A pigment laboratory is testing both dry additives and solution-based additives to see their effect on the durability rating (a number from 1 to 10) of a finished paint product. The paint to be tested is divided into four equal quantities, and a different combination of the two additives is added to one-fourth of each quantity. After a prescribed number of hours, the durability rating is obtained for each of the 16 samples, and the results are recorded below in the appropriate space.

Can an interaction be concluded between the dry and solution additives? Is there a difference in mean durability rating with respect to dry additive used? With respect to solution additive? Use α = 0.05.

Perform these steps. Assume that all variables are normally or approximately normally distributed, that the samples are independent, and that the population variances are equal.

a. State the hypotheses.

b. Find the critical value for each F test.

c. Complete the summary table and find the test value.

d. Make the decision.

e. Summarize the results. (Draw a graph of the cell means if necessary.)

Dry additive 1 Dry additive 2 Solution additive A 9, 8, 5, 6 4, 5, 8, 9 Solution additive B 7, 7, 6, 8 10, 8, 6, 7