A company that receives shipments of batteries tests a random sample of 16 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 40 hours. From past experience, it is safe to conclude that the population distribution of lifetimes is normal with a standard deviation of 4 hours. For one particular shipment the mean lifetime for a sample of 16 batteries was 38.5 hours.

a. Test, at the 10% level, the null hypothesis that the population mean lifetime is at least 40 hours.

b. Find the power of a 10%-level test when the true mean lifetime of batteries is 39 hours.