Question

Use technology to construct the confidence intervals for the proportion variance sigma2 and the population standard deviation sigma. Assume the sample is taken from a normally distributed population.

c=0.90, s2=10.89, n=25

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

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

Answer 1

Solution :

Given that,

Point estimate = s² = 10.89

n = 25

Degrees of freedom = df = n - 1 = 24

²_L = ²_/2,df = 36.415

²_R = ²_{1 - /2,df} = 13.848

The 90% confidence interval for ² is,

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

24 * 10.89 / 36.415 < ² < 24 * 10.89 / 13.848

7.18 < ² < 18.87

The 90% confidence interval for ² is, (7.18 , 18.87) .

The confidence interval for the population standard deviation is,

2.68 < < 4.34