In Exercise 39, suppose a low water temperature has been used to obtain the data. The en...

In Exercise 39, suppose a low water temperature has been used to obtain the data. The entire experiment is then repeated with a higher water temperature to obtain the following data. Use Yates’s algorithm on the entire set of 48 observations to obtain the sums of squares and ANOVA table, and then test appropriate hypotheses at level .05.

Reference exercise 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 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.