The paper "Pistachio Nut Consumption and Serum Lipid Levels" (Journal of the American College of Nutrition [2007]: 141-148) describes a study to determine if eating pistachio nuts can have an effect on blood cholesterol levels in people with high cholesterol. Fifteen subjects followed their regular diet for 4 weeks and then followed a diet in which 15% of the daily caloric intake was from pistachio nuts for 4 weeks. Total blood cholesterol was measured for each subject at the end of each of the two 4-week periods, resulting in two samples (one for the regular diet and one for the pistachio diet).
a. Are the two samples independent or paired? Explain.
b. The mean difference in total cholesterol (regular diet- pistachio diet) was 11 mg/dL. The standard deviation of the differences was 24 mg/dL. Assume that it is reasonable to regard the 15 study participants as representative of adults with high cholesterol and that total cholesterol differences are approximately normally distributed. Do the data support the claim that eating the pistachio diet for 4 weeks is effective in reducing total cholesterol level? Test the relevant hypotheses using α = .01.