Solved: An experiment was conducted to compare three types

Chapter 13, Problem 13.36

(choose chapter or problem)

An experiment was conducted to compare three types of coating materials for copper wire. The purpose of the coating is to eliminate “flaws” in the wire. Ten different specimens of length 5 millimeters were randomly assigned to receive each coating, and the thirty specimens were subjected to an abrasive wear type process. The number of flaws was measured for each, and the results are as follows:

Suppose it is assumed that the Poisson process applies and thus the model is \(Y_{ij} = \mu_i +  \epsilon_{ij}\) , where μi is the mean of a Poisson distribution and \(\sigma^2_{Y_{ij}} = \mu_i\).

(a) Do an appropriate transformation on the data and perform an analysis of variance.

(b) Determine whether or not there is sufficient evidence to choose one coating material over the other. Show whatever findings suggest a conclusion.

(c) Do a plot of the residuals and comment.

(d) Give the purpose of your data transformation.

(e) What additional assumption is made here that may not have been completely satisfied by your transformation?

(f) Comment on (e) after doing a normal probability plot on the residuals.