The following study was designed to evaluate the effectiveness of four chemicals developed to control fire ants. The type of environmental conditions in which the chemical is placed might affect the effectiveness of the treatment to kill fire ants. Thus, the researcher randomly selected five locations from a large selection of locations, with location representing a randomly ­selected environment. To reduce the effect of the different colonies of fire ants and the types of mounds they inhabit, the researcher created 40 artificial fire ant mounds and populated them with 50,000 ants having similar ancestry. The researcher randomly assigned 2 mounds to each of the 20 treatment€“ location combinations. The numbers of fire ants killed during a 1-week period were recorded. The numbers of fire ants killed (in thousands) are given here.

a. Write an appropriate linear statistical model for this study. Identify all the terms in your model.
b. Compute the sum of squares for this experiment, and report this value in an AOV table. Be sure to include the expected mean squares column in the AOV table.

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Chemicals Locations 1 2 72 4.2 9.5 54 96 35 9.3 3.9 8.5 2.9 886.3 9.6 3.3 9.2 6.0 9.1 18 7.6 6.1 8.6 2.4 7.1 5.6 82 3.6 73 5.0 90 4.4 7.0 54 7.8 3.7 9.265 8.0 3.9 8.3 6.9