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 beads (factor B) were used in the study, anditis 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) follows.

Factor A Factor B (batch) (number of coats) j = 1 j=2 j=3 j=4 i = 1 6 72.0 72.1 75.2 70.4 72.8 73.3 77.8 72.4 i = 2 8 76.9 80.3 80.2 74.3 74.2 77.2 79.9 72.9 i = 3 10 76.3 80.9 79.2 71.6 75.0 80.2 81.2 74.4

1. Test for interaction effects; use a= .05. State the alternatives, decision rule, and conclusion. What is the P-value of the test?
2. Test for factor Aand factor B main effects. For each test, use a= .05 and state the alternatives, decision rule, and conclusion. What is the P-value for each test?

c. Estimate D1= 2- 1 and D2 = 3 .- 2. by means of the Bonferroni procedure with a 90 percent family confidence coefficient State your findings.

d. Use the Satterthwaite procedure to obtain an approximate 95 percent confidence interval for ₂.. Interpret your confidence interval.

1. Use the MLS procedure to obtain an approximate 90 percent confidence interval fors²b.

Does s²b,appear to be large compared tos²?

f.Was it meaningful to test for A and B main effects in part b?

g.Obtain a point estimate ofs²ab, and interpret the result

h.Obtain a point estimate ofs²b. How does it compare with random error?

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