A semiconductor manufacturer has developed three different methods for reducing particle counts on wafers. All three methods are tested on five different wafers and the after treatment particle count obtained. The data are shown below:

Method Count 1 31 10 21 4 1 2 62 40 24 30 35 3 53 27 120 97 68

(a) Do all methods have the same effect on mean particle count?

(b) Plot the residuals versus the predicted response. Construct a normal probability plot of the residuals. Are there potential concerns about the validity of the assumptions?

(c) Based on your answer to part (b), conduct another analysis of the particle count data and draw appropriate conclusions.