If two populations are normally distributed with distributions
and
we can test the hypothesis that
using the F - distribution. We take a sample from populations 1 and 2, ofsizes
and
respectively,and find the sample variances,
and
respectively. The test statistic is then
and assuming that
will follow a
distribution with
and
We 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 the
distribution, 3.677, we see that 1.052 is less than the critical value and we do not reject the null hypothesis.