Review Exercises 409 In Exercises 49 and 50, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. 49. A reporter claims that over 56% of U.S. adults think it is likely that robots and computers will do most jobs 25 years from now. In a random sample of 1000 U.S. adults, 59% say it is likely that most jobs will be done by robots and computers 25 years from now. At a = 0.01, is there enough evidence to support the claim? (Source: Rasmussen Reports) 50. A sports analyst claims that 40% of U.S. adults have a positive view of the sports industry. In a random sample of 550 U.S. adults, 165 say they have a positive view of the sports industry. At a = 0.05, is there enough evidence to reject the sports analyst’s claim? (Source: Gallup) Section 7.5 In Exercises 51–54, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance a. 51. Right-tailed test, n = 20, a = 0.05 52. Two-tailed test, n = 14, a = 0.01 53. Two-tailed test, n = 41, a = 0.10 54. Left-tailed test, n = 6, a = 0.05 In Exercises 55–58, test the claim about the population variance s 2 or standard deviation s at the level of significance a. Assume the population is normally distributed. 55. Claim: s 2 7 2; a = 0.10. Sample statistics: s 2 = 2.95, n = 18 56. Claim: s 2 … 60; a = 0.025. Sample statistics: s 2 = 72.7, n = 15 57. Claim: s = 1.25; a = 0.05. Sample statistics: s = 1.03, n = 6 58. Claim: s ≠ 0.035; a = 0.01. Sample statistics: s = 0.026, n = 16 In Exercises 59 and 60, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic x 2, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed. 59. A bolt manufacturer makes a type of bolt to be used in airtight containers. The manufacturer claims that the variance of the bolt widths is at most 0.01. A random sample of 28 bolts has a variance of 0.064. At a = 0.005, is there enough evidence to reject the claim? 60. A restaurant claims that the standard deviation of the lengths of serving times is 3 minutes. A random sample of 27 serving times has a standard deviation of 3.9 minutes. At a = 0.01, is there enough evidence to reject the claim? 61. In Exercise 59, is there enough evidence to reject the claim at the a = 0.01 level? Explain. 62. In Exercise 60, is there enough evidence to reject the claim at the a = 0.05 level? Explain.
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