c. Does the fact that #2 - An = -11 while # 13 - #12 = 13 imply that factors A and B interact? Explain. d. Prepare a treatment means plot and determine whether the two factors interact. What do you find? Problem 3. Hay Fever Relief. A research laboratory was developing a new compound for the relief of severe cases of hay fever. In an experiment with 36 volunteers. the amounts of the two active ingredients (factors A and B ) in the compound were varied at three levels each. Randomization was used in assigning four volunteers to each of the nine treatments. The data on hours of relief follow (The complete Dataset is available on Blackboard). Factor B (ingredient 2) Factor A 1 =1 1 =2 1 =3 (ingredient 1) Low Medium High i =1 Low 2.4 4.6 4.8 . . . 2.5 4.7 4.6 i =2 Medium 5.8 89 9.1 5.3 9.0 9.4 i = 3 High 6.1 9.9 13.5 .. . . . . 6.2 10,1 13.2 a. Obtain the fitted values for ANOYA model: Yip = " to, 18 ; + (@ ), + Six subject to Zo; = 0, 28 , = 0, 2(8 ); = 0 for j = 1, ...,b, and E ( ) = 0 for i = 1, ..., a. b. Plot the residuals against the fitted values. What departures from above ANOVA model can be studied from this plot? What are your findings? c. Prepare an estimated treatment means plot. Does your graph suggest that any factor effects are present? Explain. d. Obtain the analysis of variance table. Does any one source account for most of the total variability in hours of relief in the study? Explain