ODD ANSWERS A81 (b) Left-tailed because Ha contains 6; t-test because both populations are normally distributed and the samples are dependent. (c) t0 = -2.718; Rejection region: t 6 -2.718 (d) -5.07 (e) Reject H0. (f) There is enough evidence at the 1% level of significance to support the claim that the seminar helps adults increase their credit scores. 4. (a) The claim is “the proportion of U.S. adults who approve of the job the Supreme Court is doing is greater than it was 3 years prior.” H0: p1 … p2; Ha: p1 7 p2 (claim) (b) Right-tailed because Ha contains 7; z-test because you are testing proportions, the samples are random, samples are independent, and n1p, n2p, n1q, and n2q are at least 5. (c) z0 = 1.645; Rejection region: z 7 1.645 (d) 4.051 (e) Reject H0. (f) There is not enough evidence at the 5% level of significance to support the claim that the proportion of U.S. adults who approve of the job the Supreme Court is doing is greater than it was 3 years prior. Real Statistics—Real Decisions for Chapter 8 (page 462) 1. (a) Sample answer: Divide the records into groups according to the inpatients’ ages, and then randomly select records from each group. (b) Sample answer: Divide the records into groups according to geographic regions, and then randomly select records from each group. (c) Sample answer: Assign a different number to each record, randomly choose a starting number, and then select every 50th record. (d) Sample answer: Assign a different number to each record, and then use a table of random numbers to generate a sample of numbers. 2. (a)–(b) Answers will vary. 3. Use a t-test. Independent. Yes, you need to know if the population distributions are normal or not; yes, you need to know if the population variances are equal or not. 4. There is enough evidence at the 5% level of significance to support the claim that there is a difference in the mean length of hospital stays for inpatients. This decision supports the claim. Cumulative Review for Chapters 6–8 (page 466) 1. (a) (0.758, 0.782) (b) There is enough evidence at the 5% level of significance to support the claim that more than 75% of U.S. adults say they would date or have already dated someone whose religion was different from theirs. 2. There is enough evidence at the 10% level of significance to support the claim that the fuel additive improved gas mileage. 3. (25.94, 28.00); z-distribution 4. (2.59, 4.33); t-distribution 5. (10.7, 13.5); t-distribution 6. (7.85, 8.57); z-distribution 7. H0: m Ú 33; Ha: m 6 33 (claim) 8. H0: p Ú 0.19 (claim); Ha: p 6 0.19 9. H0: s = 0.63 (claim); Ha: s ≠ 0.63 10. H0: m = 2.28; Ha: m ≠ 2.28 (claim) 11. There is enough evidence at the 10% level of significance to support the pediatrician’s claim that the mean birth weight of a single-birth baby is greater than the mean birth weight of a baby that has a twin. 12. (a) (511.95, 2283.75) (b) (22.63, 47.79) (c) There is not enough evidence at the 1% level of significance to reject the travel analyst’s claim that the standard deviation of the mean room rate for two adults at three-star hotels in Cincinnati is at most $30. 13. There is enough evidence at the 5% level of significance to support the organization’s claim that the mean SAT scores for male athletes and male non-athletes at a college are different. 14. (a) (54,793.65, 61,542.41) (b) There is not enough evidence at the 5% level of significance to reject the claim that the mean annual earnings for locksmiths is $55,000. 15. There is enough evidence at the 10% level of significance to support the medical research team’s claim that the proportion of monthly convulsive seizure reduction is greater for the group that received the extract than for the group that received the placebo. 16. (a) (41.5, 42.5) (b) There is enough evidence at the 5% level of significance to reject the zoologist’s claim that the mean incubation period for ostriches is at least 45 days. 17. A type I error will occur when the actual proportion of people who purchase their eyeglasses online is 0.05, but you reject H0. A type II error will occur when the actual proportion of people who purchase their eyeglasses online is different from 0.05, but you fail to reject H0. Chapter 9 Section 9.1 (page 481) 1. Increase. Decrease 3. The sample correlation coefficient r measures the strength and direction of a linear relationship between two variables; r = -0.932 indicates a stronger correlation because 0 -0.9320 = 0.932 is closer to 1 than 0 0.9180 = 0.918. 5. A table can be used to compare r with a critical value, or a hypothesis test can be performed using a t-test. 7. H0: r = 0 (no significant correlation) Ha: r ≠ 0 (significant correlation) Reject the null hypothesis if t is in the rejection region. 9. Explanatory variable: Amount of water consumed Response variable: Weight loss 11. Strong negative linear correlation 13. No linear correlation 15. c. You would expect a positive linear correlation between age and income.
RkJQdWJsaXNoZXIy NjM5ODQ=