(In some of the exercises that follow, we must make assumptions, such as normal distributions with equal variances.)

In order to test whether four brands of gasoline give equal performance in terms of mileage, each of three cars was driven with each of the four brands of gasoline. Then each of the (3)(4) = 12 possible combinations was repeated four times. The number of miles per gallon for each of the four repetitions in each cell is recorded in the following table:

Test the hypotheses HAB: no interaction, HA: no row effect, and HB: no column effect, each at the 5% significance level.