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

Question

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

C=0.95, S2=23.04, n=29

Answer 1

CI = 95% alpha = 0.05 alpha/2 = 0.025

S^2 = 23.04 n = 29 Degrees of Freedom (DOF) = n-1 = 28

(n-1)S^2 (n-1)S^2

------------ < variance < ------------

chi-square 0.025 chi-square 0.975

28 DOF 28 DOF

chi-square 0.025 28 DOF = 44.46

chi-square 0.975 28 DOF= 15.30

28 * 23.04/44.46 < variance < 28 * 23.04/15.30

14.51 < variance < 42.16

3.8 < standard deviation < 6.49