A company that receives shipments of batteries tests a random sample of nine of them before agreeing to take a shipment. The company is concerned that the true mean lifetime for all batteries in the shipment should be at least 50 hours. From past experience it is safe to conclude that the population distribution of lifetimes is normal with a standard deviation of 3 hours. For one particular shipment the mean lifetime for a sample of nine batteries was 48.2 hours.,a. Test, at the 10% level, the null hypothesis that the population mean lifetime is at least 50 hours.,b. Find the power of a 10%-level test when the true mean lifetime of batteries is 49 hours.

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