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, I = 3 different factor values were used, J = 5 different batches of cement were selected, and K = 2 beams were cast from each cement factor/batch combination. Sums of squares include SSA = 22,841.8, SSB = 22,265.53, SSE = 15,153.5, and SST = 64,754.7. Construct the ANOVA table. (Round your answers to two decimal places.)

Source	df	SS	MS	f
A
B
AB
Error
Total

Then, assuming a mixed model with cement factor (A) fixed and batches (B) random, test the three pairs of hypotheses of interest at level 0.05. State the appropriate hypotheses for the test for an interaction.

H_0G: _G² = 0H_aG: _G² 0

H_0G: _G² = 0 H_aG: _G² 0

H_0G: _G² = 0 H_aG: _G² < 0

H_0G: _G² = 0H_aG: _G² > 0

Find the critical value. (Round your answer to two decimal places.)F_{, 1, 2} = State the conclusion in the problem context.

Fail to reject H_0G. The data suggests that there is an interaction.

Reject H_0G. The data does not suggest that there is an interaction.

Fail to reject H_0G. The data does not suggest that there is an interaction.

Reject H_0G. The data suggests that there is an interaction.

State the appropriate hypotheses for the test for a cement factor effect.

H_0A: ₁ = ₂ = ₃ = 0 H_aA: no _i = 0

H_0A: ₁ = ₂ = ₃ = 0 H_aA: at least one _i 0

H_0A: _{1 2 3} 0 H_aA: all _i's = 0

H_0A: _{1 2 3} 0 H_aA: at least one _i = 0

Find the critical value. (Round your answer to two decimal places.)F_{, 1, 2} = State the conclusion in the problem context.

Fail to reject H_0A. The data does not suggest that there is a cement factor effect.

Reject H_0A. The data does not suggest that there is a cement factor effect.

Fail to reject H_0A. The data suggests that there is a cement factor effect.

Reject H_0A. The data suggests that there is a cement factor effect.

State the appropriate hypotheses for the test for a batch effect.

H_0B: _B² = 0 H_aB: _B² 0

H_0B: _B² = 0 H_aB: _B² 0

H_0B: _B² = 0 H_aB: _B² > 0

H_0B: _B² = 0 H_aB: _B² < 0

Find the critical value. (Round your answer to two decimal places.)F_{, 1, 2} = State the conclusion in the problem context.

Reject H_0B. The data does not suggest that there is a batch effect.Reject H_0B. The data suggests that there is a batch effect.

Fail to reject H_0B. The data suggests that there is a batch effect.

Fail to reject H_0B. The data does not suggest that there is a batch effect.

You may need to use the appropriate table in the Appendix of Tables to answer this question.