39. 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 cleaning ability of a solution in washing tests (a larger number indicates better cleaning ability than a smaller number).

Factor Levels ABC Condition Observations 1 1 1 (1) 106, 93, 116 211 a 198, 200, 214 121 b 197, 202, 185 221 ab 329, 331, 307 112 c 149, 169, 135 212 ac 243, 247, 220 122 bc 255, 230, 252 222 abc 383, 360, 364

a. After obtaining cell totals xijk., compute estimates of
1, AC 11, and AC 21.

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 
.05.