Question

2.  Test the null hypothesis that the variance of ratings of the competency of Obama for Democrats equals 50.  A sample of 30 has a variance for democrats=90.  Use a significance level of .01.

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 = 50 versus Ha: σ2 ≠ 50

This is a two-tailed test.

The test statistic formula is given as below:

Chi-square = (n – 1)*S^2/ σ2

From given data, we have

n = 30

S^2 = 90

σ2 = 50

Chi-square = (30 – 1)*90/50

Chi-square = 52.2

We are given

Level of significance = α = 0.01

df = n – 1

df =29

Critical values = 13.1211 and 52.3356

(by using Chi square table or excel)

Test statistic chi square value 52.2 is lies between critical values.

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the variance of ratings of the competency of Obama for Democrats equals 50.