An experiment, conducted in a split-plot design to determine the effect of three bacterial inoculation treatments applied to two cultivars of grasses on dry weight yields, is discussed in Littell et al. (1991). The cultivar is the whole-plot factor and inoculi, the subplot factor. Each of the two cultivars is replicated four times. The data are as follows:

Replication I II III IV Cultivar Cultivar Cultivar Cultivar Inoculi AB A B A B A B Control Use a SAS proc mixed program to analyze this data and provide answers to the following questions:

a. Write the appropriate model for the analysis of these data, explaining each term in the model and the assumptions made about these.

b. Construct an analysis of variance table needed to analyze these data.

Include a column of expected mean squares.

c. Use the ANOVA table to test whether the mean dry weights are significantly different among the three inoculation levels using α =

0.05. What is the standard error of an inoculation level mean?

d. Use the ANOVA table to test whether the mean dry weights are significantly different among the three two cultivars using α = 0.05.

What is the standard error of a cultivar mean?

e. Construct confidence intervals for comparing the cultivar means of the two inoculi with the control, adjusted for multiple testing.