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# notes509fall11sec36 - STAT 509 Section 3.6: Sampling...

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STAT 509 – Section 3.6: Sampling Distributions Definition: Parameter = a number that characterizes a population (example: population mean μ ) – it’s typically unknown . Statistic = a number that characterizes a sample (example: sample mean ) – we can calculate it from our sample data. = We use the sample mean to estimate the population mean μ . Suppose we take a sample and calculate . Will equal μ ? Will be close to μ ? Suppose we take another sample and get another . Will it be same as first ? Will it be close to first ? • What if we took many repeated samples (of the same size) from the same population, and each time, calculated the sample mean? What would that set of values look like? The sampling distribution of a statistic is the distribution of values of the statistic in all possible samples (of the same size) from the same population.

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Consider the sampling distribution of the sample mean when we take samples of size n from a population with mean μ and variance σ 2 . Picture: The sampling distribution of has mean μ and standard deviation n / σ . Notation: Central Limit Theorem We have determined the center and the spread of the sampling distribution of . What is the shape of its sampling distribution? Case I: If the distribution of the original data is normal , the sampling distribution of is normal. (This is true no matter what the sample size is.) Case II: Central Limit Theorem : If we take a random sample (of size n ) from any population with mean μ and
standard deviation σ , the sampling distribution of is approximately normal, if the sample size is large . How large does

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## This note was uploaded on 12/13/2011 for the course STAT 509 taught by Professor Chalmers during the Fall '08 term at South Carolina.

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notes509fall11sec36 - STAT 509 Section 3.6: Sampling...

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