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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 prob- ability of getting a hit on a particular at bat, call it 0. Let Y; be the Bernoulli(0) indicator equal to unity if Gwynn gets a hit during his ih at bat, and zero otherwise. Then, Y1, Y2, . .., Y, is a random sample from a Bernoulli(0) distribution, where 0 is the probability of success, and n = 419. Our best point estimate of 0 is Gwynn's batting average, which is just the proportion of suc- cesses: ỹ = .394. Using the fact that se(ỹ) = Vy(1 – ỹ)/n, construct an approximate 95% confi- dence interval for 0, using the standard normal distribution. Would you say there is strong evidence against Gwynn's being a potential .400 hitter? Explain.

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 prob- ability of getting a hit on a particular at bat, call it 0. Let Y; be the Bernoulli(0) indicator equal to unity if Gwynn gets a hit during his ih at bat, and zero otherwise. Then, Y1, Y2, . .., Y, is a random sample from a Bernoulli(0) distribution, where 0 is the probability of success, and n = 419. Our best point estimate of 0 is Gwynn's batting average, which is just the proportion of suc- cesses: ỹ = .394. Using the fact that se(ỹ) = Vy(1 – ỹ)/n, construct an approximate 95% confi- dence interval for 0, using the standard normal distribution. Would you say there is strong evidence against Gwynn's being a potential .400 hitter? Explain.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 prob- ability of getting a hit on a particular at bat, call it 0. Let Y; be the Bernoulli(0) indicator equal to unity if Gwynn gets a hit during his ih at bat, and zero otherwise. Then, Y1, Y2, . .., Y, is a random sample from a Bernoulli(0) distribution, where 0 is the probability of success, and n = 419.
Transcribed Image Text: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 prob- ability of getting a hit on a particular at bat, call it 0. Let Y; be the Bernoulli(0) indicator equal to unity if Gwynn gets a hit during his ih at bat, and zero otherwise. Then, Y1, Y2, . .., Y, is a random sample from a Bernoulli(0) distribution, where 0 is the probability of success, and n = 419.
Our best point estimate of 0 is Gwynn's batting average, which is just the proportion of suc- cesses: ỹ = .394. Using the fact that se(ỹ) = Vy(1 – ỹ)/n, construct an approximate 95% confi- dence interval for 0, using the standard normal distribution. Would you say there is strong evidence against Gwynn's being a potential .400 hitter? Explain.
Transcribed Image Text:Our best point estimate of 0 is Gwynn's batting average, which is just the proportion of suc- cesses: ỹ = .394. Using the fact that se(ỹ) = Vy(1 – ỹ)/n, construct an approximate 95% confi- dence interval for 0, 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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