Question: In a 3 × 3 two-way factorial study, fitted A main effects are a1 = 2 and a2 = 3, fitted B main effects are b1 = -1 and b2 = 2, and four of the fitted AB interactions are ab11 = 1, ab12 = -1, ab21 = 2 and ab22 = -3. The average of the 9 sample means is Y¯ = 10.
(a) What was the sample mean response where both A and B were at their third levels?
(b) Suppose in this problem m = 2 and Sp = 2. Using a 95 % confidence level, find an appropriate "margin of error" Δij for estimating each of the fitted interactions.
(c) If you were to make an interaction plot (a plot trace of sample means against level of A, one for each level of B), would you see a departure from "parallelism"? Why or why not?