Question 5 (2 parts): Baseball fans marvel at the home runs Willie Mays Hayes (from the movie "Major League"!) hits. To get an idea of how far his home runs travel, a random sample of 6 home runs is used, The distance of each home run in the sample is given below: (440, 460, 420, 470, 460, 450} a. Assuming home run distances are normally distributed (so the Central Limit Theorem applies), construct a 95% confidence interval for the mean home run distance. b. A number of teams are interested in acquiring Hayes for their teams. In particular, the Baltimore Orioles are seriously interested in pursuing him to bolster their sagging offense. The manager of the Orioles thinks that the stadium in Baltimore, Camden Yards, would hurt Hayes's home run production. He estimates that Hayes would need to average better than 430 ft per home run to maintain his home run production in Camden Yards. Is there sufficient evidence at the a - 05 level to put the manager's mind at ease? (use the p value approach) 738612780