A completely randomized design is conducted with four levels of factor A randomly selected from a population of levels, three levels of factor B randomly selected from a population of levels, and five levels of factor C randomly selected from a population of levels. The experiment will be implemented by randomly assigning five experimental units to the 60 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.