Question: Imitation pearls. Preliminary research on the production of imitation pearls entailed studying the effect of the number of coats of a special lacquer (factor A) applied to an opalescent plastic bead used as the base of the pearl on the market value of the pearl. Four batches of 12 heads (factor B) were used in the study, and it is desired to also consider their effect on the market value. The three levels of factor A (6, 8, and 10 coats) were fixed in advance, while the four batches can be regarded as a random sample of batches from the bead production process. The market value of each pearl was determined by a panel of experts. The market value data (coded) follow.

Assume that mixed ANOVA model (25.42) is applicable.

1. Test for interaction effects; use \(\alpha=.05\). State the alternatives, decision rule, and conclusion. What is the \(P\) -value of the test?
2. Test for factor \(A\) and factor \(B\) main effects. For each test, use \(\alpha=.05\) and state the alternatives, decision rule, and conclusion. What is the \(P\) -value for each test?
3. Estimate \(D_{1}=\mu_{2} .-\mu_{1}\). and \(D_{2}=\mu_{3} .-\mu_{2}\). by means of the Bonferroni procedure with a 90 percent family confidence coefficient. State your findings.

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