ODD ANSWERS A79 11. (a) The claim is “an SAT preparation course will improve the test scores of students.” H0: md Ú 0; Ha: md 6 0 (claim) (b) t0 = -2.821; Rejection region: t 6 -2.821 (c) d = -60; sd ≈ 27.889 (d) -6.803 (e) Reject H0. (f) There is enough evidence at the 1% level of significance to support the SAT preparation course’s claim that its course will improve the test scores of students. 13. (a) The claim is “a baseball clinic will help players raise their batting averages.” H0: md Ú 0; Ha: md 6 0 (claim) (b) t0 = -1.771; Rejection region: t 6 -1.771 (c) d ≈ -0.002; sd ≈ 0.015 (d) -0.499 (e) Fail to reject H0. (f) There is not enough evidence at the 5% level of significance to support the claim that the baseball clinic will help players raise their batting averages. 15. (a) The claim is “U.S. gasoline prices increased from May to June of 2021.” H0: md Ú 0; Ha: md 6 0 (claim) (b) t0 = -3.106; Rejection region: t 6 -3.106 (c) d ≈ -0.029; sd ≈ 0.0303 (d) -3.315 (e) Reject H0. (f) There is enough evidence at the 0.5% level of significance to support the claim that U.S. gasoline prices increased from May to June of 2021. 17. (a) The claim is “the product ratings have changed from last year to this year.” H0: md = 0; Ha: md ≠ 0 (claim) (b) -t0 = -2.365, t0 = 2.365 Rejection regions: t 6 -2.365, t 7 2.365 (c) d = -1; sd ≈ 1.309 (d) -2.161 (Tech: -2.160) (e) Fail to reject H0. (f) There is not enough evidence at the 5% level of significance to support the claim that the product ratings have changed from last year to this year. 19. (a) The claim is “eating a new cereal as part of a daily diet lowers total blood cholesterol levels.” H0: md … 0; Ha: md 7 0 (claim) (b) t0 = 1.943; Rejection region: t 7 1.943 (c) d ≈ 2.857; sd ≈ 4.451 (d) 1.698 (e) Fail to reject H0. (f) There is not enough evidence at the 5% level of significance to support the claim that the new cereal lowers total blood cholesterol levels. 21. Yes. P ≈ 0.0058 6 0.05, so you reject H0. 23. -1.76 6 md 6 -1.29 Section 8.4 (page 451) 1. (1) The samples are randomly selected. (2) The samples are independent. (3) n1p Ú 5, n1q Ú 5, n2p Ú 5, and n2q Ú 5 3. Can use normal sampling distribution. Fail to reject H0. There is not enough evidence at the 1% level of significance to support the claim. 5. Can use normal sampling distribution. Reject H0. There is enough evidence at the 10% level of significance to reject the claim. 7. (a) The claim is “there is a difference in the proportion of subjects who had no 12-week confirmed disability progression.” H0: p1 = p2; Ha: p1 ≠ p2 (claim) (b) -z0 = -2.575, z0 = 2.575 Rejection regions: z 6 -2.575, z 7 2.575 (c) -1.70 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to support the claim that there is a difference in the proportion of subjects who had no 12-week confirmed disability progression. 9. (a) The claim is “there is a difference in the proportion of those employed between the two groups.” H0: p1 = p2; Ha: p1 ≠ p2 (claim) (b) -z0 = -2.575, z0 = 2.575 Rejection region: z 6 -2.575, z 7 2.575 (c) -5.821 (d) Reject H0. (e) There is enough evidence at the 1% level of significance to support the claim there is a difference in the proportion of those employed between the two groups. 11. (a) The claim is “the proportion of drivers who wear seat belts is greater in the West than in the Northeast.” H0: p1 … p2; Ha: p1 7 p2 (claim) (b) z0 = 1.645; Rejection region: z 7 1.645 (c) 2.08 (d) Reject H0. (e) There is enough evidence at the 5% level of significance to support the claim that the proportion of drivers who wear seat belts is greater in the West than in the Northeast. 13. No, there is not enough evidence at the 10% level of significance to reject the claim that the proportion of 18- to 24-year-olds who benefit mentally from exercising in parks is the same as the proportion who benefit mentally from socializing in parks. 15. Yes, there is enough evidence at the 10% level of significance to support the claim that the proportion of 18- to 24-year-olds who benefit mentally from socializing in parks is greater than the proportion who benefit mentally from enjoying nature in parks. 17. Yes, there is enough evidence at the 1% level of significance to support the claim that the proportion of 18- to 24-year-olds who benefit mentally from enjoying nature in parks is less than the proportion who benefit mentally from exercising in parks. 19. Yes, there is enough evidence at the 1% level of significance to support the claim that the proportion of men who work is greater than the proportion of men who socialize and communicate on an average day. 21. Yes, there is enough evidence at the 1% level of significance to support the claim that the proportion of women who work is less than the proportion of men who work on an average day. 23. -0.0178 6 p1 - p2 6 -0.0022 25. 0.0638 6 p1 - p2 6 0.1362. Answers will vary.
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