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

If two populations are normally distributed withdistributionsandwecan test the hypothesis thatusingthe F - distribution. We take a sample from populations 1 and 2, ofsizesandrespectively,and find the sample variances,andrespectively.The test statistic is thenandassuming thatwillfollow adistributionwithandWecan find the critical value corresponding to the significance levelof the test from the table and either reject or not the nullhypothesis 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 <3.677 so we do not reject the hypothesisthat