experiment to investigate the effect of the colour of paper (blue, green, orange) on response rates for questionnaires distributed

In an experiment to investigate the effect of the colour of paper (blue, green, orange) on response rates for questionnaires distributed by the “windshield method” in supermarket parking lots, 18 representative supermarket parking lots were chosen in a metropolitan area, so that each colour was assigned at random to six lots. The response rates (in %) follow. Assume that a one-way classification model is appropriate. 

(a)    Specify the one-way classification model in a formal way. And obtain the fitted values for the model parameters.

(b)   Obtain the residuals.

(c)   Compile the ANOVA table.

(d)   Conduct a size 0.1 test to determine whether or not the mean response rates for the three colours differ.

(e)   When informed of the findings, an executive said: ”See?  I was right all along.  We might as well print the questionnaires on plain white paper, which is cheaper.”

Does this conclusion follow from the findings of the study? Discuss.

Question 2

In their report to the Senate Public Works Committee, Texaco Inc. presented a dataset as evidence that the Octel filter, developed by Associated Octel Com- pany for reducing air pollution, was at least as good as a standard silencer in controlling vehicle noise levels. The findings were based on a 2-way factorial experiment with 6 replications. The two factors are:

•    TYPE – type of filter (1 = standard silencer, 2 = Octel filter),

•    SIZE – vehicle size (1 = small, 2 = medium, 3 = large).

The response variable (NOISE) is the noise level reading in decibels. The com- plete dataset is detailed below:

 SIZE    TYPE                         NOISE

(a)    Write down an expression of a two-way classification model relevant to the above study. Specify the model assumptions carefully.

(b)   Compile an ANOVA table for testing whether there are interaction effects between the two factors at the 5% significance level.

(c)   Based on the outcome of the test in (b), it is recommended that the com- parison between standard silencer and Octel filter be made separately for the three vehicle sizes. Explain.

(d)   Denote by σ2 the variance of an individual noise level reading.

(i)   Calculate the six estimated treatment means obtained by fitting a 2- way classification model to the data.

(ii)  Show that the difference between any two estimated treatment means has variance σ2/3.

(iii)  Extract from the ANOVA table in (b) an estimate of σ2.

(iv)   Calculate a 95% confidence interval for the difference in the expected noise level reading between standard silencer and Octel filter for small vehicles.

(v)   Calculate a 95% confidence interval for the difference in the expected noise level reading between standard silencer and Octel filter for medium vehicles.