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A high-speed production line was making a small number of critical defects. A quality engineer randomly collected 100 defects. He examined them and found that

A high-speed production line was making a small number of critical defects. A quality engineer randomly collected 100 defects. He examined them and found that 22 defects were from the first quadrant of the product, 36 from the second, 21 from the third, and 21 from the fourth. He concluded that there was less than a 1% chance that 36 or more defects out of 100 would be coming from the second quadrant due to random causes alone.

So he went looking for anything suspicious on the production line that was exclusive to the second quadrant. He found a cooling nozzle from which some of the spray hit the second quadrant of the product. Since the product was very hot at that point in the process, he suspected dial stress was being introduced.

When he asked the operator why he had put the spray at that location, he was told that it was being used to cool the tooling that was adjacent to the product at this point. The engineer than designed a more directed spray method that missed the product but hit the tooling, which allowed adequate cooling and also solved the problem of excess defects in that quadrant.

At what maximum level of confidence, you can conclude that excessive defects in the second quadrant were not due to random causes alone? (You are required to show all the steps involved in the calculation.)

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