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 p be the average carry distance he can send using the new club. H03 Ha: (b) (10 pts) The player really does not want to make a mistake of not accepting the offer while the new club is still (at least) as good as current one. i. (5 pts) Which error should be controlled? ii. (5 pts) Would he prefer the error above to be low? (c) (10 pts) Consider using X, the sample mean distance from n : 60 shots using the new club, as the test statistic. He proposed rejecting Ho if his average distance out of 60 shots using the new club falls below 280 yards. i. (5 pts) Find a, the type I error probability of this test. (Hint : It barely requires calculation)