An agricultural experiment station is investigating the appropriate planting density for three commercial varieties of tomatoes: celebrity, sunbeam, and trust. The researcher decides to examine the effects of four planting densities: 5, 20, 35, and 50 thousand plants per hectare. The experiment station has three large fields that would be appropriate for the study. At each of the fields, 12 plots are prepared, and the 12 treatments are randomly assigned to the plots. A separate randomization is done at each of the three fields. The yield, in tons, from the 36 one hectare plots are given here.

a. Identify the design, and write a statistical model for this experiment.
b. Use a profile plot to display the level of interaction between treatment and level.
c. Perform appropriate F tests, and draw conclusions from these tests concerning the effect of variety and planting density on the mean yield of the tomato plants.
d. Use a normal probability plot and a plot of the residuals to determine if there are violations in the appropriate conditions for validly drawing conclusions from the F tests.

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Variety Sunbeam Celebrity Trust Density Density Density 20k 35k Field 5k 50k 5k 20k 35k 50k 5k 20k 35k 50k 32.5 39.9 42.5 38,2 33.4 47.2 44.5 43.5 411 48.7 53.5 48.4 32.2 43.2 47.6 43.5 33.4 51.3 52.244.1 418 512 55.955.9 49.9 59,0 66.3 58.3 60.8 66 70.7 60.6 60.8 67.6 73.2 67.8