Product quality assurance (QA) is a particularly tricky business in the dye manufacturing industry. A slight variation in reaction conditions can lead to a measurable change in the color of the product, and since customers usually require extremely high color reproducibility from one shipment to another, even a small color change can lead to rejection of a product batch. 

Suppose the various color frequency and intensity values that comprise a color analysis are combined into a single numerical value, C, for a particular yellow dye. During a test period in which the reactor conditions are carefully controlled and the reactor is thoroughly cleaned between successive batches (not the usual procedure), product analyses of 12 batches run on successive days yield the following color readings: 

(a) The QA specification for routine production is that a batch that falls more than two standard deviations away from the test period mean must be rejected and sent for reworking. Determine the minimum and maximum acceptable values of C. 

(b) A statistician working in quality assurance and a production engineer are having an argument. One of them, Frank, wants to raise the QA specification to three standard deviations and the other, Joanne, wants to lower it to one. Reworking is time-consuming, expensive, and very unpopular with the engineers who have to do it. Who is more likely to be the statistician and who the engineer? Explain. 

(c) Suppose that in the first few weeks of operation relatively few unacceptable batches are produced, but then the number begins to climb steadily. Think of up to five possible causes, and state how you might go about determining whether or not each of them might in fact be responsible for the drop in quality.

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Batch 2 3 4 5 6 7 8 9 | 10 11 12 C 74.3 71.8 72.0 73.1 75.1 72.6 | 75.3 73.4 74.8 72.6 73.0 73.7