Refer to Solution concentration Problem 3. 15. Suppose the chemist initially wishes to employ ANOVA model (16.2)

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Refer to Solution concentration Problem 3. 15. Suppose the chemist initially wishes to employ ANOVA model (16.2) to determine whether or not the concentration of the solution is affected by the amount of time that has elapsed since preparation.

a. State the analysis of variance model.

b. Prepare a main effects plot of the estimated factor level means Y _i What does this plot suggest about the relation between the solution concentration and time?

c. Obtain the analysis of variance table.

d. Test whether or not the factor level means are equal; use α= .025. State the alternatives, decision rule, and conclusion.

e. Make pairwise comparisons of factor level means between all adjacent lengths of time; use the Bonferroni procedure with a 95 percent family confidence coefficient. Are your conclusions in accord with those in part (b)? Do your results suggest that the regression relation is not linear?

Problem 3.15

Solution concentration. A chemist studied the concentration of a solution (Y) over time (X). Fifteen identical solutions were prepared. The is. solutions were randomly divided into five sets of three, and the five sets were measured, respectively, after I, 3, 5, 7, and 9 hours. The results follow.

a Fit a linear regression function.

b. Perform the F test to determine whether or not there is lack of fit of a linear regression function; use α = .025. State the alternatives, decision rule, and conclusion.

c. Does the test in part (b) indicate what regression function is appropriate when it leads to the conclusion that lack of fit of a linear regression function exists? Explain.