Suppose that each of two different varieties of corn is treated with two different types of fertilizer in order to compare the Yields, and that K independent replications are obtained for each of the four combinations. Let xijk denote the yield on the kth replication of the combination of variety i with fertilizer j (i = 1, 2; j = 1, 2; k = 1, . . . , K). Assume that all the observations are independent and normally distributed, each distribution has the same unknown variance, and E(Xijk) = μij for k = 1, . . . , K. Explain in words what the following hypotheses mean, and describe how to carry out a test of them:
H0: μ11 − μ12 = μ21 − μ22,
H1: The hypothesis H0 is not true.