Problem 13.8 The data below come from an experiment to compare four methods for manufacturing penicillin. Note that the blocks are displayed as rows and the treatments are displayed as columns. The raw material consisted of b = 5 blends consisting of enough material so that all a = 4 methods could be tested on each blend. It was known that the variability between blends was not negligible. The response variable is the yield (the units were not given).

(a) Calculate the ANOVA table and determine whether there are differences among the four methods for manufacturing penicillin.

(b) Check the model assumptions by graphing suitable residual plots. Methods (A) Blends (B) 12 34 1 89 88 97 94 2 84 77 92 79 3 81 87 87 85 4 87 92 89 84 5 79 81 80 88