In an experiment to investigate the effect of “cement factor”

(number of sacks of cement per cubic yard) on flexural strength of the resulting concrete (“Studies of Flexural Strength of Concrete. Part 3: Effects of Variation in Testing Procedure,” Proceedings, ASTM, 1957: 1127–1139), different factor values were used, different batches of cement were selected, and beams were cast from each cement factor/batch combination. Sums of squares include

, and . Construct the ANOVA table. Then, assuming a mixed model with cement factor (A) fixed and batches (B) random, test the three pairs of hypotheses of interest at level .05.