Chapter 9.2, Problem 10BSC

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n₁ − 1 and n₂ − 1.)

10. Second-Hand Smoke Data Set 12 “Passive and Active Smoke” in Appendix B includes cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, $\bar{x}$ = 60.58 ng/mL, s = 138.08 ng/mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, $\bar{x}$ = 16.35 ng/mL, s = 62.53 ng/mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced.

a. Use a 0.05 significance level to test the claim that nonsmokers exposed to tobacco smoke have a higher mean cotinine level than nonsmokers not exposed to tobacco smoke.

b. Construct the confidence interval appropriate for the hypothesis test in part (a).

c. What do you conclude about the effects of second-hand smoke?