Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 2

Before a strike prematurely ended the 1994 major league baseball season, Tony Gwynn of the San Diego Padres had 165 hits in 419 at bats, for a.394 batting average. There was discussion about whether Gwynn was a potential.400 hitter that year. This issue can be couched in terms of Gwynn's probability of getting a hit on a particular at bat, call it . Let Yi be the Bernoulli( ) indicator equal to unity if Gwynn gets a hit during his i th at bat, and zero otherwise. Then, Y 1 , Y 2 , …, Y n is a random sample from a Bernoulli( ) distribution, where is the probability of success, and n = 419. Our best point estimate of is Gwynn's batting average, which is just the proportion of successes: =.394. Using the fact that se( ) = , construct an approximate 95% confidence interval for , using the standard normal distribution. Would you say there is strong evidence against Gwynn's being a potential.400 hitter Explain.