Use the given information to find the number of degrees of f

Use the given information to find the number of degrees of freedom, the critical values and and the confidence interval estimate of sigma. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in Menthol cigarettes 95% confidence; n = 20, s = 0.21mg. (Round to three decimal places as needed)

XL2=

XR2=

Confidence Interval estimate of sigma=

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 =0.05
^2 right = (1 - Confidence Level)/2 = (1 - 0.95)/2 = 0.05/2 = 0.025
^2 left = 1 - ^2 right = 1 - 0.025 = 0.975
the two critical values ^2 left, ^2 right at 19 df are 32.8523 , 8.907
S.D( S^2 )=0.21
Sample Size(n)=20
Confidence Interval = [ 19 * 0.0441/32.8523 < ^2 < 19 * 0.0441/8.907 ]
Confidence for variance = [ 0.8379/32.8523 < ^2 < 0.8379/8.9065 ]
Confidence for variance = [ 0.0255 , 0.0941 ]       
Confidence for standard deviation = [ Sqrt(0.0255) < < Sqrt(0.0941) ] = [ 0.1596 < < 0.3067 ]