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 the 12 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 H0AB: all γij's = 0 (no interaction of factors) against HaAB: at least one γij ≠ 0.
c. Test at level .05 the null hypothesis H0A: a1 = a2 = a3 = 0 (factor A main effects are absent) against HaA: at least one ai ≠ 0.
d. Test H0B: β1 = β2 = β3 = β4 = 0 versus HaB: at least one βj ≠ 0 using a level .05 test.
e. The values of the x̅3..'s were x̅1.. = 4010.88, x̅2.. = 4029.10, and x̅3.. = 3960.02. Use Tukey's procedure to investigate significant differences among the three curing times.