Question

The thicknesses of 81 randomly selected aluminum sheets were found to have a variance of 3.23. Construct the 98% confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory. Round your answers to two decimal places.

Answer 1

Solution :

Given that,

Point estimate = s² = 3.23

²_R = ²_/2,df = 112.329

²_L = ²_{1 - /2,df} = 53.540

The 98% confidence interval for ² is,

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

80 * 3.23 / 112.329 < ² < 80 * 53.540 / 53.540

2.30 < ² < 4.83

(2.30 , 4.83)