ODD ANSWERS A73 39. (a) The claim is “the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams.” H0: m = 37.7 (claim); Ha: m ≠ 37.7 (b) -z0 = -2.575, z0 = 2.575 Rejection regions: z 6 -2.575, z 7 2.575 (c) -0.72 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to reject the consumer research organization’s claim that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. 41. (a) The claim is “the mean sodium content in one of its breakfast sandwiches is less than 920 milligrams.” H0: m Ú 920; Ha: m 6 920 (claim) (b) z0 = 1.645; Rejection region: z 7 1.645 (c) 1.76 (d) Reject H0. (e) There is enough evidence at the 5% level of significance to support the claim that the mean sodium content in one of its breakfast sandwiches is less than 920 milligrams. 43. (a) The claim is “the mean life of a CFL bulb is at least 10,000 hours.” H0: m Ú 10,000 (claim); Ha: m 6 10,000 (b) z0 = -1.23; Rejection region: z 6 -1.23 (c) -1.28 (d) Reject H0. (e) There is enough evidence at the 11% level of significance to reject the lamp manufacturer’s claim that the mean life of a CFL bulb is at least 10,000 hours. 45. Outside. When the standardized test statistic is inside the rejection region, P 6 a. Section 7.3 (page 383) 1. Specify the level of significance a and the degrees of freedom, d.f. = n - 1. Find the critical value(s) using the t-distribution table in the row with n - 1 d.f. When the hypothesis test is (1) left-tailed, use the “One Tail, a” column with a negative sign. (2) right-tailed, use the “One Tail, a” column with a positive sign. (3) two-tailed, use the “Two Tails, a” column with a negative and a positive sign. 3. Critical value: t0 = -1.328; Rejection region: t 6 -1.328 5. Critical value: t0 = 1.717; Rejection region: t 7 1.717 7. Critical values: -t0 = -2.056, t0 = 2.056 Rejection regions: t 6 -2.056, t 7 2.056 9. (a) Fail to reject H0 because t 7 -2.086. (b) Fail to reject H0 because t 7 -2.086. (c) Reject H0 because t 6 -2.086. 11. (a) Reject H0 because t 6 -1.725. (b) Fail to reject H0 because -1.725 6 t 6 1.725. (c) Reject H0 because t 7 1.725. 13. Fail to reject H0. There is not enough evidence at the 1% level of significance to reject the claim. 15. Reject H0. There is enough evidence at the 1% level of significance to reject the claim. 17. Fail to reject H0. There is not enough evidence at the 2% level of significance to reject the claim. 19. (a) The claim is “Apple AirPods have a mean listening time of at least 5.0 hours on a single charge.” H0: m Ú 5.0 (claim); Ha: m 6 5.0 (b) t0 = -2.567; Rejection region: t 6 -2.567 (c) -2.31 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level to reject the claim that Apple AirPods have a mean listening time of at least 5.0 hours on a single charge. 21. (a) The claim is “the mean credit card debt in Colorado is greater than $5540 per borrower.” H0: m … 5540; Ha: m 7 5540 (claim) (b) t0 = 1.699; Rejection region: t 7 1.699 (c) 0.495 (d) Fail to reject H0. (e) There is not enough evidence to support the claim that the mean credit card debt in Colorado is greater than $5540 per borrower. 23. (a) The claim is “the mean amount of carbon monoxide in the air in U.S. cities is less than 1.80 parts per million.” H0: m Ú 1.80; Ha: m 6 1.80 (claim) (b) t0 = -1.295; Rejection region: t 6 -1.295 (c) 0.691 (d) Fail to reject H0. (e) There is not enough evidence at the 10% level of significance to support the claim that the mean amount of carbon monoxide in the air in U.S. cities is less than 1.80 parts per million. 25. (a) The claim is “the mean annual salary for mid-level product engineers is $86,000.” H0: m = 86,000 (claim); Ha: m ≠ 86,000 (b) -t0 = -2.131, t0 = 2.131 Rejection region: t 6 -2.131, t 7 2.131 (c) -2.152 (d) Reject H0. (e) There is enough evidence at the 5% level of significance to reject the claim that the mean annual salary for mid-level product engineers is $86,000. 27. (a) The claim is “the mean minimum time it takes for a sedan to travel a quarter mile is greater than 15.3 seconds.” H0: m … 15.3; Ha: m 7 15.3 (claim) (b) 0.166 (c) Fail to reject H0. (d) There is not enough evidence at the 10% level of significance to support the consumer group’s claim that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 15.3 seconds. 29. (a) The claim is “the mean number of classroom hours per week for full-time faculty is 11.0.” H0: m = 11.0 (claim); Ha: m ≠ 11.0 (b) 0.3155 (c) Fail to reject H0. (d) There is not enough evidence at the 1% level of significance to reject the dean’s claim that the mean number of classroom hours per week for full-time faculty is 11.0.
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