The heights of a random sample of 38 male officers from a la

The heights of a random sample of 38 male officers from a large-city police force were measured. The standard deviation for the sample was 1.83 inches. Find a 95% confidence interval for the standard deviation of the heights of the officers. Heights of men are known to be normally distributed.

Solution

As              
              
df = n - 1 =    37          
alpha = (1 - confidence level)/2 =    0.025          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    55.66797326          
chi^2(alpha/2) =    22.10562716          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    2.225863324          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    5.605328412          
              
Thus, the confidence interval for the variance is              
              
(   2.225863324   ,   5.605328412   )
              
Also, for the standard deviation, getting the square root of the bounds,              
              
(   1.491932748   ,   2.367557478   ) [ANSWER]