Download Homework with Solution - Statistics for Engineers | STAT 4706 and more Assignments Statistics in PDF only on Docsity! Stat 4706 HW 5 Solutions Total Points Possible: 23 1) In “Orthogonal Design for Process Optimization and Its Application to Plasma Etching” (Solid State Technology, May 1987), Yin and Jillie describe an experiment to determine the effect of C2F6 on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Three flow rates are used in the experiments, and the resulting uniformity for six replicates is shown below. Observations Flow Rate 1 2 3 4 5 6 125 2.7 4.6 2.6 3.0 3.2 3.8 160 4.9 4.6 5.0 4.2 3.6 4.2 200 4.6 3.4 2.9 3.5 4.1 5.1 a) Using Minitab, generate a boxplot for each of the flow rates (either 3 separate graphs or all 3 boxplots on 1 graph like in the notes). flo w ra te Y 200 160 125 5.04.54.03.53.02.5 Boxplot of Y vs flowrate b) Calculate the SSTreatment, SSError, and SSTotal. SSTOTAL: 11.278 SSTREATMENT: 3.648 SSERROR: 7.630 c) Complete the ANOVA Table below: Source SS Df MS F0 Treatment 3.648 3-1 = 2 3.648/2 = 1.824 3.59 Error 7.630 3(6-1) = 15 7.630/15 = 0.509 otal 11.278 17 Worth 2 points Worth 3 points: each one SS worth 1 point Worth 3 points: each df, MS and F worth 1/2 point each d) Complete a hypothesis test to see if the means of all three flow rates are equal. H0: All of the treatment means are equal. H1: At least one of the treatment means is different. Test Statistic: F=3.59 Rejection Region: Reject H0 if Fcalc > F.05,2,15 = 3.68 Decision: Fail to Reject H0 Conclusion: All of the treatment means are equal. 2) From the results of an ANOVA test on the equality of 3 means, we have found the there is a difference in the means, but need to identify which ones differ. Use the following Minitab output to determine which means differ. One-way ANOVA: Score versus Method Source DF SS MS F P Method 2 416.0 208.0 14.40 0.002 Error 9 130.0 14.4 Total 11 546.0 S = 3.801 R-Sq = 76.19% R-Sq(adj) = 70.90% Level N Mean StDev 1 4 72.000 4.163 2 4 86.000 4.163 3 4 76.000 2.944 Means are significantly different if [ ] [ ] 506975.7 4 1*801.3*95.3 4 1801.3*9,3,05.1*,, ==== q n svkqHSD α 10|7686||)(| 4|7672||)(| 14|8672||)(| 32 31 21 =−=− =−=− =−=− yy yy yy [ ] n svkqyy ji 1*,,|)(| α>− Worth 1 point Worth 1 point Worth 1 point Worth 1 point Worth 3 points: HSD worth 1.5 points, identifying significant differences worth 1.5 points
