An experiment is conducted to determine the effect of C2F6 flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Three flow rates are used in the experiment, and the resulting uniformity (in percent) for six replicates is shown below:

An experiment is conducted to determine the effect of C2F6 flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Three flow rates are used in the experiment, and the resulting uniformity (in percent) for six replicates is shown below: Observations C2 F6 Flow 1 2 3 4 5 6 125 2.7 4.6 2.6 3 3.2 3.8 160 4.9 4.6 5 4.2 3.6 4.2 250 4.6 3.4 2.9 3.5 4.1 5.1 (a) Does C2F6 flow rate affect etch uniformity? Construct box plots to compare the factor levels and perform the analysis of variance. Use a = 0.05. (b) Check the homogeneity of variances and normality of residuals. Do the residuals indicate any problems with the underlying assumptions? (c) Use Fisher's LSD method with a = 0.05 test to analyze the means of the three flow rates. (d) Suppose that the true mean for uniformity (in percent) on the indicated C2F6 flow rates (125, 160, 250) are 3.3, 4.4, 4.0, respectively. Moreover, assume - = 0.5. Then, how much is the probability of detecting the effect of C2F6 flow rate on etch uniformity in this experiment? Use a = 0.05