788 APPENDIX D to be an outlier, and a normal quantile plot or histogram suggests that the sample does not appear to be from a normally distributed population. The requirements are not satisfied. 3. A t test is a hypothesis test that uses the Student t distribution, such as the method of testing a claim about a population mean as presented in this section. The letter t is used in reference to the Student t distribution, which is used in a t test. The z test methods require a known value of s, but it would be very rare to conduct a hypothesis test for a claim about an unknown value of m while we somehow know the value of s. 5. P@value = 0.0033 (Table: P@value 6 0.01). There is sufficient evidence to warrant rejection of the claim that the mean weight of quarters is equal to 5.670 g. 7. P@value = 0.0000 (Table: P@value 6 0.005). There is sufficient evidence to support the claim that the mean cotinine level of smokers is greater than 2.84 ng>mL. 9. H0: m = 8.953 g. H1: m ≠ 8.953 g. Test statistic: t = -3.423. P@value = 0.0015. Critical values assuming a 0.05 significance level: t = {2.026. Reject H0. There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean equal to 8.953 g. 11. H0: m = 30 min. H1: m 7 30 min. Test statistic: t = 0.940. P@value = 0.177. Critical value assuming a 0.05 significance level: t = 1.685. Fail to reject H0. There is not sufficient evidence to support the claim that the mean wait time is more than 30 min. 13. H0: m = 120 mm Hg. H1: m 7 120 mm Hg. Test statistic: t = 3.234. P@value = 0.0007 (Table: P@value 6 0.005). Critical value: t = 2.339. Reject H0. There is sufficient evidence to support the claim that the sample is from a population with a mean greater than 120 mm Hg. 15. H0: m = 100. H1: m ≠ 100. Test statistic: t = -6.676. P@value = 0.0000 (Table: P@value 6 0.01). Critical values: t = {2.086. Reject H0. There is sufficient evidence to warrant rejection of the claim that the sample of children is from a population with mean IQ equal to 100. These results do not “prove” that exposure to lead has an adverse effect on IQ scores of children, but it strongly suggests that such an adverse effect is very possible. 17. H0: m = 0 lb. H1: m 7 0 lb. Test statistic: t = 3.872. P-value = 0.0002 (Table: 60.005). Critical value: t = 2.426. Reject H0. There is sufficient evidence to support the claim that the mean weight loss is greater than 0. Although the diet appears to have statistical significance, it does not appear to have practical significance, because the mean weight loss of only 3.0 lb does not seem to be worth the effort and cost. 19. H0: m = 12.00 oz. H1: m ≠ 12.00 oz. Test statistic: t = 10.364. P-value = 0.0000 (Table: 60.01). Critical values: t = {2.030. Reject H0. There is sufficient evidence to warrant rejection of the claim that the mean volume is equal to 12.00 oz. Because the mean appears to be greater than 12.00 oz, consumers are not being cheated because they are getting slightly more than 12.00 oz. 21. The sample data meet the loose requirement of having a normal distribution. H0: m = 14 mg>g. H1: m 6 14 mg>g. Test statistic: t = -1.444. P-value = 0.0913 (Table: 70.05). Critical value: t = -1.833. Fail to reject H0. There is not sufficient evidence to support the claim that the mean lead concentration for all such medicines is less than 14 mg>g. degree of reliability that would justify the use of polygraph results in court, so polygraph test results should be prohibited as evidence in trials. 21. H0: p = 0.5. H1: p ≠ 0.5. Test statistic: z = -2.03. P-value = 0.0422 (Table: 0.0424). Critical values: z = {1.645. Reject H0. There is sufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses. However, their success rate of 123>280, or 43.9%, indicates that they performed worse than random guesses, so they do not appear to be effective. 23. H0: p = 0.35. H1: p ≠ 0.35. Test statistic: z = -2.17. P@value = 0.0303 (Table: 0.0300). Critical values: z = {1.96. Reject H0. There is sufficient evidence to warrant rejection of the claim that the percentage who make angry gestures while driving is equal to 35%. If the significance level is changed to 0.01, the conclusion does change to this: “There is not sufficient evidence to warrant rejection of the claim that the percentage who make angry gestures while driving is equal to 35%.” 25. H0: p = 0.5. H1: p 7 0.5. Test statistic: z = 0.14. P@value = 0.4454 (Table: 0.4443). Critical value: z = 1.645. Fail to reject H0. There is not sufficient evidence to support the claim that NFC teams win the majority of Super Bowl games. 27. H0: p = 0.5. H1: p ≠ 0.5. Test statistic: z = 2.05. P-value = 0.0402 (Table: 0.0404). Critical values: z = {1.96. Reject H0. There is sufficient evidence to warrant rejection of the claim that the coin toss is fair in the sense that neither team has an advantage by winning it. The coin toss rule does not appear to be fair. This helps explain why the overtime rules were changed. 29. H0: p = 1>3. H1: p 7 1>3. Test statistic: z = 8.72. P@value = 0.0000 (Table: 0.0001). Critical value: z = 2.33. Reject H0. There is sufficient evidence to support the claim that more than 1>3 of adults believe in ghosts. 31. H0: p = 0.791. H1: p 6 0.791. Test statistic: z = -29.09 (using pn = 0.39) or z = -29.11 (using x = 339). P-value = 0.0000 (Table: 0.0001). Critical value: z = -2.33. Reject H0. There is sufficient evidence to support the claim that the percentage of selected Americans of Mexican ancestry is less than 79.1%, so the jury selection process appears to be biased. 33. The P-values agree reasonably well with the large sample size of n = 926. The normal approximation to the binomial distribution works better as the sample size increases. Normal approximation entries: 0.0114, 0.0012, 0.1059. Exact entries: 0.0215, 0.0034, 0.1120. Exact with simple continuity correction: 0.0117, 0.0018, 0.1060. 35. a. 0.7219 (Table: 0.7224) b. 0.2781 (Table: 0.2776) c. The power of 0.7219 shows that there is a reasonably good chance of making the correct decision of rejecting the false null hypothesis. It would be better if the power were even higher, such as greater than 0.8 or 0.9. Section 8-3 1. Requirement: (1) the sample must be a simple random sample, and (2) either or both of these conditions must be satisfied: The population is normally distributed or n > 30. There is not enough information given to determine whether the sample is a simple random sample. Because the sample size is not greater than 30, we must check for normality, but the value of $36 million appears
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