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. Southern Zone Central Zone Northern Zone 76.2 80.4 74.2 79.4 87.9 86.9 84.5 85.2 80.1 Low fertilizer Medium 87.0 95.1 93.0 98.2 94.7 96.2 88.4 90.4 922 fertilizer High 84.2 87.5 83.1 90.3 89.9 93.2 81.4 84.7 82.2 fertilizer 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. 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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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.
Southern Zone Central Zone Northern Zone
76.2 80.4 74.2 79.4 87.9 86.9 84.5 85.2 80.1
Low
fertilizer
Medium 87.0 95.1 93.0 98.2 94.7 96.2 88.4 90.4 922
fertilizer
High
84.2 87.5 83.1 90.3 89.9 93.2 81.4 84.7 82.2
fertilizer
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.
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.
Transcribed Image Text: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. Southern Zone Central Zone Northern Zone 76.2 80.4 74.2 79.4 87.9 86.9 84.5 85.2 80.1 Low fertilizer Medium 87.0 95.1 93.0 98.2 94.7 96.2 88.4 90.4 922 fertilizer High 84.2 87.5 83.1 90.3 89.9 93.2 81.4 84.7 82.2 fertilizer 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. 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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