## Using the F - Distribution to Test for the Equality of the Variances of Two Normal Populations

If two populations are normally distributed with distributionsandwe can test the hypothesis thatusing the F - distribution. We take a sample from populations 1 and 2, ofsizesandrespectively,and find the sample variances,andrespectively. The test statistic is thenand assuming thatwill follow adistribution withandWe can find the critical value corresponding to the significance level of the test from the table and either reject or not the null hypothesis that

Example: Two samples are taken from two populations.

Sample 1: 11, 23, 43, 12, 14, 32, 22, 43, 35, 45

Sample 2: 15, 44, 21, 26, 30, 39, 48, 50

Comparing this with the 5% level from thedistribution, 3.677, we see that 1.052 is less than the critical value and we do not reject the null hypothesis.