When factors A and B are fixed but factor C is random and the restricted model is used (see the footnote on page 438; there is a technical complication with the unrestricted model here), and E(MSE) = (2.

E(MSA) = (2 + JL(2AC + JKL / I - 1 (α2i

E(MSB) = (2 + JL(2BC + IKL / J - 1 (β2j

E(MSC) = (2 + IJL(2c

E(MSAB) = (2 + L(2ABC

E(MSAC) = (2 + JL(2AC
E(MSBC) = (2 + IL(2BC
E(MSABC) = (2 + (2ABC
a. Based on these expected mean squares, what F ratios would you use to test H0: (2ABC = 0; H0: (2C = 0; H0: H0: γABgij = 0 for all i, j; and H0: a1 = ... = a1 = 0?
b. In an experiment to assess the effects of age, type of soil, and day of production on compressive strength of cement/soil mixtures, two ages (A), four types of soil (B), and three days (C, assumed random) were used, with L = 2 observations made for each combination of factor levels. The resulting sums of squares were SSA = 14,318.24, SSB = 9656.4 SSC = 2270.22, SSAB = 3408.93, SSAC = 1442.58, SSBC = 3096.21, SSABC = 2832.72, and SSE = 8655.60. Obtain the ANOVA table and carry out all tests using level .01?

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ΣΣ KL (I – 1)(J – 1)