In an experiment conducted by the Mining Engineering Department at Virginia Tech to study a particular filtering system for coal, a coagulant was added to a solution in a tank containing coal and sludge, which was then placed in a recirculation system in order that the coal could be washed. The factors that were varied in the experimental process included, percent solids circulated initially in the overflow, flow rate of the polymer, and pH of the tank. The amount of solids in the underflow of the cleansing system determines how clean the coal has become. Two levels of each factor were used and two experimental runs were made for each of the treatment combinations. The response measurements in percent solids by weight in the underflow of the circulation system are as specified in the following table (Data provided in spreadsheet): Treatment combination Response
1 4.65 5.81
a 21.42 21.35
b 12.66 12.56
ab 18.27 16.62
c 7.93 7.88
ac 13.18 12.87
bc 6.51 6.26
abc 18.23 17.83
Assuming that all interactions are potentially important do a complete analysis of the data. Use P-values in your conclusion. State your decision and conclusion. Assume alpha = 0.05.Include the results from your analysis to support your decision and conclusion). What levels would you select for the optimal response?