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),I =3 different factor values were used, J = 5different batches of cement were selected, and K = 2 beams were cast from each cement factor/batch combination. Sums of squares include SSA =22,941.80, SSB = 22,765.53, SSE = 15,253.50 and SST = 64, 954.70 . 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.
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