Given the following data for a two-way ANOVA, identify the sets of null and alternative hypotheses, then use the 0.05 level in testing each null hypotheses.

Solution: We have three sets of hypotheses:

We use Minitab to test these sets of hypotheses, getting the following results:

This table shows that there is a significant interaction (p = 0.000) between the factors. Also, column-factor B doesn’t affect the means (p=0.075), but the row-factor does (p = 0.014), at the 0.05 significance level.