The data given in ENGSTAT1224.MTW are from a statement by Texaco, Inc. to the Air and Pollution Subcommittee of the Senate Public Works Committee on June 26, 1973. It was stated that an automobile filter developed by Associated Octel Company was effective in reducing pollution, but questions were raised in regard to various matters, including noise. The president of Texaco, John McKinley, asserted that the Octel filter was at least equal to standard silencers in terms of silencing properties. The data in the file are in the form of a 3 × 22 design with SIZE of the vehicle being 1 = small, 2 = medium, and 3 = large; TYPE being 1= standard silencer and 2 = Octel filter, and SIDE being 1= right side and 2 = left side of the car. The response variable is NOISE.

 

(a) Are these factors fixed or random, or can that be determined? (Remember that the classification of a factor as fixed or random affects the way the analysis is performed when there is more than one factor.)

(b) Since a 3 × 2² design (a mixed factorial) was not covered explicitly in the chapter, initially ignore the SIZE factor and analyze the data as if a replicated 2² design had been used, bearing in mind that the objective of the experiment is to see if the Octel filter is better than the standard filter.

(c) Now analyze the data using all three factors, using appropriate software such as the general linear model (GLM) capability in MINITAB, and compare the results. In particular, why is one particular effect significant in this analysis that was not significant when the SIZE factor was ignored?

(d) Is there an interaction that complicates the analysis? If so, what approach would you take to explain the comparison between the standard filter and the Octel filter?