An experiment was conducted to determine the effect of Hexafluoroethane C2F6 flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Four flow rates (in standard cubic centimeter per minute) are used in the experiment and the resulting uniformity (in percent) is shown here. 125 sccm 160 sccm 200 sccm 220 sccm 4.05 3.99 3.97 4.00 4.01 4.02 3.98 4.02 4.02 4.01 3.97 3.99 4.04 3.99 3.95 4.01 4.00 4.00 4.00 a. Identify the independent (factor) and dependent (response) variables in this study. What are the treatments? What are the experimental units? How can this be modelled by a completely randomized design experiment? b. Is the assumption of homogeneity of variances among the 4 groups satisfied? Justify by doing an 8-step procedure using Levene’s approach. Use a 0.05 level of significance. STATISTICA output or PHSTAT output is also required. Is the assumption of normality for each treatment group satisfied? Justify by doing an 8-step procedure using Shapiro Wilk approach. Use a 0.05 level of significance. STATISTICA output is also required.

Question

An experiment was conducted to determine the effect of Hexafluoroethane C2F6 flow rate on the
uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Four flow rates (in
standard cubic centimeter per minute) are used in the experiment and the resulting uniformity (in
percent) is shown here.

125 sccm	160 sccm	200 sccm	220 sccm
4.05	3.99	3.97	4.00
4.01	4.02	3.98	4.02
4.02	4.01	3.97	3.99
4.04	3.99	3.95	4.01
	4.00	4.00
	4.00

a. Identify the independent (factor) and dependent (response) variables in this study. What are the
treatments? What are the experimental units? How can this be modelled by a completely
randomized design experiment?
b. Is the assumption of homogeneity of variances among the 4 groups satisfied? Justify by doing an
8-step procedure using Levene’s approach. Use a 0.05 level of significance. STATISTICA output or
PHSTAT output is also required. Is the assumption of normality for each treatment group
satisfied? Justify by doing an 8-step procedure using Shapiro Wilk approach. Use a 0.05 level of
significance. STATISTICA output is also required.

c. What are the appropriate null and alternative hypotheses for this study? What is the decision rule
using the critical number approach at the 0.05 level of significance? Make a sketch. Construct the
ANOVA table. Show complete solutions for SST, SSTr, SSE, MSTr, MSE, F. Prove that there is
sufficient evidence that different treatments have a significant effect on uniformity at ? = 5% both
by critical value and p-value approaches. STATISTICA output or PHSTAT output is also required.
d. Perform an appropriate post-hoc analysis to determine which treatment means differ. Complete
the Tukey-Kramer multiple pairwise comparisons by computing each absolute paired difference,
the HSD (Q-critical range), and copy the corresponding p-value from STATISTICA results. Or
submit the PHSTAT solution. Summarize your answer.