A simple random sample from a population with a normal distr

A simple random sample from a population with a normal distribution of 97 body temperatures has x overbar equals 98.40 degrees Upper Fands equals 0.66 degrees Upper F. Construct a 99% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Is it safe to conclude that the population standard deviation is less than

1.50 degrees Upper F?

Solution

As              
              
df = n - 1 =    96          
alpha = (1 - confidence level)/2 =    0.005          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    135.4330487          
chi^2(alpha/2) =    64.06332741          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    0.308769539          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    0.652754106          
              
Thus, the confidence interval for the variance is              
              
(   0.308769539   ,   0.652754106   )
              
Also, for the standard deviation, getting the square root of the bounds,              
              
(   0.555670351   ,   0.807931993   ) [ANSWER]

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As this whole interval is less than 1.50 degrees F, then it is safe to conclude that the population standard deviation is less than
1.50 degrees F. [conclusion]