1. It was suspected that a machine producing shafts for wrist watches is in need of an overhaul. Such machines are usually overhauled if the standard deviation of shaft diameter exceeds 0.020mm. A sample run of 30 shafts yielded a sample standard deviation of 0.023mm. Is there statistically significant evidence that the standard deviation exceeds 0.020mm at a significance level of a = 0.01? What is the corresponding P-value?

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