A survey of 150 twoinch diameter pipes made in the same fact

A survey of 150 two-inch diameter pipes made in the same factory had a standard deviation equal to 0.08 inches. Compute a 98% confidence interval for the standard deviation of all pipes made in that factory.

Solution

As              
              
df = n - 1 =    149          
alpha = (1 - confidence level)/2 =    0.01          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    192.0730484          
chi^2(alpha/2) =    111.8021719          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    0.004964778          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    0.008529351          
              
Thus, the confidence interval for the variance is              
              
(   0.004964778   ,   0.008529351   )
              
Also, for the standard deviation, getting the square root of the bounds,              
              
(0.070461179   ,   0.092354487) [ANSWER]