A medical researcher wishes to investigate the effectiveness of exercise versus diet in losing weight. Two groups of 25 overweight adults are used, with a subject in each group matched to a similar subject in the other group on the basis of a number of physiological variables. One group is placed on a regular program of vigorous exercise with no restriction on diet, and the other group is placed on a strict diet with no requirement to exercise. The weight loss after 20 weeks is determined for each subject, and the difference between the matched pairs of subjects, the weight loss of each subject in the exercise group minus the weight loss of the matched subject in the diet group, is computed. The mean of these differences in weight loss is found to be –2 pounds with standard deviation s = 6 pounds. Is this evidence of a difference in mean weight loss for the two methods? To test this, consider the population of differences, the weight loss an overweight adult would experience after 20 weeks on the exercise program minus the weight loss the same adult would experience after 20 weeks on the strict diet. Let u be the mean of this population of differences, and assume their distribution is approximately Normal. We test the hypotheses Ho : µ = 0 versus Ha : µ > 0 using the matched pairs t test. The P-value for this test is: larger than 0.1. between 0.1 and 0.05. below 0.01. O between 0.05 and 0.01 O O