Question

A random sample of 20 women have a mean height of 62.5 inches and a standard deviation of 1.3 inches. Construct a 98% confidence interval for the population variance, sigma(2)

Answer 1

Solution :

Given that,

s = 1.3

Point estimate = s² = 1.69

n = 20

Degrees of freedom = df = n - 1 = 20 - 1 = 19

(a)

At 98% confidence level the ² value is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

1 - / 2 = 1 - 0.01 = 0.99

²_L = ²_/2,df = 36.191

²_R = ²_{1 - /2,df} = 7.633

The 95% confidence interval for ² is,

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

19 * 1.69 / 36.191 < ² < 19 * 1.69 / 7.633

0.89 < ² < 4.21

A 98% confidence interval for the population variance is : ( 0.89 , 4.21)

(b)

The 98% confidence interval for is,

0.94 < < 2.05

A 98% confidence interval for the sigma is : ( 0.94 , 2.05)