Chapter 11.2, Problem 16E

In an experiment to assess the effects of curing time(factor A) and type of mix (factor B) on the compressive strength of hardened cement cubes, three different curing times were used in combination with four different mixes, with three observations obtained for each of the12 curing time–mix combinations. The resulting sums of squares were computed to be SSA = 30,763.0, SSB = 34,185.6, SSE = 97,436.8, and SST = 205,966.6.

a. Construct an ANOVA table.

b. Test at level .05 the null hypothesis H_0AB: all γ_ij’s 5 0(no interaction of factors) against H_aAB: at least one γ_ij ≠ 0.

c. Test at level .05 the null hypothesis H_0A: α₁ = α₂ = α₃ = 0 (factor A main effects are absent) against H_aA: at least one α_i ≠ 0.

d. Test H_0B: β₁ = β₂ = β₃ = β₄ = 0 versus H_aB: at least one β_j ≠ 0 using a level .05 test.

e. The values of the ${\bar{x}}_{i\mathrm{..}}$’s were ${\bar{x}}_{\mathrm{1..}}$ = 4010.88, ${\bar{x}}_{\mathrm{2..}}$ = 4029.10, and ${\bar{x}}_{\mathrm{3..}}$ = 3960.02. Use Tukey’s procedure to investigate significant differences among the three curing times.