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

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
5/31/11 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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
5/31/11 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.
Background image of page 2
5/31/11 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.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
5/31/11 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!
Background image of page 4
5/31/11 Lecture 14 5 Binomial Distribution
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
5/31/11 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 = number of boys the couple will have Answer: NO in all 3 cases. Why ?
Background image of page 6
5/31/11 Lecture 14 7 Binomial Distribution • If X ~ B ( n, p ) , then X = np, 2 X = np( 1- p ). P
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 26

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

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online