Ten women recorded their weights (in kilograms) before and after a diet. Their w

Question

Ten women recorded their weights (in kilograms) before and after a diet. Their weights before and after the diet are recorded below. Assume that the women were randomly selected, and that the weight difference is approximately normally distributed. Estimate the population mean reduction in weight by constructing a 99% confidence interval for that mean. Round weights to two decimal points. Before 89.1 68.3 77.2 91.6 85.6 83.2 73.4 84.3 96.4 87.6

After 84.3 66.2 76.8 79.3 85.5 80.2 76.2 80.3 90.5 80.3

Explanation / Answer

The differences are

-4.8
-2.1
-0.4
-12.3
-0.1
-3
2.8
-4
-5.9
-7.3

Calculating the standard deviation of the differences (third column):              
              
s =    4.102650658          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    1.297372052          
              
Calculating the mean of the differences (third column):              
              
XD =    -3.71          
              
For the   0.99   confidence level,      
              
alpha/2 = (1 - confidence level)/2 =    0.005      
df = n - 1 = 10 - 1 = 9

hence,
  
t(alpha/2) =    3.249835542          
  
Thus,
          
lower bound = [X1 - X2] - t(alpha/2) * sD =    -7.926245807          
upper bound = [X1 - X2] + t(alpha/2) * sD =    0.506245807          
              
Thus, the confidence interval is              
              
(   -7.926245807   ,   0.506245807   ) [ANSWER]

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