The article "Factorial Experiments in the Optimization of Alkaline Wastewater Pretreatment" (M. Prisciandaro, A. Del Borghi, and F. Veglio, Industrial Engineering and Chemistry Research, 2002:5034-5041) presents the results of several experiments to investigate methods of treating alkaline wastewater. One experiment was an unreplicated 24 design. The four factors were A: concentration of sulfuric acid, B: temperature, C: time, and D: concentration of calcium chloride. The outcome variable is the amount of precipitate in kg/m3. The results are presented in the following table.

a. Estimate all main effects and interactions.
b. Which effects seem to be larger than the others?
c. Assume that all third- and higher-order interactions are equal to 0, and add their sums of squares. Use the result in place of an error sum of squares to compute F statistics and P-values for the main effects. Which factors can you conclude to have an effect on the outcome?
d. The article described some replicates of the experiment, in which the error mean square was found to be 1.04, with four degrees of freedom. Using this value, compute F statistics and P-values for all main effects and interactions.
e. Do the results of part (d) help to justify the assumption that the third- and higher-order interactions are equal to 0? Explain.
f. Using the results of part (d), which factors can you conclude to have an effect on the outcome?

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A B D Outcome A B C D Outcome 1-1 1-1 1-1 1-1 6.4 12.9 8.6 12.9 7.4 12.0 10.7 15.0 11.9 13.1 12.1 16.0 12.4 16.5 15.3 18.3 1 -1 1 -1 1 -1 -1