Use technology to construct the confidence intervals for the

Use technology to construct the confidence intervals for the population variance

sigma squared 2

and the population standard deviation

.

Assume the sample is taken from a normally distributed population.

c=0.95,

s=33,

n=17

Solution

Confidence Interval
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 16 df are 28.8454 , 6.908
S.D( S^2 )=33
Sample Size(n)=17
Confidence Interval = [ 16 * 1089/28.8454 < ^2 < 16 * 1089/6.908 ]
= [ 17424/28.8454 < ^2 < 17424/6.9077 ]
Confidence Interval Variance = [ 604.0478 , 2522.4025 ]   
Confidence Interval S.D = [ Sqrt(604.0478) < < Sqrt(2522.4025) ] = [ 24.57    < < 50.22 ]