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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
10      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 u. Let Yi be the Bernoulli(u) indicator equal to unity if Gwynn gets a hit during his ith at bat, and zero otherwise. Then, Y1, Y2, …, Yn is a random sample from a Bernoulli(u) distribution, where u is the probability of success, and n  419.
Our best point estimate of u is Gwynn’s batting average, which is just the proportion of successes: y-  .394. Using the fact that se(y-)  y¯(1  y¯ )/n, construct an approximate 95% confidence interval for u, using the standard normal distribution. Would you say there is strong evidence against Gwynn’s being a potential .400 hitter? Explain.
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