Chapter 9.2, Problem 15BSC

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.)

15. Are Quarters Now Lighter? Weights of quarters are carefully considered in the design of the vending machines that we have all come to know and love. Data Set 29 “Coin Weights” in Appendix B includes weights of a sample of pre-1964 quarters (n = 40, $\bar{x}$ = 6.19267 g, s = 0.08700 g) and weights of a sample of post-1964 quarters (n = 40, $\bar{x}$ = 5.63930 g, s = 0.06194 g).

a. Use a 0.05 significance level to test the claim that pre-1964 quarters have a mean weight that is greater than the mean weight of post-1964 quarters.

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

c. Do post-1964 quarters appear to weigh less than before 1964? If so, why aren’t vending machines affected very much by the difference?