An experiment compared two different fertilizer placements (broadcast, band) and two different rates of fertilizer flow on watermelon yields. Recent research has shown that broad­cast application (scattering over the outer area) of fertilizer is superior to bands of fertilizer ­applied near the seed for watermelon yields. For this experiment, the investigators wished to compare two nitrogen€“ phosphorus€“ potassium fertilizers applied ( broadcast and band) at a rate of 160€“ 70€“ 135 pounds per acre and including two brands of micronutrients (A and B). These four combinations were to be studied in a Latin square field plot.
The treatments were randomly assigned according to a Latin square design conducted over a large farm plot, which was divided into rows and columns. A watermelon plant dry weight was obtained for each row€“ column combination 30 days after the emergence of the plants. The data are shown next.

Treatment 1€“ broadcast, A Treatment 3€“ band, A
Treatment 2€“ broadcast, B Treatment 4€“ band, B
a. Write an appropriate statistical model for this experiment.
b. Use the data to run an analysis of variance. Give the p- value for each test, and draw conclusions.

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Column Row 11 1.75 3 143 4 128 2 166 2 1.70 1 178 140 4 131 3 4 135 2 1.73 1 169 3 141 4 3 145 4 13 2165 1 173