A medical researcher wishes to investigate the effectiveness

A medical researcher wishes to investigate the effectiveness of exercise versus diet in losing weight. Two groups of 25 overweight adult subjects 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, but with no restriction on diet, and the other group on a strict diet, but with no requirement to exercise. The weight losses after 20 weeks are determined for each subject, and the difference between matched pairs of subjects (weight loss of subject in exercise group – weight loss of matched subject in diet group) is computed. The mean of these differences in weight loss is found to be –2 lbs. with standard deviations = 6 lbs. Is this evidence of a difference in mean weight loss for the two methods? To test this, consider the population of differences (weight loss overweight adult would experience after 20 weeks on the exercise program) – (weight loss the same adult would experience after 20 weeks on the strict diet). Let be the mean of this population of differences and assume their distribution is approximately Normal. We test the hypotheses H₀: = 0 versus H_a: 0, using the matched pairs t test. The P-value for this test is

Solution

As

t = Xd * sqrt(n) / sd

and Xd = -2, n = 25, sd = 6, then

t = -1.66667

Here,

df = n - 1 = 25 - 1 = 24

Thus, using a table, we see that

OPTION B: between 0.10 and 0.05. [ANSWER]