In Problems, assume that the data come from populations that are normally distributed with the same variance.

(a) Determine whether there is significant interaction between factor A and factor B.
(b) If there is no significant interaction, determine if there is a significant difference in the means for the two levels of factor A. If there is no significant interaction, determine if there is a significant difference in the means for the three levels of factor B.
(c) Draw an interaction plot of the data to support the results of parts (a) and (b).
(d) If there is a significant difference in the means for the two levels of factor A, use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05. If there is a significant difference in the means for the three levels of factor B, use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05.

Factor B Level 1 Level 2 Level 3 53.3 64.9 51.9 59.3 44.2 61.8 Level 1 32.9 46.2 68.5 Factor A 59.4 43.3 65.8 50.7 38.4 53.1 Level 2 59.3 50.7 57.9 40.2 58.1 55.7 33.5 52.6 74.4