The accompanying data resulted from a 23 experiment with three replications per combinat...

The accompanying data resulted from a 2³ experiment with three replications per combination of treatments designed to study the effects of concentration of detergent (A), concentration of sodium carbonate (B), and concentration of sodium carboxymethyl cellulose (C) on the cleaning ability of a solution in washing tests (a larger number indicates better cleaning ability than a smaller number).

a. After obtaining cell totals x_ijk compute estimates of β₁

b. Use the cell totals along with Yates’s method to compute the effect contrasts and sums of squares. Then construct an ANOVA table and test all appropriate hypotheses using α = .05.