Question

Researchers studied the effects of adding an exercise program to dieting in the achievement of weight loss. A sample of 96 men ages 18-20 (Group 1) were observed for weight loss using a diet only, and another independent sample of 46 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 8.9 pounds with a standard deviation of 4.1 pounds, and the mean weight loss for Group 2 was 15.3 pounds, with a standard deviation of 6.1 pounds.

Calculate the lower bound of a 95% 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). For the degrees of freedom value, v, for the Student's t distribution that you need to make the interval, use this website http://web.utk.edu/~cwiek/TwoSampleDoF

Take all calculations toward the answer to three (3) decimal places.

Answer 1

,  ,  

, ,  

The confidence interval is given by

The confidence interval is given by

tcritical, for = 0.05(for 2 tails) , degrees of freedom = n2-1(smaller of the 2) = 46-1 = 45 is 2.014(Taken to 3 decimal places as required)

taken to 3 decimal places as required.

The Lower Limit = -6.40 - 2.014 * 0.992 = -8.39789    -8.40 (Rounded to 2 decimal places)

The Upper Limit = -6.40 + 2.014 * 0.992 = -4.40211    -4.40 (Rounded to 2 decimal places)

Therefore,

The lower bound of the confidence interval is -8.40.

The Upper bound of the confidence interval is -4.40.