A76 ODD ANSWERS 25. (a) The claim is “the mean air concentration of nitrogen dioxide in U.S. cities is 9 parts per billion.” H0: m = 9 (claim); Ha: m ≠ 9 (b) -1.15 (c) 0.2502 (d) Fail to reject H0. (e) There is not enough evidence at the 5% level of significance to reject the researcher’s claim that the mean air concentration of nitrogen dioxide in U.S. cities is 9 parts per billion. 27. (a) The claim is “the mean annual drug overdose death rate for the 50 states is at least 25 deaths per 100,000 people.” H0: m Ú 25 (claim); Ha: m 6 25 (b) z0 = -2.33; Rejection region: z0 6 -2.33 (c) -1.29 (d) Fail to reject H0. (e) At the 1% level of significance there is not enough evidence to reject the claim that the mean annual drug overdose death rate for the 50 states is at least 25 deaths per 100,000 people. 29. Critical values: -t0 = -2.093, t0 = 2.093 Rejection regions: t 6 -2.093, t 7 2.093 31. Critical value: t0 = 2.098; Rejection region: t 7 2.098 33. Critical value: t0 = -2.977; Rejection region: t 6 -2.977 35. Reject H0. There is enough evidence at the 0.5% level of significance to support the claim. 37. Reject H0. There is enough evidence at the 1% level of significance to reject the claim. 39. Fail to reject H0. There is not enough evidence at the 10% level of significance to reject the claim. 41. (a) The claim is “the mean monthly cost of joining a health club is $25.” H0: m = 25 (claim); Ha: m ≠ 25 (b) -t0 = -1.740, t0 = 1.740 Rejection regions: t 6 -1.740, t 7 1.740 (c) 1.64 (d) Fail to reject H0. (e) There is not enough evidence at the 10% level of significance to reject the advertisement’s claim that the mean monthly cost of joining a health club is $25. 43. (a) The claim is “the mean score for grade 12 students on a science achievement test is more than 145.” H0: m … 145; Ha: m 7 145 (claim) (b) 0.0824 (c) Reject H0. (d) There is enough evidence at the 10% level of significance to support the education publication’s claim that the mean score for grade 12 students on a science achievement test is more than 145. 45. Can use normal distribution Fail to reject H0. There is not enough evidence at the 5% level of significance to reject the claim. 47. Can use normal distribution Reject H0. There is enough evidence at the 1% level of significance to support the claim. 49. (a) The claim is “over 56% of U.S. adults think it is likely that robots and computers will do most jobs 25 years from now.” H0: p … 0.56; Ha: p 7 0.56 (claim) (b) z0 = 2.33; Rejection region: z 7 2.33 (c) 1.911 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level to support the claim that over 56% of U.S. adults think it is likely that robots and computers will do most jobs 25 years from now. 51. Critical value: x2 0 = 30.144; Rejection region: x 2 7 30.144 53. Critical values: x2 L = 26.509, x 2 R = 55.758 Rejection regions: x2 6 26.509, x2 7 55.758 55. Reject H0. There is enough evidence at the 10% level of significance to support the claim. 57. Fail to reject H0. There is not enough evidence at the 5% level of significance to reject the claim. 59. (a) The claim is “the variance of the bolt widths is at most 0.01.” H0: s 2 … 0.01 (claim); Ha: s 2 7 0.01 (b) x2 0 = 49.645; Rejection region: x 2 7 49.645 (c) 172.8 (d) Reject H0. (e) There is enough evidence at the 0.5% level of significance to reject the bolt manufacturer’s claim that the variance is at most 0.01. 61. You can reject H0 at the 1% level of significance because x2 = 172.8 7 46.963. Quiz for Chapter 7 (page 410) 1. (a) The claim is “the mean hat size for a male is at least 7.25.” H0: m Ú 7.25 (claim); Ha: m 6 7.25 (b) Left-tailed because the alternative hypothesis contains 6; z-test because s is known and the population is normally distributed. (c) Sample answer: z0 = -2.33; Rejection region: z 6 -2.33; -1.28 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to reject the company’s claim that the mean hat size for a male is at least 7.25. 2. (a) The claim is “the mean daily base price for renting a full-size or less expensive vehicle in Vancouver, British Columbia, is more than $86.” H0: m … 86; Ha: m 7 86 (claim) (b) Right-tailed because the alternative hypothesis contains 7; z-test because s is known and n Ú 30. (c) Sample answer: z0 = 1.28; Rejection region: z 7 1.28; 1.582 (d) Reject H0. (e) There is enough evidence at the 10% level of significance to support the travel analyst’s claim that that the mean daily base price for renting a full-size or less expensive vehicle in Vancouver, British Columbia, is more than $86. 3. (a) The claim is “the mean amount of earnings for full-time workers ages 18 to 24 with a bachelor’s degree in a recent year is $52,133.” H0: m = 52,133 (claim); Ha: m ≠ 52,133 (b) Two-tailed because the alternative hypothesis contains ≠; t-test because s is unknown and population is normally distributed. (c) Sample answer: -t0 = -2.145, t0 = 2.145 Rejection region t 6 -2.145, t 7 2.145; -2.165
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