Determine the values of the following percentiles A rivet is

Determine the values of the following percentiles: A rivet is to be inserted into a hole. A random sample of n = 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s=0.008 millimeters. Construct a 99% two sided confidence interval for sigma^2.

Solution

As              
              
df = n - 1 =    14          
alpha = (1 - confidence level)/2 =    0.005          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    31.31934962          
chi^2(alpha/2) =    4.074674957          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    2.86085E-05          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    0.000219895          
              
Thus, the confidence interval for the variance is              
              
(   2.86085*10^-5   ,   0.000219895   ) [answer]