Use the given confidence level and sample data to find a con

Use the given confidence level and sample data to find a confidence interval for the population standard deviation sigma. Assume that a simple random sample has been selected from a population that has a normal distribution. Salaries of college graduates who took a poetry course in college 80% confidence; n = 51, x = $55,500. s = $19,232

Solution

As              
              
df = n - 1 =    50          
alpha = (1 - confidence level)/2 =    0.1          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    63.16712101          
chi^2(alpha/2) =    37.68864839          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    292770841.9          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    490691282.1          
              
Thus, the confidence interval for the variance is              
              
(   292770841.9   ,   490691282.1   )
              
Also, for the standard deviation, getting the square root of the bounds,              
              
(   17110.54768   ,   22151.55259   ) [answer]