A72 ODD ANSWERS 43. Alternative hypothesis (a) There is enough evidence to support the scientist’s claim that the mean incubation period for swan eggs is less than 40 days. (b) There is not enough evidence to support the scientist’s claim that the mean incubation period for swan eggs is less than 40 days. 45. Null hypothesis (a) There is enough evidence to reject the researcher’s claim that the standard deviation of the life of the lawn mower is at most 2.8 years. (b) There is not enough evidence to reject the researcher’s claim that the standard deviation of the life of the lawn mower is at most 2.8 years. 47. Alternative hypothesis (a) There is enough evidence to support the fitness equipment company’s claim that its competitor’s home gym does not have a customer satisfaction rate of 99%. (b) There is not enough evidence to support the fitness equipment company’s claim that its competitor’s home gym does not have a customer satisfaction rate of 99%. 49. H0: m Ú 60; Ha: m 6 60 51. (a) H0: m Ú 5; Ha: m 6 5 (b) H0: m … 5; Ha: m 7 5 53. If you decrease a, then you are decreasing the probability that you will reject H0. Therefore, you are increasing the probability of failing to reject H0. This could increase b, the probability of failing to reject H0 when H0 is false. 55. Yes; If the P-value is less than a = 0.05, then it is also less than a = 0.10. 57. (a) Fail to reject H0 because the confidence interval includes 70. (b) Reject H0 because the confidence interval does not include 70. (c) Fail to reject H0 because the confidence interval includes 70. 59. (a) Reject H0 because the confidence interval is located entirely to the right of 0.20. (b) Fail to reject H0 because the confidence interval includes values less than 0.20. (c) Fail to reject H0 because the confidence interval includes values less than 0.20. Section 7.2 (page 373) 1. The z-test using a P-value compares the P-value with the level of significance a. In the z-test using rejection region(s), the test statistic is compared with critical values. 3. (a) Fail to reject H0. (b) Reject H0. (c) Reject H0. 5. (a) Fail to reject H0. (b) Fail to reject H0. (c) Fail to reject H0. 7. (a) Fail to reject H0. (b) Fail to reject H0. (c) Reject H0. 9. (b). The smaller P-value corresponds to the smaller area. 11. (a). The smaller z-statistic corresponds to the smaller area. 13. P = 0.0934. Reject H0. 15. P = 0.0069. Reject H0. 17. P = 0.0930. Fail to reject H0. 19. Fail to reject H0. 21. (a) Fail to reject H0 because z 6 1.285. (b) Fail to reject H0 because z 6 1.285. (c) Fail to reject H0 because z 6 1.285. (d) Reject H0 because z 7 1.285. 23. Critical value: z0 = -1.88; Rejection region: z 6 -1.88 z 0 −3 −2 −1 1 2 3 z0 = −1.88 25. Critical value: z0 = 1.645; Rejection region: z 7 1.645 z 0 −3 −2 −1 1 2 3 z0 = 1.645 27. Critical values: -z0 = -2.33, z0 = 2.33 Rejection regions: z 6 -2.33, z 7 2.33 z 0 −3 −2 −1 1 2 3 −z0 = −2.33 z0 = 2.33 29. Reject H0. There is enough evidence at the 5% level of significance to reject the claim. 31. Fail to reject H0. There is not enough evidence at the 3% level of significance to support the claim. 33. (a) The claim is “the mean total score for the school’s applicants is more than 503.” H0: m … 503; Ha: m 7 503 (claim) (b) 1.89 (c) 0.0294 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to support the report’s claim that the mean total score for the school’s applicants is more than 503. 35. (a) The claim is “the mean winning times for Boston Marathon women’s open division champions is at least 2.6 hours.” H0: m Ú 2.6 (claim); Ha: m 6 2.6 (b) -2.43 (c) 0.0075 (d) Reject H0. (e) There is enough evidence at the 5% level of significance to reject the statistician’s claim that the mean winning times for Boston Marathon women’s open division champions is at least 2.6 hours. 37. (a) The claim is “the mean vertical drop of top-rated roller coasters is 163 feet.” H0: m = 163 (claim); Ha: m ≠ 163 (b) -1.66 (c) 0.097 (d) Fail to reject H0. (e) There is not enough evidence at the 5% level of significance to reject the claim that the mean vertical drop of top-rated roller coasters is 163 feet.
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