Vermont maple sugar producers sponsored a testing program to determine the benefit of a potential new fertilizer regimen. A random sample of 27 maple trees in Vermont were chosen and treated with one of three levels of fertilizer suggested by the chemical producer. In this experimental setup, nine trees (three in each of three climatic zones) were treated with each fertilizer level and the amount of sap produced (in mL) by the trees in the subsequent season was measured. The results are presented in the following table.

a. Estimate the main effects of fertilizer levels and climatic zone, and their interactions.

b. Construct an ANOVA table. You may give ranges for the P-values.

c. Test the hypothesis that there is no interaction between fertilizer levels and climatic zone.

d. Test the hypothesis that there is no difference in sap production for the three fertilizer levels.

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Southern Zone Central Zone Northern Zone Low fertilizer Medium fertilizer 76.2 80.4 74.2 79.4 87.9 86.9 84.5 85.2 80.1 87.0 95.1 93.0 98.2 94.7 96.2 88.4 90.4 92.2 High fertilizer 84.2 87.5 83.1 90.3 89.9 93.2 81.4 84.7 82.2