An agricultural researcher conducted an experiment to determine the effects of phosphorus (P) & potassium (K) fertilizer on the production of sugar from sugar beets.

There were 3 treatments in her experiment, with 12 replicate fields for each treatment. These treatments were:

control (no fertilizer)

fertilizer added in December before winter plowing

fertilizer applied in April before sowing

Prior to the experiment, two linear contrasts were planned: 1. control (treatment 1) vs. fertilizer added (treatments 2 & 3) 2. fertilizer added in December (treatment 2) vs. fertilizer added in April (treatment 3). Because these may not be orthogonal hypotheses, we can only test one of them using linear contrasts.

1. Write the null & alternative hypotheses and a contrast statement (y) for your selected contrast below: (Ho, Ha, y).
2. The researcher recorded mean yields of sugar in metric tons per field as follows: Control - 62, fertilizer in December - 67.5, and fertilizer in April - 69. The root MSE was 5. Calculate the contrast and test for significance.