Question: Fat in diets. A researcher studied the effects of three experimental diets with varying fat contents on the total lipid (fat) level in plasma. Total lipid level is a widely used predictor of coronary heart disease. Fifteen male subjects who were within 20 percent of their ideal body weight were grouped into five blocks according to age. Within each block, the three experimental diets were randomly assigned to the three subjects. Data on reduction in lipid level (in grams per liter) after the subjects were on the diet for a fixed period of time follow.

a- Why do you think that age of subject was used as a blocking variable?

b- Obtain the residuals for randomized block model (21.1) and plot them against fitted values. Also prepare a normal probability plot of the residuals. What are your findings?

c- Plot the responses \(Y_{i j}\) by blocks in the format or Figure 21.2. What does this plot suggest a bout the appropriateness of no- interaction assumption here?

d- Conduct the Tukey test for additivity of block and treatment effects; use \(\alpha=.001\). State the alternatives, decision rule, and conclusion. What is the P-value of the test?

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