ODD ANSWERS A75 15. Fail to reject H0. There is not enough evidence at the 5% level of significance to reject the claim. 17. Fail to reject H0. There is not enough evidence at the 5% level of significance to reject the claim. 19. Fail to reject H0. There is not enough evidence at the 1% level of significance to support the claim. 21. Reject H0. There is enough evidence at the 10% level of significance to support the claim. 23. (a) The claim is “the variance of the diameters in a certain tire model is 8.6.” H0: s 2 = 8.6 (claim); Ha: s 2 ≠ 8.6 (c) 4.5 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to reject the tire manufacturer’s claim that the variance of the diameters in a certain tire model is 8.6. 25. (a) The claim is “the standard deviation for grade 12 students on a mathematics assessment test is less than 37.” H0: s Ú 37; Ha: s 6 37 (claim) (b) x2 0 = 18.114; Rejection region: x 2 6 18.114 (c) 22.799 (d) Fail to reject H0. (e) There is not enough evidence at the 10% level of significance to support the school administrator’s claim that the standard deviation for grade 12 students on a mathematics assessment test is less than 37 points. 27. (a) The claim is “the standard deviation of the waiting times for patients is no more than 0.5 minute.” H0: s … 0.5 (claim); Ha: s 7 0.5 (b) x2 0 = 33.196; Rejection region: x 2 7 33.196 (c) 47.04 (d) Reject H0. (e) There is enough evidence at the 10% level of significance to reject the hospital’s claim that the standard deviation of the waiting times for patients is no more than 0.5 minute. 29. (a) The claim is “the standard deviation of the annual salaries of senior level graphic design specialists is different from $13,056.” H0: s = 13,056 (claim); Ha: s ≠ 13,056 (b) x 2 L = 5.629, x 2 R = 26.119 Rejection region: x2 6 5.629, x2 7 26.119 (c) 27.464 (d) Reject H0. (e) There is enough evidence at the 5% level of significance to support the claim that the standard deviation of the annual salaries of senior level graphic design specialists is different from $13,056. 31. P-value = 0.304; Fail to reject H0. 33. P-value = 0.0033; Reject H0. Uses and Abuses for Chapter 7 (page 404) 1. H0: p = 0.5; Answers will vary. 2–3. Answers will vary. Review Exercises for Chapter 7 (page 406) 1. H0: m … 375 (claim); Ha: m 7 375 3. H0: p Ú 0.205; Ha: p 6 0.205 (claim) 5. H0: s … 1.9; Ha: s 7 1.9 (claim) 7. (a) H0: p = 0.81 (claim); Ha: p ≠ 0.81 (b) A type I error will occur when the actual proportion of U.S. adults who believe that Earth’s temperature has been increasing over the past 100 years is 81%, but you reject H0: p = 0.81. A type II error will occur when the actual proportion is not 81%, but you fail to reject H0: p = 0.81. (c) Two-tailed because the alternative hypothesis contains ≠. (d) There is enough evidence to reject the polling organization’s claim that the proportion of U.S. adults who believe that Earth’s temperature has been increasing over the past 100 years is 81%. (e) There is not enough evidence to reject the polling organization’s claim that the proportion of U.S. adults who believe that Earth’s temperature has been increasing over the past 100 years is 81%. 9. (a) H0: s … 2900 (claim); Ha: s 7 2900 (b) A type I error will occur when the actual standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900, but you reject H0: s … 2900. A type II error will occur when the actual standard deviation of the starting prices of its top-rated vehicles for a recent year is more than $2900, but you fail to reject H0: s … 2900. (c) Right-tailed because the alternative hypothesis contains 7. (d) There is enough evidence to reject the nonprofit consumer organization’s claim that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900. (e) There is not enough evidence to reject the nonprofit consumer organization’s claim that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900. 11. 0.1736. Fail to reject H0. 13. Critical value: z0 = -2.05; Rejection region: z 6 -2.05 z 0 −3 −2 −1 1 2 3 z0 = −2.05 15. Critical value: z0 = 1.96; Rejection region: z 7 1.96 z 0 −3 −2 −1 1 2 3 z0 = 1.96 17. Fail to reject H0 because -1.645 6 z 6 1.645. 19. Fail to reject H0 because -1.645 6 z 6 1.645. 21. Fail to reject H0. There is not enough evidence at the 5% level of significance to reject the claim. 23. Fail to reject H0. There is not enough evidence at the 1% level of significance to support the claim.
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