suppose a farmer wants to test the effectiveness of two new fertilizers (Fertilizers A and B) on the crop yield of corn plants. He selects five plots, each 1212 acres in size, in his field to test. He divides each plot into equally sized thirds, randomly applying Fertilizer A to one third, Fertilizer B to one third, and the current fertilizer, serving as the control, to one third of the plot.

As there is some variability in the sunlight exposure and natural fertility of the soil in the different plots, the farmer wants to account for the plot variability. A month after planting and fertilizer application, the farmer measures the crop yield across the plots. He fits a linear model to the data to predict crop yield.

1/ Determine the number of treatment groups analyzed.

Number of treatment groups =

2/ Determine the set of model statements that represent the null and alternative hypotheses for testing the model fit.

a/ Null model: CROP YIELD = CONSTANT + BLOCK + FERTILIZER

Alternate model: CROP YIELD = CONSTANT + BLOCK

b/Null model: CROP YIELD = CONSTANT

Alternate model: CROP YIELD = CONSTANT + FERTILIZER

c/ Null model: CROP YIELD = CONSTANT + CONTROL

Alternate model: CROP YIELD = CONSTANT + CONTROL + FERTILIZER

d/ Null model: CROP YIELD = CONSTANT + BLOCK + FERTILIZER

Alternate model: CROP YIELD = CONSTANT + BLOCK + FERTILIZER + BLOCK * FERTILIZER

e/ Null model: CROP YIELD = CONSTANT + BLOCK

Alternate model: CROP YIELD = CONSTANT + BLOCK + FERTILIZER