Question: Weight of Quarters: Weights of quarters are used by vending machines as one way to detect counterfeit coins. Data set 14 in Appendix B includes weights of pre-1964 silver quarters and post-1964 quarters. Here are the summary statistics:

Pre-1964: n = 40, \(\bar{X}\) = 6.19267 g. s = 0. 08700 g

Post-1964: n = 40, \(\bar{X}\) = 5.63930 g, s = 0.06194

Use a 0.05 significance level to test the claim that the two populations of quarters have the same standard deviation. If the amounts of variation are different, vending machines might need more complicated adjustments. Does it appear that such adjustments are necessary?