α= 4 and β=7
Because of safety considerations, in May 2021 the Federal Aviation Administration (FAA) changed its guidelines for how small commuter airlines must estimate passenger weights. Under the old rule, airlines used 160 pounds as a typical passenger weight (including carry-on luggage) in warm months. A journal reported that an airline conducted a study to estimate average passenger plus carry-on weights. They found an average summer weight of 10aß pounds. Suppose that each of these estimates was based on a random sample of 100 passengers and that the sample standard deviations were 15 pounds for the summer weights, Construct a 95% confidence interval for the mean summer weight (including carry-on luggage) of this airline's passengers. (Show the detailed steps, and round your answer to three decimal places.)