WEEK 9.ppt - IE 220 PROBABILITY AND STATISTICS 2009-2010...

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IE 220 PROBABILITY AND STATISTICS 2009-2010 Spring Chapter 7 Sampling Distributions
Introduction Parameters are numerical descriptive measures for populations. For the normal distribution, the location and shape are described by and For a binomial distribution consisting of n trials, the location and shape are determined by p . Often the values of parameters that specify the exact form of a distribution are unknown. You must rely on the sample to learn about these parameters.
Sampling Distributions Numerical descriptive measures calculated from the sample are called statistics statistics . Statistics vary from sample to sample and hence are random variables. The probability distributions for statistics are called sampling distributions sampling distributions . In repeated sampling, they tell us what values of the statistics can occur and how often each value occurs.
Possible samples 3, 5, 2 3, 5, 1 3, 2, 1 5, 2, 1 Possible samples 3, 5, 2 3, 5, 1 3, 2, 1 5, 2, 1 x Sampling Distributions Definition: The sampling distribution of a sampling distribution of a statistic statistic is the probability distribution for the possible values of the statistic that results when random samples of size n are repeatedly drawn from the population. Population: 3, 5, 2, 1 Draw samples of size n = 3 without replacement Population: 3, 5, 2, 1 Draw samples of size n = 3 without replacement 67 . 2 3 / 8 2 3 / 6 3 3 / 9 33 . 3 3 / 10 Each value of x-bar is equally likely, with probability 1/4 x p(x) 1/4 2 3
Sampling Distributions Sampling distributions for statistics can be Approximated with simulation techniques Derived using mathematical theorems

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