≤ 1.20 d. H0: σ2 ≥ 1.44 ANSWER: d 3. A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is _____. a. 100 b. 10 c. 51.25 d. 50 ANSWER: d 4. The value of F.05 with 8 numerator and 19 denominator degrees of freedom is _____. a. 2.48 b. 2.58 c. 3.63 d. 2.96 ANSWER: a 5. To avoid the problem of not having access to tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with the _____. a. larger sample size b. smaller sample size c. larger sample variance d. smaller sample variance ANSWER: c 6. The symbol used for the variance of the population is _____. a. σ Copyright Cengage Learning. Powered by Cognero.

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Chapter 12: Tests of Goodness of Fit, Independence, and Multiple Proportions Fine Arts Health Sciences Total

13 3 150

15 12 200

7 4 80

25 21 270

60 40 700

State the critical value of the chi-square random variable for this test of independence of categories. b. Calculate the value of the test statistic. c. What is the conclusion for this test? ANSWER: a. 21.0261 b. 8.674 c. Do not reject the null hypothesis that fields of specialization and region are independent. a.

67. During "sweeps week" last year, the viewing audience was distributed as follows: 36% NBC, 22% ABC, 24% CBS, and 18% FOX. This year during sweeps week, a random sample of 50 homes yielded the following data. Use Excel to test at α = .05 to determine if the audience proportions have changed. ABC FOX ABC FOX NBC ABC CBS ABC ABC FOX NBC CBS NBC NBC NBC NBC CBS CBS FOX FOX ANSWER: Value Sheet:

ABC NBC CBS FOX NBC

ABC NBC NBC ABC CBS

CBS NBC NBC FOX FOX

NBC CBS ABC NBC CBS

FOX FOX FOX FOX FOX

FOX ABC FOX CBS NBC

Home

Network

Hypoth. Obs. Category Propor. Freq.

2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8

ABC NBC ABC NBC CBS FOX ABC FOX

ABC NBC CBS FOX

NBC

11 12 13 14 15

10 11 12 13 14

CBS ABC CBS NBC NBC

Number of Categories

0.22 0.36 0.24 0.18 Total

10 15 10 15 50

Exp. Freq.

J Sqd. Diff. Sqd. Divided by Diff. Differ. Exp. Freq.

11 18 12 9

-1 -3 -2 6

1 9 4 36

0.09091 0.50000 0.33333 4.00000 4.92424

Test Statistic 4.92424 Degrees of Freedom 3 p-value

0.17743

Formula Sheet: D

1 2 3

Category

Hyp. Propor.

Obs. Frequency

Exp. Freq.

Diff.

Sqrd. Diff.

ABC

0.22

=COUNTIF(B2:B51,"ABC") =E4*F8

NBC

0.36

=F4G4 =COUNTIF(B2:B51,"NBC") =E5*F8 =F5-

J Sqrd. Diff. Divided by Exp. Freq.

=H4^2 =I4/G4 =H5^2 =I5/G5 Page 15

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Chapter 12: Tests of Goodness of Fit, Independence, and Multiple Proportions 6

CBS

0.24

FOX

0.18

8 9 10

G5 =F6=COUNTIF(B2:B51,"CBS") =E6*F8 G6 =F7=COUNTIF(B2:B51,"FOX") =E7*F8 G7 =SUM(F4:F7)

Total No. of Categories

=H6^2 =I6/G6 =H7^2 =I7/G7 =SUM(J4:J7)

11 12 Test Statistic Degr. of 13 Freedom 14 15 p-value

=J8 =F10-1 =CHISQ.TEST(F12,F13)

Do not reject the null hypothesis; there is not sufficient evidence to conclude the audience proportions have changed 68. Members of a focus group stated their preferences between three possible slogans. The results follow. Use Excel to test at α = .05 to determine any difference in preference among the three slogans. Slogan Preferences A A C C C B B A B C A B C C C B C B C C A A C A ANSWER: Value Sheet:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Person

Pref.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A C B C C A A B C C B A C B A

B A C B A B

Categ.

Hypoth. Propor.

Obs. Freq.

Exp. Freq.

Diff.

Sqrd. Diff.

0.33333 0.33333 0.33333 Total

9 9 12 30

9.99999 9.99999 9.99999

-1 -1 2

0.99998 0.99998 4.00004

A B C

J Sqrd. Diff. Divided by Exp. Freq.

0.099998 0.099998 0.400004 0.600001

No. of Categories 3 Test Statistic 0.600001 Degr. of Freedom 2 p-value

0.74082

Formula Sheet: Copyright Cengage Learning. Powered by Cognero.

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Chapter 12: Tests of Goodness of Fit, Independence, and Multiple Proportions D

Categ.

Hypoth. Proportion

Observed Frequency

Exp. Freq.

Diff.

Sqrd. Diff.

0.33333 0.33333 0.33333 Total

=COUNTIF(B2:B31,"A") =COUNTIF(B2:B31,"B") =COUNTIF(B2:B31,"C") =SUM(F4:F6)

=E4*F7 =F4-G4 =H4^2 =I4/G4 =E5*F7 =F5-G5 =H5^2 =I5/G5 =E6*F7 =F6-G6 =H6^2 =I6/G6 =SUM(J4:J6)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

A B C

J Sqrd. Diff. Divided by Exp. Freq.

No. of Categories 3 Test Statistic =J7 Degr. of Freedom =F10-1 p-value

=CHISQ.TEST(F12,F13)

Do not reject the null hypothesis; there is not sufficient evidence to conclude that there is a difference in preference among the three slogans.

69. A study of wage discrimination at a local store compared employees' race and status. Partial results of the study follow. Use Excel and test at α = .05 to determine if race is independent of status. Employee 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Race white non-white white white white non-white non-white white non-white white non-white non-white white non-white white white non-white non-white white non-white white non-white non-white

Status manager associate district mgr. manager manager associate associate associate associate manager manager associate associate associate district mgr. district mgr. associate associate associate manager district mgr. district mgr. manager

Employee 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Race non-white white non-white white non-white non-white white white non-white white non-white non-white non-white white non-white non-white non-white white white non-white non-white non-white white

Status associate district mgr. manager associate district mgr. district mgr. district mgr. district mgr. associate district mgr. associate manager associate district mgr. associate manager district mgr. manager district mgr. associate associate district mgr. manager Page 17

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Chapter 12: Tests of Goodness of Fit, Independence, and Multiple Proportions 24 25

non-white non-white

associate associate

49 50

non-white non-white

manager associate

ANSWER: Value Sheet: E Count of Employee Race white non-white Grand Total

Status associate 4 18 22

G Grand Total manager 6 7 13

district mgr. 10 5 15

20 30 50

associate 8.8 13.2

manager 5.2 7.8

district mgr. 6 9

p-value

0.01104

Expected Frequencies white non-white

Formula Sheet:

5 6 7 8 9 10 11 12 13 14

E Count of Employee Race white non-white Grand Total

Status associate 4 18 22

G Grand Total manager 6 7 13

district mgr. 10 5 15

20 30 50

associate =F7*I5/I7 =F7*I6/I7

manager =G7*I5/I7 =G7*I6/I7

district mgr. =H7*I5/I7 =H7*I6/I7

p-value

=CHISQ.TEST(F5:H6,F11:H12)

Expected Frequencies white non-white

Reject the null hypothesis; there is sufficient evidence to conclude that race is dependent of status. 70. City planners are evaluating three proposed alternatives for relieving the growing traffic congestion on a north-south highway in a booming city. The proposed alternatives are: (1) designate high-occupancy vehicle (HOV) lanes on the existing highway, (2) construct a new, parallel highway, and (3) construct a light (passenger) rail system. In an analysis of the three proposals, a citizen group has raised the question of whether preferences for the three alternatives differ among residents near the highway and nonresidents. A test of independence will address this question, with the hypotheses being: H0: Proposal preference is independent of the residency status of the individual Ha: Proposal preference is not independent of the residency status of the individual A simple random sample of 500 individuals has been selected. A crosstabulation of the residency statuses and proposal Copyright Cengage Learning. Powered by Cognero.

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Chapter 14: Simple Linear Regression n = 10 ∑x = 55 ∑y = 55 ∑x2 = 385 ∑y2 = 385 ∑xy = 220 52. Refer to Exhibit 14-1. The least squares estimate of b1 equals _____. a. 1 b. –1 c. 5.5 d. 11 ANSWER: b 53. Refer to Exhibit 14-1. The least squares estimate of b0 equals _____. a. 1 b. –1 c. 5.5 d. 11 ANSWER: d 54. Refer to Exhibit 14-1. The point estimate of y when x = 20 is _____. a. 0 b. 31 c. 9 d. –9 ANSWER: d 55. Refer to Exhibit 14-1. The sample correlation coefficient equals _____. a. 0 b. –1 c. 1 d. –0.5 ANSWER: b 56. Refer to Exhibit 14-1. The coefficient of determination equals _____. a. 0 b. –1 c. 1 d. –0.5 ANSWER: c Exhibit 14-2 You are given the following information about x and y. Copyright Cengage Learning. Powered by Cognero.

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Chapter 14: Simple Linear Regression x Independent Variable 15 12 10 7

y Dependent Variable 5 7 9 11

57. Refer to Exhibit 14-2. The least squares estimate of b1 equals _____. a. –0.7647 b. –0.13 c. 21.4 d. 16.412 ANSWER: a 58. Refer to Exhibit 14-2. The least squares estimate of b0 equals _____. a. –7.647 b. –1.3 c. 21.4 d. 16.41176 ANSWER: d 59. Refer to Exhibit 14-2. The sample correlation coefficient equals _____. a. –86.667 b. –.99705 c. .9941 d. .99705 ANSWER: b 60. Refer to Exhibit 14-2. The coefficient of determination equals _____. a. –.99705 b. –.9941 c. .9941 d. .99705 ANSWER: c Exhibit 14-3 Regression analysis was applied between sales data (in $1000s) and advertising data (in $100s), and the following information was obtained. = 12 + 1.8x n = 17 SSR = 225 SSE = 75 Copyright Cengage Learning. Powered by Cognero.

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Chapter 14: Simple Linear Regression = 0.2683

61. Refer to Exhibit 14-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is _____. a. $66,000 b. $5,412 c. $66 d. $17,400 ANSWER: a 62. Refer to Exhibit 14-3. The F statistic computed from the above data is _____. a. 3 b. 45 c. 48 d. 38 ANSWER: b 63. Refer to Exhibit 14-3. The critical F value at α = .05 is _____. a. 3.59 b. 3.68 c. 4.45 d. 4.54 ANSWER: d 64. Refer to Exhibit 14-3. The t statistic for testing the significance of the slope is _____. a. 1.80 b. 1.96 c. 6.709 d. .555 ANSWER: c 65. Refer to Exhibit 14-3. Using α = .05, the critical t value for testing the significance of the slope is _____. a. 1.753 b. 2.131 c. 1.746 d. 2.120 ANSWER: b Exhibit 14-4 The following information regarding a dependent variable (y) and an independent variable (x) is provided. x 2 1

y 4 3

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Chapter 14: Simple Linear Regression 4 4 3 6 5 8 SSE = 6 SST = 16 66. Refer to Exhibit 14-4. The least squares estimate of the y-intercept is _____. a. 1 b. 2 c. 3 d. 4 ANSWER: b 67. Refer to Exhibit 14-4. The least squares estimate of the slope is _____. a. 1 b. 2 c. 3 d. 4 ANSWER: a 68. Refer to Exhibit 14-4. The coefficient of determination is _____. a. .7096 b. –.7906 c. .625 d. .375 ANSWER: c 69. Refer to Exhibit 14-4. The sample correlation coefficient is _____. a. .7906 b. –.7906 c. .625 d. .375 ANSWER: a 70. Refer to Exhibit 14-4. The MSE is _____. a. 1 b. 2 c. 3 d. 4 ANSWER: b Exhibit 14-5 You are given the following information about x and y. x

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Chapter 14: Simple Linear Regression questions: Week 1 2 3 4 5 6 7 a. b. c. d.

Price 0.33 0.25 0.44 0.40 0.35 0.39 0.29

Sales 20 14 22 21 16 19 15

What is the estimated regression equation? Perform a t test and determine whether x and y are related. Use α = .05. Perform an F test and determine whether x and y are related. Use α = .05. Find and interpret the coefficient of determination.

ANSWER:

Price 0.33 0.25 0.44 0.4 0.35 0.39 0.29

Sales 20 14 22 21 16 19 15

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Sq. Standard Error Observations

0.877760967 0.770464315 0.724557178 1.643764862 7

ANOVA Regression Residual Total

df 1 5 6

Standard t Stat Error 3.581788441 3.608215 0.992676 41.60305344 10.15521 4.096719 Coefficients

Intercept Price

SS MS 45.34733 45.34733 13.50981 2.701963 58.85714

a. b. c. d. Copyright Cengage Learning. Powered by Cognero.

F 16.78311

Significance F 0.009385

P-value

Lower 95%

0.366447 0.009385

-5.69341 15.49829

= 3.581788441 + 41.60305344x Since the p-value .009385 < .05, reject H0. Therefore, the competitor's price and sales are related. Since the p-value .009385 < .05, reject H0. r2 = .770464315; 77.05% of the variation in sales is explained by Page 22

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Chapter 14: Simple Linear Regression the variation in the competitor's price.

94. Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel to Compute a 95% confidence interval for E(y) when x = 5. Compute a 95% prediction interval for y when x = 5.

a. b. x 2 3 6 7 8 7 9

y 12 9 8 7 6 5 2

ANSWER: A

Value Sheet B C

2 3 4 5

2 3 6 7

12 9 8 7

7 8 9 10 11 12 13 14

7 9

5 2

Multiple R

0.91855865

16 17 18 19 20 21 22 23 24 25 26

R Square Adjusted R Square Standard Error Observations

0.84375 0.8125 1.36930639 7

SUMMARY OUTPUT

D E Confidence Interval Given value of x 5 xbar 6 x-xbar -1 (x-xbar)sq 1 Sum of (x40 xbar)sq Var of yhat 0.3147321 Stdev of yhat 0.5610099 t value 2.5705776 Margin of Error 1.4421196 Point Estimate 8.125 Lower Limit 6.6828804 Upper Limit 9.5671196

Regression Statistics

Prediction Interval Var of yind 2.1897321 Stdev of yind 1.4797744 Margin of Error 3.8038749 Lower Limit 4.3211251 Upper Limit 12.446125

ANOVA Regression Residual Total

df 1 5 6

SS 50.625 9.375 60

MS 50.625 1.875

F 27

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Chapter 08: Interval Estimation news every day is between .199 and .261. 104. Six hundred consumers were asked whether they would like to purchase a domestic or a foreign automobile. Their responses are given below. Preference Frequency Domestic 240 Foreign 360 Develop a 95% confidence interval for the proportion of all consumers who prefer to purchase domestic automobiles. ANSWER: .3608 to .4392 105. A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 32 current students and discovers that 12 will return for summer school. a. Construct a 90% confidence interval estimate for the proportion of current spring students who will return for summer school. b. With a .95 probability, what sample size would have to be selected to provide a margin of error of 3% or less? ANSWER: a. b.

.234 to .516 1001

106. A new brand of breakfast cereal is being market tested. One hundred boxes of the cereal were given to consumers to try. The consumers were asked whether they liked or disliked the cereal. You are given their responses below. Response Liked Disliked a. b. c. d.

Frequency 60 40 100

What is the point estimate of the proportion of people who will like the cereal? Construct a 95% confidence interval for the proportion of all consumers who will like the cereal. What is the margin of error for the 95% confidence interval that you constructed in part (b)? With a .95 probability, what sample size needs to be selected to provide a margin of error of .09 or less?

ANSWER: a. b. c. d.

.6 .504 to .696 .096 114

107. A marketing firm is developing a new television advertisement for a large discount retail chain. A sample of 30 people is shown two potential ads and asked their preference. The results for ad #1 follow. Use Excel to develop a 95% confidence interval estimate of the proportion of people in the population who will prefer ad #1. yes no no

no no no

Prefer Advertisement #1 no yes no yes yes yes

yes no yes

no yes no Page 20

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Chapter 08: Interval Estimation yes yes ANSWER:

yes no

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A Prefer Ad 1 yes no no yes yes no no no no yes no yes no no

no yes

no no

yes no

C Sample size Response of Interest Count for Response Sample Proportion

D =COUNTA(A2:A31) yes =COUNTIF(A2:A31,"yes") =D3/D1

Value for D 30 yes 14 0.466667

Confidence Coefficient Level of Significance z value

0.95 =1-D5 =NORM.S.INV(1-D7/2)

0.95 0.05 1.959961

Standard Error Margin of Error

=SQRT((D4*(1-D4)/D1)) =D8*D10

0.091084 0.178521

Point Estimate Lower Limit Upper Limit

=D4 =D13-D11 =D13+D11

0.466667 0.28815 0.64519

108. A survey of 40 students at a local college asks, "Where do you buy the majority of your books?" The responses fell into three categories: "at the campus bookstore," "on the Internet," and "other." The results follow. Use Excel to develop a 95% confidence interval estimate of the proportion of college students who buy their books on the Internet. Where Most Books Bought bookstore bookstore Internet other bookstore bookstore bookstore bookstore bookstore other other other other other Internet bookstore Internet Internet

other bookstore Internet other other other

Internet bookstore Internet other bookstore bookstore

other bookstore other Internet bookstore

bookstore other other bookstore other

ANSWER: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A where bought bookstore bookstore Internet other Internet other bookstore bookstore bookstore bookstore bookstore bookstore bookstore Internet

C Sample size Response of Interest Count for Response Sample Proportion

D =COUNTA(A2:A41) Internet =COUNTIF(A2:A41,"internet") =D2/D1

Value for D 40 Internet 8 0.2

Confidence Coefficient Level of Significance z value

0.95 =1-D6 =NORM.S.INV(1-D6/2)

0.95 0.05 1.95996108

Standard Error Margin of Error

=SQRT((D4*(1-D4)/D1)) =D8*D10

0.06324555 0.12395882

Point Estimate Lower Limit Upper Limit

=D4 =D13-D11 =D13+D11

0.2 0.07604 0.32396

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Chapter 08: Interval Estimation 109. A health club annually surveys its members. Last year, 33% of the members said they use the treadmill at least four times a week. What size sample should be selected this year to estimate the percentage of members who use the treadmill at least four times a week? The estimate is desired to have a margin of error of 5% with a 95% level of confidence. ANSWER: 340 110. A local hotel wants to estimate the proportion of its guests that are from out of state. Preliminary estimates are that 45% of the hotel guests are from out-of-state.What sample size should be selected to estimate the proportion of out of state guests with a margin of error no larger than 5% and with a 95% level of confidence? ANSWER: 381 111. The manager of a department store wants to determine what proportion of people who enter the store use the store's credit card for their purchases. What size sample should he take so that at 99% confidence the error will not be more than 8%? ANSWER: 260 112. The manager of Hudson Auto Repair wants to advertise one price for an engine tune-up, with parts included. Before he decides the price to advertise, he needs a good estimate of the average cost of tune-up parts. A sample of 20 customer invoices for tune-ups has been selected and the costs of parts, rounded to the nearest dollar, are listed below. 91 104

78 74

93 62

57 68

75 97

52 73

99 77

80 65

105 80

62 109

Provide a 90% confidence interval estimate of the mean cost of parts per tune-up for all of the tune-ups performed at Hudson Auto Repair. ANSWER: 73.51 to 86.59 113. The manager of University Credit Union (UCU) is concerned about checking account transaction discrepancies. Customers are bringing transaction errors to the attention of the bank’s staff several months after they occur. The manager would like to know what proportion of his customers balance their checking accounts within 30 days of receiving a transaction statement from the bank. Using random sampling, 400 checking account customers are contacted by telephone and asked if they routinely balance their accounts within 30 days of receiving a statement. 271 of the 400 customers respond Yes. a. Develop a 95% confidence interval estimate for the proportion of the population of checking account customers at UCU who routinely balance their accounts in a timely manner. b. Suppose UCU wants a 95% confidence interval estimate of the population proportion with a margin of error of E = .025. What sample size is needed? ANSWER: a. .6317 to .7233 b. 1343 114. National Discount has 260 retail outlets throughout the United States. National evaluates each potential location for a new retail outlet in part on the mean annual income of the households in the marketing area of the new location. National develops an interval estimate of the mean annual income in a potential marketing area after taking a random sample of households. For a marketing area being studied, a sample of 36 households was selected. The sample mean income was $21,100.39. Based on past experience, National Discount assumes a known value of $4500 for the population standard deviation of incomes. a. Develop a 95% confidence interval for the mean annual income of households in this marketing area. Interpret the interval. Copyright Cengage Learning. Powered by Cognero.

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Chapter 08: Interval Estimation b. Suppose that National’s management team wants a 95% confidence interval estimate of the population mean with a margin of error of E = $500. What sample size is needed to meet these requirements? ANSWER: a. $19,630.39 to $22,570.39 We are 95% confident that the average annual income for all households in the market area being studied falls in the interval $19,630.39 to $22,570.39. b. We need to sample 312 households to reach a desired margin of error of $500 at 95% confidence.

115. A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was selected of 10 one-bedroom units within a half-mile of campus and the rents paid. The sample mean is $550 and the sample standard deviation is $60.05. Assume this population is normally distributed. Develop a 95% confidence interval estimate of the mean rent per month for the population of one-bedroom units within a half-mile of campus. Interpret the interval. ANSWER: $507.05 to $592.95 We are 95% confident that the mean rent per month for the population of one-bedroom units within a halfmile of campus is between $507.05 and $592.95. 116. Political Science, Inc. (PSI) specializes in voter polls and surveys designed to keep political office seekers informed of their position in a race. Using telephone surveys, interviewers ask registered voters who they would vote for if the election were held that day. In a recent election campaign, PSI found that 220 registered voters, out of 500 contacted, favored a particular candidate. a. Develop a 95% confidence interval estimate for the proportion of the population of registered voters that favors the candidate. Interpret the interval. b. Suppose that PSI would like 99% confidence that the sample proportion is within ± .03 of the population proportion. What sample size is needed to provide the desired margin of error? ANSWER: a. .3965 to .4835 We are 95% confident that the proportion of the population of registered voters that favors the candidate is between .3965 and .4835. b. The required sample size is 1816. 117. An apartment complex developer is considering building apartments in College Town, but first wants to do a market study. A sample was selected of monthly rent values for 70 studio apartments in College Town. The sample mean is $490.80. Based on past experience, the developer assumes a known value of  = $55 for the population standard deviation. a. Develop a 98% confidence interval for the mean monthly rent for all studio apartments in this city. b. Suppose the apartment developer wants a 98% confidence interval estimate of the population mean with a margin of error of E = $10. What sample size is needed? ANSWER: a. 475.48 to 506.12 b. 162

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