A74 ODD ANSWERS 31. Use the t-distribution because s is unknown, the sample is random, and the population is normally distributed. Fail to reject H0. There is not enough evidence at the 5% level of significance to reject the car company’s claim that the mean gas mileage for the luxury sedan is at least 23 miles per gallon. 33. More likely. The tails of a t-distribution curve are thicker than those of a standard normal distribution curve. So, if you incorrectly use a standard normal sampling distribution instead of a t-sampling distribution, then the area under the curve at the tails will be smaller than what it would be for the t-test, meaning the critical value(s) will lie closer to the mean. This makes it more likely for the test statistic to be in the rejection region(s). This result is the same regardless of whether the test is left-tailed, right-tailed, or two-tailed; in each case, the tail thickness affects the location of the critical value(s). Section 7.3 Activity (page 386) 1 – 3. Answers will vary. Section 7.4 (page 391) 1. If np Ú 5 and nq Ú 5, then the normal distribution can be used. 3. Cannot use normal distribution 5. Can use normal distribution Fail to reject H0. There is not enough evidence at the 5% level of significance to support the claim. 7. (a) The claim is “more than 80% of U.S. adults feel children should be vaccinated to attend school.” H0: p … 0.8; Ha: p 7 0.8 (claim) (b) z0 = 2.33; Rejection region: z 7 2.33 (c) 1.414 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to support the claim that more than 80% of U.S. adults feel children should be vaccinated to attend school. 9. (a) The claim is “at least 60% of tax filers are expecting a tax refund.” H0: p Ú 0.60 (claim); Ha: p 6 0.60 (b) z0 = -1.645; Rejection region: z 6 -1.645 (c) -4.078 (d) Reject H0. (e) There is enough evidence at the 5% level of significance to reject the analyst’s claim that at least 60% of tax filers are expecting a tax refund. 11. (a) The claim is “more than half of all nurses feel they became better professionals during the coronavirus pandemic.” H0: p … 0.5; Ha: p 7 0.5 (claim) (b) z0 = 2.33; Rejection region: z 7 2.33 (c) 2.771 (d) Reject H0. (e) At the 1% level of significance, there is enough evidence to support the manager’s claim that more than half of all nurses feel they became better professionals during the coronavirus pandemic. 13. (a) The claim is “27% of U.S. adults would travel into space on a commercial flight if they could afford it.” H0: p = 0.27 (claim); Ha: p ≠ 0.27 (b) 0.03 (c) Reject H0. (d) There is enough evidence at the 5% level of significance to reject the research center’s claim that 27% of U.S. adults would travel into space on a commercial flight if they could afford it. 15. (a) The claim is “more than 25% of U.S. adults believe moral values in the country are getting better.” H0: p … 0.25; Ha: p 7 0.25 (claim) (b) 0.071 (c) Reject H0. (d) At the 10% level of significance, there is enough evidence to support the politician’s claim that more than 25% of U.S. adults believe moral values in the country are getting better. 17. Fail to reject H0. There is not enough evidence at the 5% level of significance to reject the claim that at least 64% of adults make an effort to live in ways that help protect the environment some of the time. 19. (a) The claim is “more than 80% of U.S. adults feel children should be vaccinated to attend school.” H0: p … 0.08; Ha: p 7 0.8 (claim) (b) z0 = 2.33; Rejection region: z 7 2.33 (c) 1.414 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to support the claim that more than 80% of U.S. adults feel children should be vaccinated to attend school. Results are the same. Section 7.4 Activity (page 393) 1 – 2. Answers will vary. Section 7.5 (page 400) 1. Specify the level of significance a. Determine the degrees of freedom. Determine the critical values using the x2-distribution. For a right-tailed test, use the value that corresponds to d.f. and a; for a left-tailed test, use the value that corresponds to d.f. and 1 - a; for a two-tailed test, use the values that correspond to d.f. and 1 2a, and d.f. and 1 - 1 2a. 3. As a decreases, the right critical value for a two-tailed test increases and the left critical value for a two-tailed test decreases. 5. The requirement of a normal distribution is more important when testing a standard deviation than when testing a mean. When the population is not normal, the results of a chi-square test can be misleading because the chi-square test is not as robust as the tests for the population mean. 7. Critical value: x2 0 = 38.885; Rejection region: x 2 7 38.885 9. Critical value: x2 0 = 0.872; Rejection region: x 2 6 0.872 11. Critical values: x2 L = 60.391, x 2 R = 101.879 Rejection regions: x2 6 60.391, x2 7 101.879 13. (a) Fail to reject H0 because x 2 6 6.251. (b) Fail to reject H0 because x 2 6 6.251. (c) Reject H0 because x 2 7 6.251.
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