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 data for this experiment is below: Fertilizer Zone Sap Production
Low Southern Zone 76.2
Low Southern Zone 80.4
Low Southern Zone 74.2
Low Central Zone 79.4
Low Central Zone 87.9
Low Central Zone 86.9
Low Northern Zone 84.5
Low Northern Zone 85.2
Low Northern Zone 80.1
Medium Southern Zone 87
Medium Southern Zone 95.1
Medium Southern Zone 93
Medium Central Zone 98.2
Medium Central Zone 94.7
Medium Central Zone 96.2
Medium Northern Zone 88.4
Medium Northern Zone 90.4
Medium Northern Zone 92.2
High Southern Zone 84.2
High Southern Zone 87.5
High Southern Zone 83.1
High Central Zone 90.3
High Central Zone 89.9
High Central Zone 93.2
High Northern Zone 81.4
High Northern Zone 84.7
High Northern Zone 82.2
A. Construct the ANOVA table.
1. What is the MSE?
2. What is the MS Fertilizer?
3. What is the MS Interaction?
B. Is the additive model plausible at the 5% level?
1. What is the test statistics?
C. Is it meaningful to test for differences in the average (over the three zones) sap production between the three fertilizer levels in this situation?
1. Assuming it is meaningful to do this, what would the test statistic for doing it:
2. Are there differences in sap production between the three fertilizer levels at the 5% level?