2. Consider a two-factor study in the table below. Factor A has two levels and factor B has three levels. The number of replicates is n 4. The boxed numbers are the cell averages of the four replicates. The grand average of all 24 observations is 89.125. Factor B B2 110 B1 B3 1 56 60 240 A1 217 225 71 A2 53 206 222 10358 118 68 60.5 I 58 -37 95 Factor A 4733 38.75 62.25 52 44.75 68 57 31 49 40 45 (a) Assume both A and B arefired effects. Calculate the main effect estimate 2. Based on the interaction plot below, is there any sign of factor interaction? Interaction Plot for y 21 (b) Assume both A and B are fixed effects. The ANOVA tabl the significance of AB interaction at level a 0.05 is partially given as below. Test Source DF ss 1 39447 2 36412 A*B 2 20165 Error 18 1550 Total 23 97575 (c) Assume both A and B are random effects. Test the significance of effect B, based on information from the partial ANOVA table in (b)