To assess the effect of piston ring type and oil type on piston ring wear, three types of piston ring and four types of oil were studied. Three replications of an experiment, in which the number of milligrams of material lost from the ring in four hours of running was measured, were carried out for each of the 12 combinations of oil type and piston ring type. With oil type as the row effect and piston ring type as the column effect, the following sums of squares were observed: SSA = 1.0926, SSB = 0.9340, SSAB = 0.2485, SSE = 1.7034
a) Construct an ANOVA table using the outline below. You do not need to specify p-values.
b) Is the additive model plausible? State the hypotheses, provide the value of the test statistic, and state your conclusion, testing at the alpha = 0.05 level.
c) Is it plausible that the main effects of oil type are all equal to 0? State the hypotheses, provide the value of the test statistic, and state your conclusion, testing at the alpha = 0.05 level.
d) Based on your conclusion to part (b), what would you expect the interaction plot between oil type and piston ring type to look like?