A 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 based on several physiological variables. One group is placed on a regular program of vigorous exercise without restriction on diet, and the other group is placed on a strict diet without 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 pounds with standard deviation σ= 6 pounds. Is this evidence of a difference in mean weight loss for the two methods?
To test this, consider the population of differences (weight loss that an overweight adult would experience after 20 weeks on the exercise program) - (weight loss that the same adult would experience after 20 weeks on the strict diet) . Let μ be the mean of this population of differences, and assume their distribution is approximately Normal. We test the hypotheses H₀: μ= 0 versus H_a: μ≠0, using the matched pairs t test. What is the P-value for this test?

Question

Quizplus · Accepted Answer

The mean difference of -2 pounds with a standard deviation of 6 pounds and a sample size of 25 pairs does not provide strong evidence against the null hypothesis (μ = 0) in a two-tailed test. The calculated t-value would not be large enough to suggest a significant difference in weight loss between the two methods, leading to a P-value greater than 0.10.

A Researcher Wishes to Investigate the Effectiveness of Exercise Versus