L14-09

# L14-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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10/20/09 Lecture 14 1 STOR 155 Introductory Statistics ( Chap 5 ) Lecture 14: Sampling Distributions for Counts and Proportions The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

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10/20/09 Lecture 14 2 • A statistic is any numeric measure calculated from data. It is a random variable, its value varies from sample to sample. – count/proportion: • Ex: number/proportion of free throws made by a Tar Heel player who shoots 20 free throws in a practice – sample mean • Ex: average SAT score of a group of 10 students randomly selected from STAT 155 • The probability distribution of a statistic is called its sampling distribution . – It depends on the population distribution, and the sample size.
10/20/09 Lecture 14 3 Binomial Experiment n trials (with n fixed in advance). • Each trial has two possible outcomes, “success” ( S ) and “failure” ( F ). • The probability of success, p , remains the same from one trial to the next. • The trials are independent, i.e. the outcome of each trial does not affect outcomes of other trials.

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10/20/09 Lecture 14 4 Example • The experiment: randomly draw n balls with replacement from an urn containing 10 red balls and 20 black balls. • Let S represent {drawing a red ball} and F represent {drawing a black ball}. • Then this is a binomial experiment with p =1/3. Q : Would it still be a binomial experiment if the balls were drawn without replacement? No!
10/20/09 Lecture 14 5 Binomial Distribution

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Lecture 14 6 Do they follow binomial distributions (approximately) ? X = number of stocks on the NY stock exchange whose prices increase today X = number of games the Tar Heel will win next season • A couple decides to have children until they have a girl. X
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## This note was uploaded on 11/17/2011 for the course STOR 155 taught by Professor Andrewb.nobel during the Fall '08 term at UNC.

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L14-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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