2. An experiment was conducted to determine the effects of various pesticides on the

yield of fruit from three different varieties (B1, B2, B3) of lemon tree. The pesticide

conditions utilized in the experiment were A1=Control (no pesticide), A2=Chemical

X, A3=Chemical Y, A4=Mixture of chemicals X and Y. The lemon varieties used

were B1=Standard variety (the variety that is currently most commonly grown),

B2=New genetically engineered variety 1, and B3=New genetically engineered variety

2. Eight trees from each variety were randomly selected from an orchard. The

four levels of pesticide were then randomly assigned to two trees of each variety and

pesticide applications were made. Yields of fruit, in bushels per tree, were obtained

after the test period. The data appear below:

Pesticide

Variety A1 A2 A3 A4

B1 49, 39 50, 55 43, 38 53, 48

B2 55, 41 67, 58 53, 42 80, 73

B3 66, 68 85, 92 69, 62 89, 99

(a) Write the appropriate two-way ANOVA model for analyzing these data. Perform

the analysis of variance corresponding to this model and draw conclusions

about the effects.

(b) Construct and test a set of orthogonal contrasts to address the following questions

about the marginal effects of the pesticide treatments:

i. Does using chemical X increase the mean yield?

ii. Does using chemical Y increase the mean yield?

iii. Do chemicals X and Y interact, so that the effect of using chemical X

differs when chemical Y is used from its effect when chemical Y is not

used?

1(c) Construct and test contrasts in the marginal variety means to address the

following questions:

i. Does genetically engineered variety 1 produce higher mean yields than the

standard variety?

ii. Does genetically engineered variety 2 produce higher mean yields than the

standard variety?

(d) Use the contrasts that you formed in parts (b) and (c) to form interaction

contrasts. (You should end up with 3 2 = 6 interaction contrasts.) Interpret

these contrasts (i.e., what questions do they address?). Test these interaction

contrasts as planned comparisons and state your conclusions.

(e) Were the contrasts in par (b) mutually orthogonal? How about the contrasts

in part (c)?