The New York Yankees have won the American League pennant 40 times.Of those 40 t
ID: 2954655 • Letter: T
Question
The New York Yankees have won the American League pennant 40 times.Of those 40 times, the Yankees have won the series 27 times.Calculate all probabilities to at least tenth of a percent.a) Assuming the probability of either team winning any given WorldSeries is 50%, what is the the probability that the Yankees win 27out of 40 World Series?
b) The Yankees empirical probability of winning the World Series is67.5%. Suppose the Yankees are so good that this is the correctprobability of them winning any given World Series that they'veappeared in. What is the probability that they win 27 out of 40World Series under this assumption?
c)Go back tot the assumption that either team winning any givenWorld Series is 50%. Do you think this accomplishment by theYankees is statistically significant? Preform all fours steps of aone-proportion z-test to confirm or deny?
Explanation / Answer
a) Assuming the probability of either team winning any given WorldSeries is 50%, what is the the probability that the Yankees win 27out of 40 World Series? Given p=0.5, phat=27/40=0.675 The probability is P(phat>0.675) =P((phat-p)/p*(1-p)/n >(0.675-0.5)/sqrt(0.5*(1-0.5)/40)) =P(Z>2.21) =0.0135 (check normal table) b) The Yankees empirical probability of winning the World Series is67.5%. Suppose the Yankees are so good that this is the correctprobability of them winning any given World Series that they'veappeared in. What is the probability that they win 27 out of 40World Series under this assumption? The probability is P(phat>0.675) =P((phat-p)/p*(1-p)/n >(0.675-0.675)/sqrt(0.5*(1-0.5)/40)) =P(Z>0) =0.5 (check normal table) c)Go back tot the assumption that either team winning any givenWorld Series is 50%. Do you think this accomplishment by theYankees is statistically significant? Preform all fours steps of aone-proportion z-test to confirm or deny? The test hypothesis is Ho:p=0.5 Ha:p > 0.5 The test statistic is Z=(phat-p)/p*(1-p)/n =(0.675-0.5)/sqrt(0.5*0.5/40) =2.21 If =0.05, Z(0.05)=1.645, Z=2.21>1.645, we reject Ho.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.