Question

researchers studied the effects of adding an exercise program to dieting in the achievement of weight loss. A sample of 75 men ages 18-20 (Group 1) were observed for weight loss using a diet only, and another indeperndent sample of 66 men ages 18-20 (Group 2) were put on the same diet, but with an added exercise program. The mean weight loss of Group 1 was 9.5 pounds with a standard deviation of 4 pounds, and the eman weight loss for Group 2 was 13.7 pounds, with a stanadard deviation of 5.5 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).

Answer 1

For n₁ + n₂ - 2 = 75 + 66 - 2 = 139 degrees of freedom, we have from the t distribution tables here:
P( t₁₃₉ < 2.612) = 0.995

Therefore, due to symmetry, we have here:
P( - 2.612 < t₁₃₉ < 2.612) = 0.99

The standard error here is computed as:

The 99% confidence for the difference in means is therefore computed here as:

This is the required 99% confidence interval for the difference in two means.