Problem 13.21 Refer to Example 13.16. An exploratory analysis of the data indicated that the effect of the factor X4 (deposition time) on Y1 was significant, but its effect on Y2 was not. This suggests that we study both Model (Y1 | X4, X8, X4*X8) and Model (Y2 | X4, X8, X4*X8).

(a) Rearrange the data for Model (Y1 | X4, X8, X4*X8) in the standard order; use the for[1]mat of Table 13.17.

(b) Perform the analysis of variance and test for the existence of main effects and interac[1]tions. Use α = 0.05.

(c) Consider the Model (Y2 | X4, X8, X4*X8). Rearrange the data for this model in the standard order; use the format of Table 13.15.

(d) Perform the analysis of variance and test for the existence of main effects and interac[1]tions. Use α = 0.05.

(e) Combining the results from parts

(b) and

(d) is it reasonable to conclude that the effect of deposition time on epitaxial thickness is significant and that its effect on Y2 (process variance) is not? Justify your answer.

Problem 13.22 The following data came from a complete 23 factorial experiment with three replicates for each treatment combination.

Treatment Replicates Combination 1 48, 37, 58 a 94, 90, 107 b 94, 91, 93 ab 160, 156, 154 c 70, 75, 68 ac 117, 114, 110 bc 123, 105, 126 abc 187, 170, 182

(a) Prepare a table similar in format to Table 13.23 listing all the contrasts and estimates of the main effects and interactions.

(b) Using the results obtained in part

(a) compute the sums of squares for each main and interaction effect.

(c) Given the information that SST = 39811.96 and SSE = 863.33 compute the proportion of the total variability explained by each main effect and interaction. Rank the effects in decreasing order of importance as measured by SS(effect)/SST.

(d) Using the information obtained in parts

(b) and

(c) compute the ANOVA table in a format similar to Table 13.24. Are your final results consistent with the preliminary con[1]clusions you obtained in part (c)? Comment.