1. (70 pts) A professional golf player considers accepting a sponsoring offer from a new equipment company which requires the use of its product for next several years. He rst wants to see whether the new club can send the ball at least as far as his current club. Driver carry distance of his current club is 280 yards on average, with standard deviation of 5 yards. He believes the standard deviation from the new club will be the same. (a) (5 pts) He wants to accept the offer (because he can make extra money!) as long as he doesn't nd any evidence that the new club sends ball shorter than 280 yards on average. To help him perform a HT, write appropriate hypotheses below. Let 'u be the average carry distance he can send using the new club. H01 Ha: (d) (10 pts) Find the rejection region for X, to obtain a : 0.001. (e) (10 pts) It's possible that he accept the offer While the new club is actually inferior than current one. Although he likes extra money, he doesn't want to use a club that sends 5 yards shorter than current one on average. What is the probability to make this mistake, i.e., 6(275), if the rejection region obtained above is used? (If you could not nd the rejection region above, use :3 g 278)