Beer is pasteurized by subjecting it to processes in manufacturing and packaging that attempt to kill, inactivate, or remove all yeast cells or other microorganisms, thereby preventing any further fermentation or microbiological decomposition of the packaged beer that might otherwise take place. Pasteurization impacts both the safety of the product and, more important, the taste of the beer. Therefore, in order to guarantee that the pasteurization has been effectively implemented, beer manufacturers have well-defined testing procedures. A large beer manufacturer has numerous breweries and is concerned about the variability in the effectiveness of the pasteurization process across its many facilities. Preliminary studies indicated that the manufacturer€™s many testing laboratories had varying ability to accurately determine the level of contamination in the beer. The manufacturer€™s quality control staff decided to concentrate its efforts on examining the variability in the level of contamination due to the effectiveness of the pasteurization processes and the variability due to the laboratory€™s determination of level of contamination.
The manufacturer€™s research staff designed the following study. Six laboratories are selected at random from the manufacturer€™s many breweries. Ten different pasteurization processes are randomly selected, and 12 samples of beer are selected from each of these processes. Two samples from each process are then sent to each laboratory. The laboratories count the microorganisms in each sample. The beer samples are coded so that the laboratories do not know which pasteurization process had treated the beer. The counts (units per μ1) from the 10 laboratories are given here.

a. Write an appropriate linear statistical model, identifying all terms in the model.
b. Write down the expected mean squares.
c. State the null and alternative hypotheses for testing for an interaction effect, an effect due to laboratory, and an effect due to process.

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