A completely randomized design is conducted with five levels of factor A randomly selected from a population of levels, six levels of factor B randomly selected from a population of levels, and three levels of factor C the only levels of interest to the researcher. The experiment will be implemented by randomly assigning 10 experimental units to the 90 treatments obtained by crossing the levels of factors A, B, and C.
a. Write a linear statistical model for this experiment. Identify all the terms in your model, and state all the conditions that are imposed on these terms.
b. Display a partial AOV table, including degrees of freedom and expected mean squares for all sources of variation.
c. For each of the main effects and interactions, display the ratio of mean squares that would be the appropriate F statistic for testing the significance of each of the terms.