When factors A and B are fixed but factor C is random and the restricted model is used (see the footnote on page 438;

there is a technical complication with the unrestricted model here), and

a. Based on these expected mean squares, what F ratios would you use to test for all i, j; and ?

b. In an experiment to assess the effects of age, type of soil, and day of production on compressive strength of cement/soil mixtures, two ages (A), four types of soil (B), and 3 days (C, assumed random) were used, with observations made for each combination of factor levels.

The resulting sums of squares were and . Obtain the ANOVA table and carry out all tests using level .01.