15.49 Refer to Exercise 15.31. Having carried out the experiment to compare mean yields per acre of four varieties of corn and three brands of fertilizer, an agricultural researcher suggested that there might be some interaction between variety and fertilizer. To check this possibility, another set of trials was carried out, producing the yields in the table.

Variety Fertilizer A B C D 1 80 88 73 88 2 94 91 79 93 3 81 78 83 83

a. What would be implied by an interaction between variety and fertilizer?

b. Combine the data from the two sets of trials and set up an analysis of variance table.

c. Test the null hypothesis that the population mean yield is the same for all four varieties of corn.

d. Test the null hypothesis that the population mean yield is the same for all three brands of fertilizer.

e. Test the null hypothesis of no interaction between variety of corn and brand of fertilizer.