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An experimenter is studying the performance of 3 machines. E…

An experimenter is studying the performance of 3 machines. Each machine has two heads that produce the output product. She runs a two-stage nested design in which output from all three machines, both heads on each machine, and 4 observations on each machine-head combination are collected. However, the only computer program she has will only analyze factorial designs, so she (incorrectly) analyzes her experiment as a 2-factor factorial with 4 replicates and obtains the following results:   Factor Sum of Squares Degrees of Freedom Machines 50.00 2 Heads 45.00 1 Machine-head interaction 20.00 2 Error 10.00 18 Total 115.00 23   What is the correct sum of squares for the heads-within-machines nested effect?

A 23 factorial experiment with only two replicates (16 runs)…

A 23 factorial experiment with only two replicates (16 runs) has been run in a chemical process. The response variable is molecular weight. The engineer has used the following factors with their natural low and high levels as shown:  A (40, 80), B(100, 130), and C(25, 75).  After conducting the experiment, the engineer computes the quantities in the following table (using coded units):   Term Effect Estimate Sum of Squares % Contribution A 4.50 81.00 19.95 B 6.00 144.00 X C X 16.00 3.94 AB 5.00 100.00 24.63 AC 3.00 36.00 8.87 BC 2.50 X 6.16 ABC 1.00 4.00 0.99   Answer the following questions (1 – 5) about this experiment.  Each question is worth 8 points. Please select the correct answer.