2. In the manufacture of silicon wafers, we wish to see if the machine (A), the operator of the machine (B), and the composition of the material (C) have an effect on the quality of the final product. The company owns only two machines (one at each of their two sites), and they employ many operators. For each of the two machines, three operators will be randomly selected. For the first machine, five large batches of raw product will be prepared. The batches are slightly different in composition, in a way that cannot be pre- cisely controlled. Each operator will conduct three runs of the machine with material from each of the five batches. At the second site, the experiment is conducted in an identical manner. The quality of the material is measured after each run, giving a total of 235x3=90 observations. Unfortunately, their statisticians have never learned about nested and crossed effects, nor about fixed and random effects, and they produce the ANOVA table shown below. They conclude that there are significant differences between operators and between batches. Your job is to correct their work. Source SS df MS F A 4 1 4.0 1.74 B 17 2 8.5 3.70 C 25 4 6.2 2.70 AB 5 2 2.5 1.09 AC 12 4 3.0 1.30 BC 32 8 4.0 1.74 ABC 12 8 1.5 0.65 Error 138 60 2.3 Total 245 89 pval < 0.05 a) Write the correct form of the model, including all details. Make sure to specify the range of all of the indices, and include all of the necessary assumptions about the random terms and restrictions on the fixed terms. b) Produce the corrected ANOVA table, including the expected mean squares and the correct F statistics. If an exact F test is not available, construct an approximate F statistic (for which you need not compute the degrees of freedom).