Question

A random sample of25students taken from a university gave the variance of their GPAs equal to0.21. The variance of GPAs of all students at this university was0.18two years ago. Assume that the GPAs of all students are (approximately) normally distributed.

Construct the95%confidence interval for the population variance.

Round your answers to three decimal places.

The95%confidence interval for the population variance is

lower to upper?

Answer 1

Solution :

Given that,

Point estimate = s² = 0.18

n = 25

Degrees of freedom = df = n - 1 = 24

²_L = ²_/2,df = 39.361

²_R = ²_{1 - /2,df} = 12.401

The 95% confidence interval for ² is,

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

24 * 0.18 / 39.361 < ² < 24 * 0.18 / 12.401

0.110 < ² < 0.348

Lower = 0.110

Upper = 0.348