A private research corporation conducted an experiment to investigate the toxic effects of three chemicals (I, II, and III) used in the tire-manufacturing industry. In this experiment, three adjacent 1-inch squares were marked on the back of each of eight rats, and the three chemicals were applied separately to the three squares on each rat. The squares were then rated from 0 to 10, depending on the degree of irritation. The data are as shown in the following table.

a. What are the blocks and what are the treatments in this randomized-blocks design?
b. Complete the ANOVA table in the accompanying computer output for the data set given.
c. Do the data provide sufficient evidence to indicate a significant difference in the toxic effects of the three chemicals?
d. Using a confidence interval of the form

where v is the degrees of freedom, find a 98% confidence interval for the true difference in the toxic effects of chemicals I and II.
e. Provide a reasonable measure of the proportion of total variation that is explained by the particular statistical model used in analyzing this data set.
f. State the fixed-effects ANOVA model and the corresponding regression model for this analysis.
g. State the assumptions on which the validity of the analysis depends.

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Rat Chemical 2 3 7 Total Total 14 22 18 1923 17 18 19 150 Dependent Variable: score Source Model Error Corrected Total DF Sum of Squares Mean Square F ValuePr> F 43.50000000 4 83333333 2.71 00463 14 23 68.5000000 R-SquareCoeff Var Root MSE score Mean 0.635036 21.38090 336306 6.250000 Source F Type I SS Mean Square F Value Pr> F chem rat 7.00 0.0078 7 18.50000000 2.64285714 1.48 0.2518 Source DF Type ll ss chem Mean Square F Value Pr> F 25.00000000 12.50000000 7.00 0.0078 7 18.50000000 2.64285714 1.48 0.2518