Use technology to construct the confidence intervals for the

Use technology to construct the confidence intervals for the population variance sigma squared and the population standard deviation sigma . Assume the sample is taken from a normally distributed population

c=0.90, s^2=12.25, n=29

Solution

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

Since aplha =0.1
^2 right = (1 - Confidence Level)/2 = (1 - 0.9)/2 = 0.1/2 = 0.05
^2 left = 1 - ^2 right = 1 - 0.05 = 0.95
the two critical values ^2 left, ^2 right at 28 df are 41.3371 , 16.928
Variacne( S^2 )=12.25
Sample Size(n)=29
Confidence Interval = [ 28 * 12.25/41.3371 < ^2 < 28 * 12.25/16.928 ]
= [ 343/41.3371 < ^2 < 343/16.9279 ]
Population for variance = [ 8.2976 < ^2 < 20.2624 ]