Researchers studied the effects of adding an exercise progra

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 5.3 pounds with a standard deviation of 4 pounds, and the mean weight loss for Group 2 was 15.5 pounds, with a standard deviation of 4 2 Pounds. Calculate the upper bound of a 99% confidence interval for the difference in mean weight loss for the two groups. Assume the population standard deviations are equal.

Solution

  
Calculating the means of each group,              
              
X1 =    5.3          
X2 =    15.5          
              
Calculating the standard deviations of each group,              
              
s1 =    4          
s2 =    4.2          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    45   , n2 =    52  
              
Then              
              
S =    4.108578958          
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    0.836506993          
              
For the   0.99   confidence level, then      
              
alpha = (1 - confidence level) =    0.01          
z(alpha) =    2.326347874          
              
upper bound = [X1 - X2] + t(alpha) * Sd =    -8.220621217          
              
Thus, the confidence interval is              
              
u1 - u2 < -8.2206 [ANSWER]