Question

A random sample of size 17 is taken from a normally distributed population, and a sample variance of 23 is calculated.

If we are interested in creating a 95% confidence interval for σ2, the population variance, then:

a) What is the appropriate degrees of freedom for the χ2distribution?

b) What are the appropriate χ2Rand χ2L values, the right and left Chi-square values?

Round your responses to at least 3 decimal places.

χ2R=

χ2L=

Answer 1

Solution :

Given that,

Point estimate = s² = 23

n = 17

(a)

Degrees of freedom = df = n - 1 = 17 - 1 = 16

(b)

At 95% confidence level the ² value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

²_L = ²_/2,df = 28.845

²_R = ²_{1 - /2,df} = 6.908