PSLS.PPT.Ch13

# PSLS.PPT.Ch13 - Samplingdistributions PSLS chapter 13 2009...

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Sampling distributions PSLS chapter 13 © 2009 W. H. Freeman and Company

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Objectives (PSLS chapter 13) Sampling distributions Parameter versus statistic The law of large numbers Sampling distributions Sampling distribution of the sample mean x ̅ The central limit theorem Sampling distribution of the sample proportion p ̂
Reminder:  Parameter versus statistic Sample: the part of the population we actually examine and for which we do have data. A s tatistic is a number describing a characteristic of a s ample. We often use a statistic to estimate an unknown population parameter. Population: the entire group of individuals in which we are interested but can’t usually assess directly. A p arameter is a number describing a characteristic of the p opulation. Parameters are usually unknown. Population Sample

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The law of large numbers Law of large numbers : As the number of randomly-drawn observations ( n ) in a sample increases, the mean of the sample ( ) gets closer and closer to the population mean μ (quantitative variable). the sample proportion ( ) gets closer and closer to the population proportion p (categorical variable). x ˆ p
Sampling distributions Different random samples taken from the same population will give different statistics. But there is a predictable pattern in the long run. A statistic computed from a random sample is a random variable. The sampling distribution of a statistic is the probability distribution of that statistic for samples of a given size n taken from a given population.

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Note: When sampling randomly from a given population: The law of large numbers describes what would happen if we took samples of increasing size n . A sampling distribution describes what would happen if we took all possible random samples of a fixed size n . Both are conceptual ideas with many important practical applications.
Simulating a sampling distribution Sampling distributions are theoretical concepts. We don’t actually build them. You can get a feeling for the concept with simulation: take many random samples of a given size n from a population with known mean μ and standard deviation σ. Some sample means will be above the population mean μ and some will be below, making up the sampling distribution. Sampling distribution of x ̅ Histogram of some sample averages

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The mean of the sampling distribution of x ̅ is μ. There is no tendency for a sample average to fall systematically
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## This note was uploaded on 10/07/2011 for the course BSTT 400 taught by Professor Sallyfreels during the Fall '11 term at Ill. Chicago.

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PSLS.PPT.Ch13 - Samplingdistributions PSLS chapter 13 2009...

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