A casting machine is supposed to produce units for which the standard deviation of weights is 0.4 ounces. According to the maker of the machine, it should be shut down and thoroughly examined for wear if the standard deviation becomes greater than the 0.4 ounces that has been specified. In a random sample of 30 units recently produced by the machine, the standard deviation is found to be 0.82 ounces.
Given this information, and assuming a normally distributed population of weights, would you feel very secure in advising management that the machine should be shut down?
Use the approximate p-value of the test for assistance in formulating your answer.