In an Experiment to Assess the Effects of Curing Time $H _ { o A B } : \text { all } \gamma _ { \mathrm { ij } } { } ^ { \prime } s = 0$

Essay

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 $H _ { o A B } : \text { all } \gamma _ { \mathrm { ij } } { } ^ { \prime } s = 0$
(no interaction of factors) against $H _ { o A B } \text { : at least one } \gamma _ { \mathrm { ij } } \neq 0$
c. Test at level .05 the null hypothesis $H _ { o A } : \alpha _ { 1 } = \alpha _ { 2 } = \alpha _ { 3 } = 0$
(factor A main effects are absent) against $H _ { o A } \text { : at least one } \alpha _ { i } \neq 0$
d. Test $H _ { o B } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = 0 \text { ver sus } H _ { o B } :$
at least one $\beta _ { j } \neq 0$
using a level .05 test.
e. The values of the $\bar { x } _ { 1 00 } \text { 's were } \bar { x } _ { 100 } = 4010.88 , \bar { x } _ { 2 00 } = 4029.10 \text {, and } \bar { x } _ { 300 } = 3960.02$
Use Tukey's procedure to investigate significant differences among the three curing times.