According to a study published in the New England Journal of Medicine, overweight people on low-carbohydrate and Mediterranean diets lost more weight and got greater cardiovascular benefits than people on a conventional low-fat diet (Boston Globe, July 17, 2008). A nutritionist wishes to verify these results and documents the weight loss (in pounds) of 30 dieters on the low-carbohydrate and Mediterranean diets and 30 dieters on the low-fat diet. The data set, labeled Different_Diets, can be found on the text website.
a. Set up the hypotheses to test the claim that the mean weight loss for those on low-carbohydrate or Mediterranean diets is greater than the mean weight loss for those on a conventional low-fat diet.
b. Using the appropriate commands in Excel, find the value of the test statistic. Assume that the population variances are equal and that the test is conducted at the 5% significance level. Specify the critical value(s) and the decision rule.
c. At the 5% significance level, can the nutritionist conclude that people on low-carbohydrate or
Mediterranean diets lost more weight than people on a conventional low-fat diet?