A simple random sample from a population with a normal distr

A simple random sample from a population with a normal distribution of 107 body temperatures has x bar=98.70 F and s=0.64 F. Construct a 98% 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 1.70 F?

Solution

CI = (n-1) S^2 / ^2 right < ^2 < (n-1) S^2 / ^2 left
Where,
S = Standard Deviation
^2 right = (1 - Confidence Level)/2
^2 left = 1 - ^2 right
n = Sample Size

Since aplha =0.02
^2 right = (1 - Confidence Level)/2 = (1 - 0.98)/2 = 0.02/2 = 0.01
^2 left = 1 - ^2 right = 1 - 0.01 = 0.99
the two critical values ^2 left, ^2 right at 106 df are 142.7804 , 75.092
S.D( S^2 )=0.64
Sample Size(n)=107
Confidence Interval = [ 106 * 0.4096/142.7804 < ^2 < 106 * 0.4096/75.092 ]
Population Variance= [ 43.4176/142.7804 < ^2 < 43.4176/75.0918 ]
Population Variance = [ 0.3041 < ^2 < 0.5782 ]
       
Population S.D = [ Sqrt(0.3041) < < Sqrt(0.5782) ]
Population S.D = [ 0.5514 < < 0.7603 ]

Yes, it is safe to conclude that the population standard deviation is less than 1.70 F