a simple random sample from a population with a normal distr

a simple random sample from a population with a normal distribution of 100 body temperatures has x=98.50 and s=0.58. construct an 80% confidence interval estimate of the standard devation. is it safe to conclude that the population standard deviation is less that 1.80?

Solution

As              
              
df = n - 1 =    99          
alpha = (1 - confidence level)/2 =    0.1          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    117.4068832          
chi^2(alpha/2) =    81.44925275          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    0.283659689          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    0.408887729          
              
Thus, the confidence interval for the variance is              
              
(   0.283659689   ,   0.408887729   )
              
Also, for the standard deviation, getting the square root of the bounds,              
              
(   0.532597117   ,   0.639443296   ) [ANSWER]

As 1.8 is not inside the interval above, then yes, it is safe to say that the population standard deviation is less than 1.8. [ANSWER]