Question

Use technology to construct the confidence intervals for the population variance σ2 and the population standard deviation σ.

Assume the sample is taken from a normally distributed population.

c=0.90​

s=33​

n=20

The confidence interval for the population variance is (_, _ ) ​(Round to two decimal places as​ needed.)

The confidence interval for the population standard deviation is (_, _ ) ​(Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

s = 33

Point estimate = s² = 1089

²_L = ²_/2,df = 30.143

²_R = ²_{1 - /2,df} = 10.117

The 90% confidence interval for ² is,

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

19 * 1089 / 30.143 < ² < 19 * 1089 / 10.117

686.42 < ² < 2045.17

(686.42 , 2045.17 )

The 90% confidence interval for is,

26.20 < < 45.22

(26.20 , 45.22)