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tutorial05w - ISMT 111 BUSINESS STATISTICS TUTORIAL 5...

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1 ISMT 111 B USINESS S TATISTICS T UTORIAL 5 created by Andrew Yam Sampling Distribution of Sample Statistics The sampling distribution of a statistic is the probability distribution of all the possible values of this statistic which are computed from random samples with same sample size ( n ). Notations: n = Sample size X = Random variable µ = Population mean X = Sample mean σ = Population standard deviation s = Sample standard deviation se = Standard error p = Population proportion p ˆ = Sample proportion Central Limit Theorem (CLT) Regardless of the population distribution of X which is with a mean µ and a standard deviation σ , if the sample size n is sufficiently large, the sampling distribution of the sample mean X will be APPROXIMATELY normally distributed with mean m m = X and standard deviation n X / s s = (also called standard error of the mean, denoted as ( 29 X se ). Note: There are four possible cases Normal Population Non-normal Population n is large n N X 2 , ~ s m n N X 2 , ~ s m , by CLT n is small n N X 2 , ~ s m Not applicable Sampling Distribution of Sample Proportion

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2 Sample Proportion: n X p = ˆ , where X is the number of successes in the sample.
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This note was uploaded on 09/15/2008 for the course ISMT 111 taught by Professor Wanxuhu during the Fall '08 term at HKUST.

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tutorial05w - ISMT 111 BUSINESS STATISTICS TUTORIAL 5...

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