Chapter 11.1, Problem 2E

Four different coatings are being considered for corrosion protection of metal pipe. The pipe will be buried in three different types of soil. To investigate whether the amount of corrosion depends either on the coating or on the type of soil, 12 pieces of pipe are selected. Each piece is coated with one of the four coatings and buried in one of the three types of soil for a fixed time, after which the amount of corrosion (depth of maximum pits, in .0001 in.) is determined. The data appears in the table.

		Soil Type (B)
		1	2	3
Coating (A)	1	64	49	50
	2	53	51	48
	3	47	45	50
	4	51	43	52

a. Assuming the validity of the additive model, carry out the ANOVA analysis using an ANOVA table to see whether the amount of corrosion depends on either the type of coating used or the type of soil. Use α = .05.

b. Compute $\hat{\mu }$, ${\hat{\alpha }}_1$, ${\hat{\alpha }}_2$, ${\hat{\alpha }}_3$, ${\hat{\alpha }}_4$, ${\hat{\beta }}_1$, ${\hat{\beta }}_2$, and ${\hat{\beta }}_3$.