Question

A population parameter has a normal distribution and has a mean of 45 and variance of 15. From
this population a sample is selected with a size of 19 and the variance of the sample is 17. Does
this sample support the population variance? Evaluate.

Answer 1

Solution:

Here, we have to use Chi square test for the population variance or standard deviation.

The null and alternative hypotheses for this test are given as below:

H0: σ2 = 15 versus Ha: σ2 ≠ 15

This is a tailed test.

The test statistic formula is given as below:

Chi-square = (n – 1)*S^2/ σ2

From given data, we have

n = 19

S^2 = 17

σ2 = 15

Chi-square =(19 - 1)*17/15

Chi-square = 20.3999

We are given

Level of significance = α = 0.05

df = n – 1

df = 18

P-value = 0.3108

(by using Chi square table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the population variance is

The sample supports the population variance.