Researchers studied the effects of adding an exercise program to dieting in the

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 5.3 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.

Explanation / Answer

  
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]

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