Question

Problem 3.1. Cardiac pacemakers contain electrical connections that are platinum pins soldered onto a substrate. The question of interest is whether different operators produce solder joints with the same strength. Twelve substrates are randomly assigned to four operators. Each operator solders four pins on each substrate, and then these solder joints are assessed by measuring shear strength of the pins Strength (lbs) Substrate 2 5.60 6.80 8.32 8.707.64 7.44 7.48 7.80 7.72 8.40 6.98 8.00 5.04 7.38 5.56 6.96 8.30 6.86 5.62 7.22 5.72 6.40 7.54 7.50 8.36 7.04 6.92 8.186.20 6.10 2.75 8.14 9.00 8.64 6.60 8.18 8.30 8.54 7.68 8.92 8.46 7.38 8.08 8.128.68 8.24 8.09 8.06 Operator Substrate 1 Substrate 3 4 a) Describe the design and write the model equation in both the means and effect:s parameterization. What dependent variable did you use? Define model equation terms State any assumptions about the random effects terms in the model equation Use PROC GLM to obtain the analysis of variance (ANOVA) table for these data. Test the null hypothesis that the mean solder joint strength is the same for the different operators. Express your conclusion to the hypothesis test in terms of the application (as opposed to a purely statistical conclusion) b) c)

Answer 1

Data frame of the randomized block design to study the joining strengths of the 4 operators: Operators A B C D E FGHIJK L 5.6 6.8 8.328.7 7.64 7.44 7.48 7.8 7.72 8.4 6.988 2 5.04 7.38 5.56 6.96 8.3 6.86 5.62 7.22 5.72 6.4 7.54 7.5 3 8.36 7.04 6.92 8.18 6.2 6.1 2.75 8.14 9 8.64 6.6 8.18 4 8.3 8.54 7.68 8.92 8.46 7.38 8.08 8.12 8.68 8.24 8.09 8.06 5.6 6.8 8.32 8.7 7.64 7.44 7.48 7.8 7.72 8.4 6.98 5.04 7.38 5.56 6.96 8.3 6.86 5.62 7.22 5.72 6.4 7.54 7.5 | 8.36 7.04 6.92 8.18 6.2 6.1 2.75 8.14 9 8.64 6.6 8.18 8.3 8.54 7.68 8.92 8.46 7.38 8.08 8.12 8.68 8.24 8.09 8.06 Data- trows(Data)-4 ci cols (Data) 12 T.c-48 it 0,1..r-1 X.Data