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

Type:

Test Bank

Resource:

Essentials of Modern Business Statistics with Microsoft Excel

Edition:

8th Edition

Author(s):

David Anderson Dennis Sweeney Thomas Williams Jeffrey Camm James Cochran

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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

b.

and

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and

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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 09: Hypothesis Tests c. the confidence level d. 1 − level of significance ANSWER: a 30. The level of significance is symbolized by _____. a.  b. ß c. σ d. p ANSWER: a 31. In hypothesis testing, the critical value is _____. a. a number that establishes the boundary of the rejection region b. the probability of a Type I error c. the probability of a Type II error d. the same as the p-value ANSWER: a 32. A one-tailed test is a hypothesis test in which rejection region is _____. a. in both tails of the sampling distribution b. in one tail of the sampling distribution c. only in the lower tail of the sampling distribution d. only in the upper tail of the sampling distribution ANSWER: b 33. A two-tailed test is a hypothesis test in which the rejection region is _____. a. in both tails of the sampling distribution b. in one tail of the sampling distribution c. only in the lower tail of the sampling distribution d. only in the upper tail of the sampling distribution ANSWER: a 34. A two-tailed test at a .0694 level of significance has z values of _____. a. –1.96 and 1.96 b. –1.48 and 1.48 c. –1.09 and 1.09 d. –.86 and .86 ANSWER: b 35. A one-tailed test (lower tail) at a .063 level of significance has a z value of _____. a. –1.86 b. –1.53 c. –1.96 d. –1.645 Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests ANSWER: b 36. A one-tailed test (upper tail) at a .123 level of significance has a z value of _____. a. 1.54 b. 1.96 c. 1.645 d. 1.16 ANSWER: d 37. When the hypotheses H0: µ ≥ 100 and Ha: µ < 100 are being tested at a level of significance of α, the null hypothesis will be rejected if the test statistic z is _____. a. ≥ zα b. > –zα c. ≤ –zα d. < 100 ANSWER: c 38. In order to test the hypotheses H0: μ ≤ 100 and Ha: μ > 100 at an α level of significance, the null hypothesis will be rejected if the test statistic z is _____. a. ≥ zα b. < zα c. ≤ –zα d. < 100 ANSWER: a 39. For a one-tailed test (upper tail) with a sample size of 900, the null hypothesis will be rejected at the .05 level of significance if the test statistic is _____. a. less than or equal to –1.645 b. greater than or equal to 1.645 c. less than 1.645 d. less than –1.96 ANSWER: b 40. For a two-tailed test with a sample size of 40, the null hypothesis will NOT be rejected at a 5% level of significance if the test statistic is _____. a. between –1.96 and 1.96, exclusively b. greater than 1.96 c. less than 1.645 d. greater than –1.645 ANSWER: a 41. If a hypothesis is rejected at a 5% level of significance, it _____. a. will always be rejected at the 1% level b. will always be accepted at the 1% level Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests c. will never be tested at the 1% level d. may be rejected or not rejected at the 1% level ANSWER: d 42. If a hypothesis is not rejected at a 5% level of significance, it _____. a. will also not be rejected at the 1% level b. will always be rejected at the 1% level c. will sometimes be rejected at the 1% level d. may be rejected or not rejected at the 1% level ANSWER: a 43. A p-value is the _____. a. probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed b. value of the test statistic c. probability of a Type II error d. probability corresponding to the critical value(s) in a hypothesis test ANSWER: a 44. Which of the following does NOT need to be known in order to compute the p-value? a. knowledge of whether the test is one-tailed or two-tailed b. the value of the test statistic c. the level of significance d. All three pieces of information above are needed to compute a p-value. ANSWER: c 45. When the p-value is used for hypothesis testing, the null hypothesis is rejected if _____. a. p-value ≤ α b. α < p-value c. p-value > α d. p-value = z ANSWER: a 46. A two-tailed test is performed at a 5% level of significance. The p-value is determined to be .09. The null hypothesis _____. a. must be rejected b. should not be rejected c. may or may not be rejected, depending on the sample size d. has been designed incorrectly ANSWER: b 47. Excel's _____ function can be used to calculate a p-value for a hypothesis test. a. RAND b. NORM.S.DIST Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests c. NORM.S.INV d. COUNTIF ANSWER: b 48. When using Excel to calculate a p-value for an upper-tail hypothesis test, which of the following must be used? a. RAND b. 1 − NORM.S.DIST c. NORM.S.DIST d. COUNTIF ANSWER: b 49. When using Excel to calculate a p-value for a lower-tail hypothesis test, which of the following must be used? a. RAND b. 1 − NORM.S.DIST c. NORM.S.DIST d. COUNTIF ANSWER: c 50. For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test _____. a. will result in the rejection region being smaller b. will result in the rejection region being larger c. would have no effect on the rejection region d. will result in the accepting region being smaller ANSWER: a 51. For a two-tailed test with a sample size of 20 and a .20 level of significance, the t value is _____. a. 1.328 b. 2.539 c. 1.325 d. 2.528 ANSWER: a 52. For a one-tailed test (upper tail) with a sample size of 18 and a .05 level of significance, the t value is _____. a. 2.12 b. 1.734 c. –1.740 d. 1.740 ANSWER: d 53. For a one-tailed test (lower tail) with a sample size of 10 and a .10 level of significance, the t value is _____. a. 1.383 b. –1.372 c. –1.383 Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests d. –2.821 ANSWER: c 54. Excel's _____ function can be used to calculate a p-value for a hypothesis test when σ is unknown. a. RAND b. T.DIST c. NORM.S.DIST d. COUNTIF ANSWER: b 55. The school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is _____. a. H0: p < .30 Ha: p ≥ .30 b. H0: p ≤ .30 Ha: p > .30 c. H0: p ≥ .30 Ha: p < .30 d. H0: p > .30 Ha: p ≤ .30 ANSWER: c 56. In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually INCREASED the proportion of tourists visiting Rock City. The correct set of hypotheses is _____. a. H0: p > .75 Ha: p ≤ .75 b. H0: p < .75 Ha: p ≥ .75 c. H0: p ≥ .75 Ha: p < .75 d. H0: p ≤ .75 Ha: p > .75 ANSWER: d 57. The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is _____. a. H0: p > .35 Ha: p ≥ .35 b. H0: p ≤ .35 Ha: p > .35 c. H0: p ≥ .35 Ha: p < .35 d. H0: p > .35 Ha: p ≤ .35 ANSWER: c 58. Which Excel function would NOT be appropriate to use when conducting a hypothesis test for a population proportion? a. NORM.S.DIST b. COUNTIF c. STDEV d. Excel cannot be used to conduct a hypothesis test of a proportion. Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests ANSWER: c Exhibit 9-1

59. Refer to Exhibit 9-1. The test statistic equals _____. a. 2.3 b. .38 c. –2.3 d. –.38 ANSWER: a 60. Refer to Exhibit 9-1. The p-value is _____. a. .5107 b. .0214 c. .0107 d. 2.1 ANSWER: c 61. Refer to Exhibit 9-1. If the test is done at a .05 level of significance, the null hypothesis should _____. a. not be rejected b. be rejected c. be tested again d. Not enough information is given to answer this question. ANSWER: b Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. 62. Refer to Exhibit 9-2. The test statistic is _____. a. 1.96 b. 1.64 c. 2.00 d. .056 ANSWER: c 63. Refer to Exhibit 9-2. The p-value is _____. a. .025 b. .0456 c. .05 Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests d. .0228 ANSWER: d 64. Refer to Exhibit 9-2. At a .05 level of significance, it can be concluded that the mean of the population is _____. a. significantly greater than 3 b. not significantly greater than 3 c. significantly less than 3 d. significantly greater than 3.18 ANSWER: a Exhibit 9-3 n = 49 = 54.8

H0: μ = 50 Ha: μ ≠ 50

σ = 28 65. Refer to Exhibit 9-3. The test statistic equals _____. a. .1714 b. .3849 c. –1.2 d. 1.2 ANSWER: d 66. Refer to Exhibit 9-3. The p-value is equal to _____. a. .1151 b. .3849 c. .2698 d. .2302 ANSWER: d 67. Refer to Exhibit 9-3. If the test is done at a 5% level of significance, the null hypothesis should _____. a. not be rejected b. be rejected c. be tested again d. Not enough information is given to answer this question. ANSWER: a Exhibit 9-4 A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years. 68. Refer to Exhibit 9-4. The test statistic is _____. a. 1.96 b. 2.00 c. 1.645 Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests d. .05 ANSWER: b 69. Refer to Exhibit 9-4. At a .05 level of significance, it can be concluded that the mean age is _____. a. not significantly different from 24 b. significantly different from 24 c. significantly less than 24 d. significantly less than 25 ANSWER: a Exhibit 9-5 n = 16 = 75.607

H0: μ ≥ 80 Ha: μ < 80

σ = 8.246 Assume the population is normally distributed. 70. Refer to Exhibit 9-5. The test statistic equals _____. a. –2.131 b. –.53 c. .53 d. 2.131 ANSWER: a 71. Refer to Exhibit 9-5. The p-value is equal to _____. a. –.0166 b. .0166 c. .0332 d. .9834 ANSWER: b 72. Refer to Exhibit 9-5. If the test is done at a 2% level of significance, the null hypothesis should _____. a. not be rejected b. be rejected c. be tested again d. Not enough information is given to answer this question. ANSWER: a Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. 73. Refer to Exhibit 9-6. The test statistic is _____. a. .80 b. .05 Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests c. 1.25 d. 2.00 ANSWER: c 74. Refer to Exhibit 9-6. The p-value is _____. a. .2112 b. .05 c. .025 d. .1251 ANSWER: d 75. Refer to Exhibit 9-6. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is _____. a. significantly greater than 75% b. not significantly greater than 75% c. significantly greater than 80% d. not significantly greater than 80% ANSWER: b 76. For a two-tailed hypothesis test about a population mean, the null hypothesis can be rejected if the confidence interval _____. a. is symmetric b. is non-symmetric c. includes µ0 d. does not include µ0 ANSWER: d 77. In a two-tailed hypothesis test, the null hypothesis should be rejected if the p-value is _____. a. less than or equal to  b. less than or equal to 2 c. greater than or equal to  d. greater than or equal to 2 ANSWER: a 78. If a hypothesis test has a Type I error probability of .05, that means if the null hypothesis is _____. a. false, it will not be rejected 5% of the time b. false, it will be rejected 5% of the time c. true, it will not be rejected 5% of the time d. true, it will be rejected 5% of the time ANSWER: d 79. For a two-tailed hypothesis test with a test statistic value of z = 2.05, the p-value is _____. a. .0101 Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests b. .0202 c. .0404 d. .4899 ANSWER: c 80. The rejection region for a one-tailed hypothesis test _____. a. has an area of 1 – ß b. has an area equal to the confidence coefficient c. is in the tail that supports the null hypothesis d. is in the tail that supports the alternative hypothesis ANSWER: d 81. The smaller the p-value, the _____. a. greater the evidence against H0 b. greater the chance of committing a Type II error c. greater the chance of committing a Type I error d. less likely one will reject H0 ANSWER: a Subjective Short Answer 82. A researcher is testing a new painkiller that claims to relieve pain in less than 15 minutes, on average. a. State the hypotheses associated with the researcher's test. b. Describe a Type I error for this situation. c. Describe a Type II error for this situation. ANSWER: a. H0: μ ≥ 15 b. c.

Ha: μ < 15 A Type I error for this situation would be to incorrectly conclude that the average pain relief time is less than 15 minutes. A Type II error for this situation would be to fail to conclude that the average relief time is less than 15 minutes when the average relief time actually is less than 15 minutes.

83. At a certain manufacturing plant, a machine produced ball bearings that should have a diameter of 0.50 mm. If the machine produces ball bearings that are either too small or too large, the ball bearings must be scrapped. Every hour, a quality control manager takes a random sample of 30 ball bearings to test to see if the process is "out of control" (i.e., to test to see if the average diameter differs from 0.50 mm). a. State the hypotheses associated with the manager's test. b. Describe a Type I error for this situation. c. Describe a Type II error for this situation. ANSWER: a. H0: μ = .50 b. c.

Ha: μ ≠ .50 A Type I error for this situation would be to incorrectly conclude that the process is out of control. A Type II error for this situation would be to fail to conclude that an out of control process is

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Chapter 09: Hypothesis Tests out of control.

84. A fast-food restaurant is considering a promotion that will offer customers to purchase a toy featuring a cartoon movie character. If more than 20% of the customers purchase the toy, the promotion will be profitable. A sample of 50 restaurants is used to test the promotion. a. State the hypotheses associated with the restaurant's test. b. Describe a Type I error for this situation. c. Describe a Type II error for this situation. ANSWER: a. H0: p ≤ .20 b. c.

Ha: p > .20 A Type I error for this situation would be to incorrectly conclude that the promotion would be profitable. A Type II error for this situation would be to conclude that the promotion would not be profitable when more than 20% of customers would purchase the toy.

85. The average gasoline price of one of the major oil companies has been $1.00 per gallon. Because of shortages in production of crude oil, it is believed that there has been a significant INCREASE in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $1.10. Assume that the standard deviation of the population (σ) is $0.12. a. State the null and alternative hypotheses. b. Test the claim at  = .05. c. What is the p-value associated with the above sample results? ANSWER: a. b. c.

H0: μ ≤ 1 Ha: μ > 1 z = 5; therefore, reject H0. There is sufficient evidence at  = .05 to conclude that there has been an increase in the average price. almost zero

86. "D" size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved production process, the company believes that there has been an INCREASE in the life expectancy of its D size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. a. Use a .01 level of significance, and test to determine if there has been an increase in the life expectancy of the D size batteries. b. What is the p-value associated with the sample results? What is your conclusion, based on the p-value? ANSWER: a.

b.

H0: μ ≤ 87 Ha: μ > 87 z = 1; therefore do not reject H0. There is not sufficient evidence at  = .01 to conclude that there has been an increase in the life expectancy in the D size batteries. p-value = 0.1587; therefore, do not reject H0 (same conclusion as part a)

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Chapter 09: Hypothesis Tests

87. At a local university, a sample of 49 evening students was selected in order to determine whether the average age of the evening students is significantly different from 21. The average age of the students in the sample was 23 years. The population standard deviation is known to be 3.5 years. Determine whether or not the average age of the evening students is significantly different from 21. Use a .1 level of significance. ANSWER: H0: μ = 21 Ha: μ ≠ 21 z = 4; therefore, reject H0. There is sufficient evidence at a = .1 to conclude that the average age of the evening students is significantly different from 21. 88. In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112. The population standard deviation is known to be $16. Use a .05 level of significance and determine whether or not the average room price is significantly different from $108.50. ANSWER: H0: μ = 108.50 Ha: μ ≠ 108.50 z = 1.75; therefore, do not reject H0. There is not sufficient evidence at  = .05 to conclude that the average room price is significantly different from $108.50. 89. A sample of 81 account balances of a credit company showed an average balance of $1,200. The population standard deviation is $126. You want to determine if the mean of all account balances is significantly different from $1,150. Use a .05 level of significance. ANSWER: H0: μ = 1150 Ha: μ ≠ 1150 z = 3.57; therefore, reject H0. There is sufficient evidence at  = .05 to conclude that the mean of all account balances is significantly different from $1,150. 90. A lathe is set to cut bars of steel into lengths of 6 cm. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 cm. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 cm. The population standard deviation is 0.44 cm. Determine whether or not the lathe is in perfect adjustment. Use a .05 level of significance. ANSWER: H0: μ = 6 Ha: μ ≠ 6 z = 2; therefore, reject H0. There is sufficient evidence at  = .05 to conclude that the lathe is NOT in perfect adjustment. 91. Bastien, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 6 miles per gallon. a. With a .05 level of significance, test to determine whether or not the manufacturer's advertising campaign is legitimate. b. What is the p-value associated with the sample results? ANSWER: a.

b.

H0: μ ≤ 50 Ha: μ > 50 z = 1.5, therefore, do not reject H0. There is not sufficient evidence at  = .05 to conclude that the new cars average more than 50 miles per gallon. .0668

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Chapter 09: Hypothesis Tests

92. A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be 5.6 days. a. State the null and alternative hypotheses. b. Using a critical value, test the null hypothesis at the 5% level of significance. c. Using a p-value, test the hypothesis at the 5% level of significance. d. What type of error may have been committed for this hypothesis test? ANSWER: a. H0: μ ≤ 15 b. c. d.

Ha: μ > 15 Do not reject H0, 1.5 < 1.645. There is not sufficient evidence at  = .05 to conclude that the average delivery time is more than what is advertised Do not reject H0, .0668 > 0.05 (same conclusion as part b) A Type II error may have been committed since we did not reject H0.

93. A student believes that the average grade on the statistics final examination is 87. A sample of 36 final examinations is taken. The average grade in the sample is 83.96. The population variance is 144. a. State the null and alternative hypotheses. b. Using a critical value, test the hypothesis at the 5% level of significance. c. Using a p-value, test the hypothesis at the 5% level of significance. d. Using a confidence interval, test the hypothesis at the 5% level of significance. e. Compute the probability of a Type II error if the average grade on the final is 85. ANSWER: a. H0: μ = 87 b. c. d. e.

Ha: μ ≠ 87 Do not reject H0, –1.96 < –1.52 < 1.96. There is not sufficient evidence at α = .05 to conclude that the average statistics final exam grade differs from 87. Do not reject H0, 0.1286 > 0.05 (same conclusion as part b) 80.04 to 87.88; do not reject H0 (same conclusion as part b) .8315

94. A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The population standard deviation is 5.6 days. a. State the null and alternative hypotheses. b. Using a critical value, test the null hypothesis at the 5% level of significance. c. Using a p-value, test the hypothesis at the 5% level of significance. Compute the probability of a Type II error if the true average delivery time is 17 days after d. purchase. ANSWER: a. H0: μ ≤ 15 b. c. d.

Ha: μ > 15 Do not reject H0, 1.5 < 1.645 Do not reject H0, .0668 > .05 .1949

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Chapter 09: Hypothesis Tests

95. The sponsors of televisions shows targeted at the market of 5- to 8-year olds want to test the hypothesis that children watch television AT MOST 20 hours per week. The population of viewing hours per week is known to be normally distributed with a standard deviation of 6 hours. A market research firm conducted a random sample of 30 children in this age group. The resulting data follow: 19.5 29.7 17.5 10.4 19.4 18.4 14.6 10.1 12.5 18.2 19.1 30.9 22.2 19.8 11.8 19.0 27.7 25.3 27.4 26.5 16.1 21.7 20.6 32.9 27.0 15.6 17.1 19.2 20.1 17.7 At a .10 level of significance, use Excel to test the sponsors' hypothesis. ANSWER: A B C D Values for D 1 Hours Sample Size =COUNT(A2:A31) 30 2 19.5 Sample Mean =AVERAGE(A2:A31) 20.266667 3 14.6 4 22.2 Popul. Std. Dev. 6 6 5 27.4 Hypothesized Value 20 20 6 27.0 7 29.7 Standard Error =D4/SQRT(D1) 1.095445 8 10.1 Test Statistic z =(D2-D5)/D7 0.243432 9 19.8 10 26.5 p-value (Lower Tail) =NORM.S.DIST(D8,TRUE) 0.596165 11 15.6 p-value (Upper Tail) =1-D10 0.403835 12 17.5 p-value (Two Tail) =2*(MIN(D10,D11)) 0.807670 13 12.5 Do not reject H0, .403835 > .10, cannot conclude that children watch TV more than 20hrs/week at .10 level of significance 96. At a certain manufacturing plant, a machine produces ball bearings that should have a diameter of 0.500 mm. If the machine produces ball bearings that are either too small or too large, the ball bearings must be scrapped. Every hour, a quality control manager takes a random sample of 36 ball bearings to test to see if the process is "out of control" (i.e., to test to see if the average diameter differs from 0.500 mm). Assume that the process is maintaining the desired standard deviation of 0.06 mm. The results from the latest sample follow: 0.468 0.521 0.421 0.476 0.448 0.346 0.452 0.513 0.465 0.395 0.558 0.526 0.354 0.474 0.447 0.405 0.411 0.453 0.456 0.477 0.529 0.440 0.570 0.319 0.471 0.480 0.499 0.446 0.405 0.557 0.468 0.521 0.421 0.476 0.448 0.346 At a .01 level of significance, use Excel to test whether the process is out of control. ANSWER: A B C D 1 Diameter Sample Size =COUNT(A2:A37) 2 0.468 Sample Mean =AVERAGE(A2:A37) 3 0.452 4 0.354 Popul. Std. Dev. 0.06 Copyright Cengage Learning. Powered by Cognero.

Values for D 36 0.457278 0.06 Page 19

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Chapter 09: Hypothesis Tests 5 0.456 Hypothesized Value 0.500 0.500 6 0.471 7 0.468 Standard Error =D4/SQRT(D1) 0.01 8 0.521 Test Statistic z =(D2-D5)/D7 -4.272223 9 0.513 10 0.474 p-value (Lower Tail) =NORM.S.DIST(D10,TRUE) 0.00001 11 0.477 p-value (Upper Tail) =1-NORM.S.DIST(D10,TRUE) 0.99999 12 0.480 p-value (TwoTail) =2*MIN(D12,D13) 0.00002 13 0.521 Reject H0, .00002 < .01. There is sufficient evidence at α = .01 to conclude that the process is out of control. 97. From a population of cans of coffee marked "12 ounces," a sample of 25 cans is selected and the contents of each can are weighed. The sample revealed a mean of 11.8 ounces and a standard deviation of 0.5 ounces. Test to see if the mean of the population is at least 12 ounces. (Assume the population is normally distributed.) Use a .05 level of significance. ANSWER: H0: μ ≥ 12 Ha: μ < 12 t = –2; therefore, reject H0. There is sufficient evidence at α = .05 to conclude that the population mean amount of coffee is less than 12 ounces. 98. In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an INCREASE in the average age of all the employees, a sample of 25 employees was selected. The average age in the sample was 45 years with a standard deviation of 5 years. Assume the distribution of the population is normal. Let α = .05. a. State the null and the alternative hypotheses. Test to determine whether or not the mean age of all employees is significantly more than 40 b. years. ANSWER: a. H0: μ ≤ 40 b.

Ha: μ > 40 t = 5; therefore, reject H0. There is sufficient evidence at α = .05 to conclude that average age of all employees of the large corporation has increased.

99. A soft drink filling machine, when in perfect adjustment, fills bottles with 12 ounces of soft drink. A random sample of 25 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces, with a standard deviation of 0.24 ounces. With a .05 level of significance, test to see if the machine is in perfect adjustment. Assume the distribution of the population is normal. ANSWER: H0: μ = 12 Ha: μ ≠ 12 t = –2.5; therefore, reject H0. There is sufficient evidence at α = .05 to conclude that the machine is NOT in perfect adjustment. 100. A sample of 16 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.875 with a standard deviation of 1. Assume the distribution of the population is normal. a. State the null and alternative hypotheses. b. Using a critical value, test the hypothesis at the 1% level of significance. c. Using a p-value, test the hypothesis at the 1% level of significance. d. Compute the probability of a Type II error if the true number of chocolate chips per cookie is 8. ANSWER: a. H0: μ ≥ 9 Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests b. c. d.

Ha: μ < 9 Reject H0, –4.5 < –2.602 Reject H0; the p-value is less than .005 A Type II error has not been committed since H0 was rejected.

101. Nancy believes that the average running time of movies is equal to 140 minutes. A sample of four movies was taken, and the following running times were obtained. Assume the distribution of the population is normally distributed. 150 a. b. c. d. e.

150

180

170

State the null and alternative hypotheses. Using a critical value, test the hypothesis at the 10% level of significance. Using a p-value, test the hypothesis at the 10% level of significance. Using a confidence interval, test the hypothesis at the 10% level of significance. Could a Type II error have been committed in this hypothesis test?

ANSWER: a. b. c. d. e.

H0: μ = 140 Ha: μ ≠ 140 Reject H0, 3 > 2.353. There is sufficient evidence at α = .10 to conclude that the average running time of movies differs from 140 minutes. The p-value is approximately equal to .06. Reject H0; .06 < 0.1 (same conclusion as part b) 144.85 to 180.15; reject H0 (same conclusion as part b) A Type II error could not have been committed since H0 was rejected.

102. You are given the following information obtained from a random sample of five observations. 20 18 17 22 18 At a 10% level of significance, use Excel to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) ANSWER: A B C D Value of D 1 x Sample Size =COUNT(A2:A6) 5 2 20 Sample Mean =AVERAGE(A2:A6) 19 3 18 Sample Std. Dev. =STDEV(A2:A6) 2 4 17 5 22 Hypoth. Value 21 21 6 18 7 Standard Error =D3/SQRT(D1) 0.8944272 8 Test Statistic t =(D2-D5)/D7 -2.236068 9 Degr. of Freedom =D1-1 4 10 11 p-value (Low. Tail) =T.DIST(D8,D9,TRUE) 0.04450 12 p-value (Up. Tail) =1-D11 0.95550 13 p-value (TwoTail) =2*MIN(D11,D12) 0.08901 14 Copyright Cengage Learning. Powered by Cognero.

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Chapter 09: Hypothesis Tests Reject H0, .04450 <.10, there is sufficient evidence at α = .10. To conclude the population mean is significantly less than 21. 103. You are given the following information obtained from a random sample of four observations. 25 47 32 56 At a .05 level of significance, use Excel to determine whether or not the mean of the population from which this sample was taken is significantly different from 48. (Assume the population is normally distributed.) ANSWER: A B C D Values for D 1 x Sample Size =COUNT(A2:A5) 4 2 25 Sample Mean =AVERAGE(A2:A5) 40 3 47 Sample Std. Dev. =STDEV(A2:A5) 14.07125 4 32 5 56 Hypothesized Value 48 48 6 7 Standard Error =D3/SQRT(D1) 7.03562 8 Test Statistic t =(D2-D5)/D7 -1.13707 9 Degrees of Freedom =D1-1 3 10 11 p-value (Lower Tail) =T.DIST(D8,D9,TRUE) 0.16906 12 p-value (Upper Tail) =1-D11 0.83094 13 p-value (Two Tail) =2*MIN(D11,D12) 0.33811 14 Do not reject H0, .33811 > .05. There is not sufficient evidence at α = .05 to conclude that the mean of the population is significantly different from 48. 104. A group of young businesswomen wish to open a high fashion boutique in a vacant store, but only if the average income of households in the area is more than $45,000. A random sample of nine households showed the following results. $48,000 $44,000 $46,000 $43,000 $47,000 $46,000 $44,000 $42,000 $45,000 Use the statistical techniques in Excel to advise the group on whether or not they should locate the boutique in this store. Use a .05 level of significance. (Assume the population is normally distributed.) ANSWER: A B C D Values for D 1 Income Sample Size =COUNT(A2:A10) 9 2 48000 Sample Mean =AVERAGE(A2:A10) 45000 3 44000 Sample Std. Dev. =STDEV(A2:A10) 1936.49167 4 46000 5 45000 Hypothesized Value 45000 45000 6 43000 7 47000 Standard Error =D3/SQRT(D1) 645.49722 8 46000 Test Statistic t =(D2-D5)/D7 0 9 42000 Degrees of Freedom =D1-1 8 10 44000 11 p-value (Lower Tail) =T.DIST(D8,D9,TRUE) 0.50000 Copyright Cengage Learning. Powered by Cognero.

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