The F test used for testing the difference in two population variances is always a one-tail test.

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The F test for testing the difference in two population variances is a two-tail test. This is because the null hypothesis is that the two variances are equal, while the alternative hypothesis is that they are not equal, which could be in either direction (one variance being larger or smaller than the other). Therefore, the F distribution has two tails and the critical values for rejection of the null hypothesis are found in both tails of the distribution.

The F Test Used for Testing the Difference in Two