Suppose that in Problem 13-13 a large number of power settings could have been used and that the two selected for the experiment were chosen randomly. Obtain the expected mean squares for this situation assuming the restricted form of the mixed model and modify the previous analysis appropriately.

Problem 13-13

A process engineer is testing the yield of a product manufactured on three machines. Each machine can be operated at two power settings. Furthermore, a machine has three stations on which the product is formed. An experiment is conducted in which each machine is tested at both power settings, and three observations on yield are taken from each station. The runs are made in random order, and the results follow. Analyze this experiment, assuming that all three factors are fixed.

 

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Machine 1 Machine 2 Machine 3 Station 1 2 3 1 2 3 1 2 3 34.1 33.7 36.2 31.1 33.1 32.8 32.9 33.8 33.6 Power setting 1 30.3 34.9 36.8 33.5 34.7 35.1 33.0 33.4 32.8 31.6 35.0 37.1 34.0 33.9 34.3 33.1 32.8 31.7 24.3 28.1 25.7 24.1 24.1 26.0 24.2 23.2 24.7 Power setting 2 26.3 29.3 26.1 25.0 25.1 27.1 26.1 27.4 22.0 27.1 28.6 24.9 26.3 27.9 23.9 25.3 28.0 24.8