Question

Researchers studied the effects of adding an exercise program to dieting in the achievement of weight loss. A sample of 45 men ages 18-20 (Group 1) were observed for weight loss using a diet only, and another independent sample of 52 men ages 18-20 (Group 2) were put on the same diet, but with an added exercise program. The mean weight loss for Group 1 was 5.7 pounds with a standard deviation of 5.4 pounds, and the mean weight loss for Group 2 was 15.7 pounds, with a standard deviation of 6.3 pounds.

Calculate the upper bound of a 99% confidence interval for the difference in mean weight loss for the two groups to two decimal places. Assume the population standard deviations are not equal (Case 2). Take all calculations toward the answer to three (3) decimal places. Use the following website to help you calculate v: http://web.utk.edu/~cwiek/TwoSampleDoF.

Answer 1

DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

     = ((5.4)^2/45 + (6.3)^2/52)^2/(((5.4)^2/45)^2/44 + ((6.3)^2/52)^2/51)

     = 95

At 99% confidence interval the critical value is t_{0.99, 95} = 2.366

So the upper bound of a 99% confidence interval is

() - t_{0.99, 95} * sqrt(s1^2/n1 + s2^2/n2)

= (5.7 - 15.7) - 2.366 * sqrt((5.4)^2/45 + (6.3)^2/52)

= -10 - 2.811

= -12.811

So the upper bound of a 99% confidence interval is (-12.811, ).