2. A 2-1 fractional factorial was conducted to study the effects of four factors on the bond strength of an integrated circuit mounted on metallized glass substrate. The four factors and their levels) that engineers identified as potentially important determiners of bond strength are listed in the table below. Factor Levels A- Adhesive Type D2A (-) vs. H-1-E (+) B - Conductor Material Copper (-) vs. Nickel (+) C- Cure Time at 90C 90 min (-) vs. 120 min (+) D- Deposition Material Tin (-) vs. Silver (+) Let a = main effect of A, B = main effect of B, Xx = main effect of C, 8, = main effect of D, and y = interaction effect. Summary statistics and the results of the Yates algorithm for computing fitted effects are given below. Treatment Replication (1) bd Sample Sample Variance s2 Mean Cycle 1 2.452 73.48 157.36 4.233 83.88 157.18 0.647 81.58166.60 26.711 75.60 | 169.70 0.503 87.06 | 10.40 8.562 79.54 -5.98 1.982 79.38 -7.52 3.977 90.32 10.94 Yates Algorithm Cycle 2 Cycle 3 314.54 650.84 336.30 7.84 4.42 2.92 3.42 2.08 -0.18 21.76 3.10 -1.00 -16.38 3.28 18.46 34.84 ab cd ac Fitted Effect 81.355 0.980 0.365 0.260 2.720 -0.125 0.410 4.355 bc abcd a. The replications and the sample variances of the 8 treatment combinations are given in the 2nd and 3rd columns, respectively, in the table above. Computer(0.05) for judging if a fitted effect is statistically significant at the a = 0.05 level. Note that the sum of the variances is 49.067. [8 pts] b. The generator and defining relation were D-ABC and I=ABCD, respectively. If you have no answer in (a), use r(0.05) = 0.400. i. Based on your answer in (a), is the fitted effect 0.980 statistically significant? [2 pts] Select one: NO YES ii. What sum of effects does the fitted effect 0.980 estimate? Your answer should be a sum of subscripted/superscripted Greek letters (e.g., az + y22) (4 pts] 2. A 2-1 fractional factorial was conducted to study the effects of four factors on the bond strength of an integrated circuit mounted on metallized glass substrate. The four factors and their levels) that engineers identified as potentially important determiners of bond strength are listed in the table below. Factor Levels A- Adhesive Type D2A (-) vs. H-1-E (+) B - Conductor Material Copper (-) vs. Nickel (+) C- Cure Time at 90C 90 min (-) vs. 120 min (+) D- Deposition Material Tin (-) vs. Silver (+) Let a = main effect of A, B = main effect of B, Xx = main effect of C, 8, = main effect of D, and y = interaction effect. Summary statistics and the results of the Yates algorithm for computing fitted effects are given below. Treatment Replication (1) bd Sample Sample Variance s2 Mean Cycle 1 2.452 73.48 157.36 4.233 83.88 157.18 0.647 81.58166.60 26.711 75.60 | 169.70 0.503 87.06 | 10.40 8.562 79.54 -5.98 1.982 79.38 -7.52 3.977 90.32 10.94 Yates Algorithm Cycle 2 Cycle 3 314.54 650.84 336.30 7.84 4.42 2.92 3.42 2.08 -0.18 21.76 3.10 -1.00 -16.38 3.28 18.46 34.84 ab cd ac Fitted Effect 81.355 0.980 0.365 0.260 2.720 -0.125 0.410 4.355 bc abcd a. The replications and the sample variances of the 8 treatment combinations are given in the 2nd and 3rd columns, respectively, in the table above. Computer(0.05) for judging if a fitted effect is statistically significant at the a = 0.05 level. Note that the sum of the variances is 49.067. [8 pts] b. The generator and defining relation were D-ABC and I=ABCD, respectively. If you have no answer in (a), use r(0.05) = 0.400. i. Based on your answer in (a), is the fitted effect 0.980 statistically significant? [2 pts] Select one: NO YES ii. What sum of effects does the fitted effect 0.980 estimate? Your answer should be a sum of subscripted/superscripted Greek letters (e.g., az + y22) (4 pts]
