In a study11 at Iowa State University, a large field was partitioned into 20 equal-size plots. Each plot was planted with the same amount of seed corn, using a fixed spacing pattern between the seeds. The goal was to study how the yield of corn later harvested from the plots depended on the levels of use of nitrogen-based fertilizer (low = 45 kg per hectare, high = 135 kg per hectare)

and manure (low = 84 kg per hectare, high = 168 kg per hectare). The corn yields (in metric tons) for this completely randomized two-factor study are shown in the table:

Fertilizer Manure Observations, by Plot High High 13.7 15.8 13.9 16.6 15.5 High Low 16.4 12.5 14.114.4 12.2 Low High 15.0 15.1 12.0 15.7 12.2 Low Low 12.4 10.6 13.7 8.7 10.9

a. Conduct a two-way ANOVA, assuming a lack of interaction between fertilizer level and manure level in their effects on crop yield. Report the ANOVA table. Summarize the main effect tests, and interpret the P-values.

b. If yield were instead measured in some other units, such as pounds or tons, then in your ANOVA table, what will change and what will stay the same?

c. Follow up the main-effect tests in

(a) by forming 95% Bonferroni confidence intervals for the two main-effect comparisons of means. Interpret.

d. Now allow for interaction, and show results of the F test of the hypothesis of a lack of interaction. Interpret.