Question: Public Health and Nutrition Magnesium is used by every cell in your body, is required for over 300 biochemical reactions, and helps muscles and nerves function properly. According to the U.S. Department of Agriculture National Nutritional Database, 1 2 cup of vegetarian baked beans and one medium baked potato without the skin contain the same amount of magnesium (40 milligrams). To check this claim, independent random samples of baked beans and potatoes were obtained, and the amount of magnesium in each serving was recorded (in milligrams). The summary statistics and known variances are given in the following table.
a. Assume the underlying distributions are normal. Is there any evidence to refute the claim? Use a = 0.01.
b. Suppose that, instead, the sample sizes are n1 = n2 = 38. Now, is there any evidence to refute the claim? Find the p value for this hypothesis test.
c. How large would the sample sizes (n1 = n2) have to be for the hypothesis test to be significant at the a = 0.01 level?