The data to the right represent the number of days of the gr

The data to the right represent the number of days of the growing season over the last 10 years in a certain geographic area. It is known that the data are normally distributed and that s = 22.33 days. Using these values as a simple random sample, construct a 95% confidence interval for the population standard deviation of the number of days in the growing season. The 95% confidence interval is

Solution

As              
              
df = n - 1 =    9          
alpha = (1 - confidence level)/2 =    0.025          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    19.0227678          
chi^2(alpha/2) =    2.7003895          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    235.9099447          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    1661.856595          
              
Thus, the confidence interval for the variance is              
              
(   235.9099447   ,   1661.856595   )
              
Also, for the standard deviation, getting the square root of the bounds,              
              
(   15.35936017   ,   40.76587538   ) [ANSWER]