In their report to the Senate Public Works Committee, Texaco Inc. presented a dataset as evidence that the Octel filter, developed by Associated Octel Company 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 complete dataset is detailed below:

Denote by ? ² 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 ? ²/3.

(iii) Extract from the ANOVA table in (b) an estimate of ? 2 .

(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.

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

With reference to the above findings, do you think that the claim of Texaco Inc. is supported by the observed data? Explain.