APPENDIX D 787 Section 8-2 1. a. 877 b. pn = 0.86 c. p = 3>4 or 0.75 3. (1) It was stated that the sample is a simple random sample. (2) There is a fixed number of trials (1020), the trials are independent because any respondent is independent of the others, there are two categories of success, and the probability remains the same for all respondents. (3) With n = 1020 and p = 3>4, the conditions np Ú 5 and nq Ú 5 are both satisfied (because 765 and 255 are both greater than 5). 5. a. Left-tailed b. z = -4.46 c. P-value: 0.000004 d. H0: p = 0.10. Reject the null hypothesis. e. There is sufficient evidence to support the claim that fewer than 10% of treated subjects experience headaches. 7. a. Left-tailed. b. z = -6.32 c. P-value: 0.000 d. H0: p = 0.50. Reject the null hypothesis. e. There is sufficient evidence to support the claim that fewer than 50% of adults search for themselves online. 9. H0: p = 0.40. H1: p 7 0.40. Test statistic: z = 0.41. P@value = 0.3399 (Table: 0.3409). Critical value: z = 1.645. Fail to reject H0. There is not sufficient evidence to support the claim that the sample of cast and crew members is from a population in which the rate of cancer is greater than 40%. There is not sufficient evidence to support a conclusion that the movie was cursed because of a significantly high number of cancer cases. 11. 11% of 2005 is 221, so 221 of those surveyed knew what the symbol designates. H0: p = 0.5. H1: p 6 0.5. Test statistic: z = -34.91. P@value = 0.0000 (Table: 0.0001). Critical value: z = -2.33. Reject H0. There is sufficient evidence to support the claim that fewer than half of all Americans know what the symbol designates. Because it appears that so few Americans know what the symbol designates, the symbol should be replaced with one that is much more obvious. 13. H0: p = 0.20. H1: p 7 0.20. Test statistic: z = 1.10. P-value = 0.1367 (Table: 0.1357). Critical value: z = 1.645. Fail to reject H0. There is not sufficient evidence to support the claim that more than 20% of OxyContin users develop nausea. However, with pn = 0.229, we see that a large percentage of OxyContin users experience nausea, so that rate does appear to be very high. 15. H0: p = 0.50. H1: p 6 0.50. Test statistic: z = -4.06. P@value = 0.00002 (Table: 0.0001). Critical value z = -2.33. Reject H0. There is sufficient evidence to support the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. 17. H0: p = 0.512. H1: p ≠ 0.512. Test statistic: z = -0.98. P-value = 0.3286 (Table: 0.3270). Critical values: z = {1.96. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that 51.2% of newborn babies are boys. The results do not support the belief that 51.2% of newborn babies are boys; the results merely show that there is not strong evidence against the rate of 51.2%. 19. H0: p = 0.80. H1: p 6 0.80. Test statistic: z = -1.11. P-value = 0.1332 (Table: 0.1335). Critical value: z = -1.645. Fail to reject H0. There is not sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time. However, based on the sample proportion of correct results in 75.5% of the 98 cases, polygraph results do not appear to have the high Chapter 8 Answers Section 8-1 1. a. H0: m = 40 minutes b. H1: m ≠ 40 minutes c. Reject the null hypothesis or fail to reject the null hypothesis. d. No. In this case, the original claim becomes the null hypothesis. For the claim that the mean wait time is equal to 40 minutes, we can either reject that claim or fail to reject it, but we cannot state that there is sufficient evidence to support that claim. 3. The P-value of 0.001 is preferred because it corresponds to the sample evidence that most strongly supports the alternative hypothesis that the method is effective. 5. a. p 6 0.10 b. H0: p = 0.10; H1: p 6 0.10 7. a. m 6 123 mm Hg b. H0: m = 123 mm Hg; H1: m 6 123 mm Hg 9. z = -17.77 (or z = -17.76 if using x = 935) 11. t = -0.044 13. a. Left-tailed b. P@value = 0.2266 c. Fail to reject H0. 15. a. Two-Tailed b. P@value = 0.0719 (Table: 0.0718) c. Fail to reject H0. 17. a. z = -1.645 b. Fail to reject H0. 19. a. z = {1.96 b. Fail to reject H0. 21. a. Fail to reject H0. b. There is not sufficient evidence to support the claim that more than 58% of adults would erase all of their personal information online if they could. 23. a. Reject H0. b. There is sufficient evidence to warrant rejection of the claim that the mean pulse rate (in beats per minute) of adult males is 72 bpm. 25. Type I error: In reality p = 0.1, but we reject the claim that p = 0.1. Type II error: In reality p ≠ 0.1, but we fail to reject the claim that p = 0.1. 27. Type I error: In reality p = 0.25, but we support the claim that p 7 0.25. Type II error: In reality p 7 0.25, but we fail to support that claim. 29. The power of 0.96 shows that there is a 96% chance of rejecting the null hypothesis of p = 0.08 when the true proportion is actually 0.18. That is, if the proportion of Chantix users who experience abdominal pain is actually 0.18, then there is a 96% chance of supporting the claim that the proportion of Chantix users who experience abdominal pain is greater than 0.08. 31. 617 (or 618 or 619 depending on precision used)
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