An experiment was conducted to investigate the effects of three factors—paper stock, bleaching compound, and coating type—on the whiteness of fine bond paper. Three paper stocks (factor A), four types of bleaches (factor B), and two types of coatings (factor C) were used for the experiment. Six paper specimens were prepared for each of the 3 × 4 × 2 stock– bleach–coating combinations and a measure of whiteness was recorded.

a. Construct an analysis of variance table showing the sources of variation and the respective degrees of freedom.

b. Suppose MSE = .14, MS(AB) = .39, and the mean square for all interactions combined is .73. Do the data provide sufficient evidence to indicate any interactions among the three factors? Test using α = .05.

c. Do the data present sufficient evidence to indicate an AB interaction? Test using α = .05. From a practical point of view, what is the significance of an AB interaction? 

d. Suppose SS(A) = 2.35, SS(B) = 2.71, and SS(C) = .72. Find SS(Total). Then find R² and interpret its value.