An entomologist employed by a chemical company is planning a study to evaluate two new chemicals that are potential agents for eliminating fire ants. The chemicals will be evalu­ated at three different dose levels under four different environmental conditions. One hundred ants will be exposed to each of the combinations of a chemical, dose level, and environmental condition, and the number of surviving ants after 3 hours of exposure will be recorded. It is well documented in the literature that there is large variability in the degree of tolerance of fire ants to various chemicals previously used as insecticides. Thus, the company’s statistician recommended that five colonies of ants be used in the study. There are thousands of fire ants per colony.
a. Display how you would randomly assign the groups of 100 ants to the various combinations of chemical– dose– environmental condition.
b. Provide an analysis of variance table for this experiment.