Question

Use technology to construct the confidence intervals for the population variance sigmasquared and the population standard deviation sigma. Assume the sample is taken from a normally distributed population. c=0.95​, s=34​, n=16

Answer 1

Solution :

Given that,

s = 34

Point estimate = s² = 1156

²_R = ²_/2,df = 27.488

²_L = ²_{1 - /2,df} = 6.262

The 95% confidence interval for ² is,

(n - 1)s² / ²_/2 < ² < (n - 1)s² / ²_{1 - /2}

(15)(1156) / 27.488 < ² < (15)(1156) / 6.262

630.81 < ² < 2769.04

(630.81 , 2769.04)