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, x̅ = 6.19267 g, s = 0.08700 g) and weights of a sample of post-1964 quarters (n = 40, x̅ = 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?