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 = 30,973.7, SSB = 35,640.6, SSE = 95,494.1, and SST = 205,367.9. a. Construct an ANOVA table. (Round your SS to one decimal place and your MS and f to two decimal places.)
b. Test at level 0.05 the null hypothesis H0AB : all γ ij's = 0 (no interaction of factors) against HaAB: at least one γ ij 0. (Round your answer to two decimal places.)
c. Test at level 0.05 the null hypothesis H0AB: α 1 = α 2 = α3 = 0 (factor A main effects are absent) against HaA: at least one α i 0. (Round your answer to two decimal places.)
d. Test HOB: β1 = β 2 = β3 = β4 = 0 versus HaB at least one β j = 0 using a level 0.05 test. (Round your answer to two decimal places.)
e. The values of the s were = 4010.88, = 4029.10, and = 3960.02. Use Tukey's procedure to investigate significant differences among the three curing times. (Round your answer to two decimal places.)