Question

Construct the confidence interval for the population standard deviation for the given values. Round your answers to one decimal place.

n=20, s=3.9, and c=0.8

Answer 1

Solution :

Given that,

s = 3.9

s² = 15.21

n = 20

Degrees of freedom = df = n - 1 = 19

At 80% confidence level the ² value is ,

²_L = ²_/2,df = 27.204

²_R = ²_{1 - /2,df} = 11.651

The 80% confidence interval for is,

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

  19 * 15.21 / 27.204 < < 19 * 15.21 / 11.651

3.3 < < 5.0

(3.3 , 5.0)