In controlling the quality of a new drug, a dose of medicine is supposed to contain an average of 247 parts per million (ppm) of a certain chemical. If the concentration is higher than 247 ppm, the drug may cause some side effects; and if the concentration is below 247 ppm, the drug may be ineffective. The manufacturer wants to check whether the average concentration in a large shipment is the required 247 ppm or not. A random sample of 60 portions is tested, and the sample mean is found to be 250 ppm and the sample standard deviation 12 ppm. Test the null hypothesis that the average concentration in the entire large shipment is 247 ppm versus the alternative hypothesis that it is not 247 ppm using a level of significance α = 0.05. Do the same using α = 0.01. What is your conclusion? What is your decision about the shipment? If the shipment were guaranteed to contain an average concentration of 247 ppm, what would your decision be, based on the statistical hypothesis test? Explain.
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