13. Catalytic reaction experiment J.R. Bainbridge, in his 1951 article in the journal Industrial and Engineering Chemistry, described a factorial experiment conducted at a small plant carrying out a catalytic gaseous synthesis reaction to remove the product as a liquid solution. A 2-replicate 23 experiment was conducted to study the effects of converter reaction temperature (factor A), throughput rate through the converter (factor B), and the concentration of the active ingredient in the makeup gas (factor C) on each of several response variables, including the strength of the product solution (yhijk ). The design was composed of four blocks of size four, with the ABC interaction completely confounded. The design and data are provided in Table 13.28, including the run order. (The observations in Table 13.28 are “uncoded,” each value being 80 plus one-tenth the coded value given by Bainbridge.)

(a) Based on the run order, discuss how the design was probably randomized.

(b) Fit an appropriate model, and use residual plots to check the standard model assumptions.

(c) Conduct the analysis of variance, and discuss the results.

(d) Using a simultaneous confidence level of 95% for all six factorial effects, construct confidence intervals for those effects found to be significant in the analysis of variance.