Suppose that the student body in a large university have nor

Suppose that the student body in a large university have normally distributed GPAs with a mean of mu = 3.11 and standard deviation a sigma = 0.4 You randomly select a sample of n = 23 students. The probability is 0.9 (with the complement split evenly between the tails) that the standard deviation of your sample will be between what two numbers? Round your answers to four decimal places.

Solution

As              
              
df = n - 1 =    22          
alpha = (1 - confidence level)/2 =    0.05          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    33.92443847          
chi^2(alpha/2) =    12.33801458          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    0.103760008          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    0.285297118          
              
Thus, the confidence interval for the variance is              
              
(   0.103760008   ,   0.285297118   )
              
Also, for the standard deviation, getting the square root of the bounds,              
              
(   0.322118003   ,   0.534132117   ) [ANSWER]