Question: Hay fever relief. A research laboratory was developing a new compound for the relief of severe cases of hay fever. In an experiment with 36 volunteers. The amounts of the two active ingredients (factors A and B) in the compound were varied at three levels each. Randomization was used in assigning four volunteers to each of the nine treatments. The data on hours of relief follow.

1. Obtain the fitted values for ANOVA model
2. Obtain the residuals.
3. Plot the residuals against the fitted values. What departure from ANOVA model (19.23) can be studied from this plot? What are your findings'?
4. Prepare a normal probability plot of the residuals. Also obtain the coefficient of correlation between the ordered residuals and their expected values under normality. Does the normality assumption appear to be reasonable here?
5. Test whether or not the two factors interact: use $\alpha=0.05$. State the alternatives, decision rule, and conclusion. What is the P-value of the test?
6. Test whether or not main effects for the two ingredients are present. Use Test whether or not main effects for the two ingredients are present. Use $\alpha=.05$ in each case and state the alternatives. Decision rule, and conclusion. What is the P-value of each test'! Is it meaningful here to test for main factor effects? Explain.

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