ODD ANSWERS A77 (d) Reject H0. (e) There is enough evidence at the 5% level of significance to reject the government agency’s claim that 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. 4. (a) The claim is “program participants have a mean weight loss of at least 10.5 pounds after 1 month.” H0: m Ú 10.5 (claim); Ha: m 6 10.5 (b) Left-tailed because the alternative hypothesis contains 6; t-test because s is unknown and n Ú 30. (c) Sample answer: t0 = -2.462; Rejection region: t 6 -2.462; -3.09 (d) Reject H0. (e) There is enough evidence at the 1% level of significance to reject the weight loss program’s claim that program participants have a mean weight loss of at least 10.5 pounds after 1 month. 5. (a) The claim is “less than 25% of the televisions the organization rated in a recent year have an overall score of 70 or more.” H0: p Ú 0.25; Ha: p 6 0.25 (claim) (b) Left-tailed because the alternative hypothesis contains 6; z-test because np Ú 5 and nq Ú 5. (c) Sample answer: z0 = -1.645 Rejection region: z0 6 -1.645; -0.273 (d) Fail to reject H0. (e) There is not enough evidence at the 5% level of significance to support the claim that less than 25% of the televisions the organization rated in a recent year have an overall score of 70 or more. 6. (a) The claim is “the standard deviation of the television rating scores is 10.1.” H0: s = 10.1 (claim); Ha: s ≠ 10.1 (b) Two-tailed because the alternative hypothesis contains ≠; chi-square test because the test is for a standard deviation and the population is normally distributed. (c) Sample answer: x2 L = 18.493, x 2 R = 43.773 Rejection region: x2 6 18.493, x2 7 43.773; 39.599 (d) Fail to reject H0. (e) There is not enough evidence at the 10% level of significance to reject the claim that the standard deviation of the TV rating scores is 10.1. Real Statistics—Real Decisions for Chapter 7 (page 412) 1. Answers will vary. 2. (a) Not random; Sample answer: Randomly select students from the student directory. (b) Random (c) Random 3. Alternative hypothesis because you cannot use a hypothesis test to support your claim if your claim is the null hypothesis. 4. No 5. No 6. Answers will vary. Chapter 8 Section 8.1 (page 424) 1. Two samples are dependent when each member of one sample corresponds to a member of the other sample. Example: The weights of 22 people before starting an exercise program and the weights of the same 22 people 6 weeks after starting the exercise program. Two samples are independent when the sample selected from one population is not related to the sample selected from the other population. Example: The weights of 25 cats and the weights of 20 dogs. 3. Use P-values. 5. Dependent because the same football players were sampled. 7. Independent because different boats were sampled. 9. Reject H0. 11. Reject H0. There is enough evidence at the 1% level of significance to reject the claim. 13. Fail to reject H0. There is not enough evidence at the 5% level of significance to support the claim. 15. (a) The claim is “the mean braking distances are different for the two categories of SUVs.” H0: m1 = m2; Ha: m1 ≠m2 (claim) (b) -z0 = -1.645, z0 = 1.645 Rejection region: z 6 -1.645, z 7 1.645 (c) -0.409 (d) Fail to reject H0. (e) There is not enough evidence at the 10% level of significance to support the claim that the mean braking distances are different for the two categories of SUVs. 17. (a) The claim is “the wind speed in Region A is less than the wind speed in Region B.” H0: m1 Ú m2; Ha: m1 6 m2 (claim) (b) z0 = -1.645; Rejection region: z 6 -1.645 (c) -1.94 (d) Reject H0. (e) There is enough evidence at the 5% level of significance to support the claim that the wind speed in Region A is less than the wind speed in Region B. 19. (a) The claim is “ACT mathematics and science scores are equal.” H0: m1 = m2 (claim); Ha: m1 ≠m2 (b) -z0 = -2.575, z0 = 2.575 Rejection region: z 6 -2.575, z 7 2.575 (c) -0.399 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to reject the claim that ACT mathematics and science scores are equal. 21. (a) The claim is “the mean home sales price in Casper, Wyoming, is the same as in Cheyenne, Wyoming.” H0: m1 = m2 (claim); Ha: m1 ≠m2 (b) -z0 = -2.575, z0 = 2.575 Rejection region: z 6 -2.575, z 7 2.575 (c) -2.388 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to reject the claim that the mean home sales price in Casper, Wyoming, is the same as in Cheyenne, Wyoming.
RkJQdWJsaXNoZXIy NjM5ODQ=