The state highway department does an experiment to compare three types of surfacing treatments and the response \(y\) is road roughness. The following table also gives average daily traffic volume \(x\).

Suppose the data are, in suitable units,

(a) Perform an analysis of variance on the response variable road roughness. Take \(\alpha=0.05\).

(b) Is there one surface treatment that is better than the others? Answer by finding the Bonferroni 95% simultaneous confidence intervals for the differences of the means.

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Treatment I Treatment 2 Treatment 3 957 423 y 9 5 x y x Y x 552 12 3 3 5 10 2 2 5 1 1