In a study reported in Dunn and Clark (1987), each of three different sprays were applied to four trees selected at random. After 1 week, the concentration of nitrogen was measured on each of six leaves obtained in a random way from each tree. The data are given in the following table.

a. Write the appropriate model for the analysis of these data, stating the effect each term used in the model represents and the assumptions made about these effects.

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

Include a column of expected mean squares.

Tree Spray Leaf 1234 6.81

c. Use the ANOVA table to test whether the mean nitrogen content resulting from the three sprays is significantly different using α =

0.05.

d. Test an appropriate hypothesis about the variability of nitrogen content among the trees within each spray using α = 0.05.

e. Estimate the variance components of relevant effects of this model by constructing 95% confidence intervals for them.

f. Carry out comparisons of pairwise differences among the mean nitrogen content resulting from the three sprays adjusted for multiple comparisons using the Tukey adjustment.