A State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 900 hours. A manufacturer claims that its new brands of bulbs, which cost the same as the brand the university currently uses, has a mean life of more than 900 hours. The university has decided to purchase the new brand if, when tested, the test evidence supports the manufacturer's claim at the .05 significance level. Suppose 64 bulbs were tested with the following results: the sample mean is 920 hours and s = 80 hours.
a) Find the rejection region for the test of interest to the State University.
b) Conduct the test using alpha = .05.