State University Uses Thousands of Fluorescent Light Bulbs Each Year $.05$

State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 800 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 800 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the $.05$ significance level. Suppose 121 bulbs were tested with the following results: $\bar { x } = 830$ hours, $s = 110$ hours. Conduct the test using $\alpha = .05$ .