Question

Use technology to construct the confidence intervals for the population variance σsquared2 and the population standard deviation sigmaσ.

Assume the sample is taken from a normally distributed population.

c=0.99, s=33​, n=16

a) The confidence interval for the population variance is (_,_) ??

b) The confidence interval for population standard deviation is (_,_) ??

Please explain how you got these answers for a thumbs up!! Thanks :)

Answer 1

a)

Confidence interval for ² is

(n-1) S² / /2 < ² < (n-1) S² / 1-/2

(16 - 1) * 33² / 32.801 < ² < (16-1) * 33² / 4.601

498.003 <  ² < 3550.315

99% C I for  ² is ( 498.003 , 3550.315)

b)

Confidence interval for is

Sqrt [ (n-1) S² / /2 ] < < Sqrt [(n-1) S² / 1-/2 ]

Sqrt [ (16 - 1) * 33² / 32.801 ] < < [ (16-1) * 33² / 4.601 ]  

22.316 < < 59.585

99% CI is (22.316 , 59.585)