11.2 Consider a 22 factorial experiment in a randomized complete block design with b blocks. (i) Define, in terms of the true treatment effects, the main effects and two- factor interaction. (ii) Show that the main effects and the two-factor interaction are orthogonal contrasts among the treatment effects. (iii) Suppose each experimental unit has 3 observational units. Give an expres- sion for the variance of the estimators for the main effects and interaction. (iv) Outline the ANOVA table for the design with b blocks and 3 observational units per experimental unit giving source of variation, d.f., E(MS), and the F-ratios for testing hypotheses about the main effects and interaction.