Question

A sample of 20 items provides a sample standard deviation of 5. Compute the 95% confidence interval estimate of the population variance.

Select one:

a. 23.61 ≤≤ σσ² ≤≤ 72.16

b. 14.46 ≤≤ σσ² ≤≤ 53.31

c. 2.08 ≤≤ σσ² ≤≤ 16.7

d. 16.35 ≤≤ σσ² ≤≤ 33.32

Answer 1

The 95% confidence interval estimate of the population variance ² is:

n = sample size

s^{​​​​​​2}​​​= sample variance &

²_n-1,/2 and ²_n-1,1-/2 is chi-square table value at (n-1) degrees of freedom and level of Significance for two tailed test.

In the given example,

n= sample size= 20

S = sample standard deviation= 5

S^{​​​​​​2}= sample variance=25

= 5% level of Significance=0.05

From chi-square table,

²_n-1,/2= ²_20-1,0.05/2=  ²_19,0.025=32.852

²_n-1,1-/2= ²_{20-1,1-0.05/2}= ²_19,0.975=8.91

The 95% confidence interval estimate of the population variance ² is:

The 95% confidence interval estimate of the population variance ² is :

The option (b) is the correct option.