Test the given claim. Use a significance level of a = 0.05 and assume that all populations are normally distributed.
11. Hypothesis Test for Magnet Treatment of Pain. Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below (based on data from "bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study," by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 238, No. 10). These values represent measurements of pain using the visual analog scale. Use a 0.05 significance level to test the claim that those given a sham treatment (similar to a placebo) have pain reductions that vary more than the pain reductions for those treated with magnets.
Reduction in pain level after sham treatment: n = 20, x bar = 0.44, s = 1.4
Reduction in pain level after magnet treatment: n = 20, x bar = 0.49, s = 0.96
15. Weights 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, x bar = 6.19267 g., s = 0.08700 g; post-1964 n = 40, x bar = 5.63930, 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?
This solution provides calculations and explanations for hypothesis tests of equal variances.