The mean replacement time for a random sample of 12 microwav

The mean replacement time for a random sample of 12 microwave oven is 8.6 years with a standard deviation of 3.7 years. Construct the 98% confidence interval for the population variance sigma^2. Assume the sample is from a normally distributed population. (5.744, 42.17) (1.645, 13.331) (6.091, 49.325) (2.468, 7.023)

Solution

As              
              
df = n - 1 =    11          
alpha = (1 - confidence level)/2 =    0.01          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    24.72497031          
chi^2(alpha/2) =    3.053484107          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    6.090603876          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    49.31743371          
              
Thus, the confidence interval for the variance is              
              
(   6.091   ,   49.325   ) [ANSWER, C]