Section 7 Operation Management Statistics

Section 7 Operation Management Statistics - Dr. Harvey A....

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© 2008 by Harvey A. Singer 1 OM 210:  Statistical Analysis for  Management The Sampling Distribution of the Sample Mean Dr. Harvey A. Singer School of Management George Mason University
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© 2008 by Harvey A. Singer 2 Learning Objectives Describe the sampling distribution of the sample mean. Model the sampling distribution of . Special issues: sampling from Non-normal populations. Finite populations. x
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© 2008 by Harvey A. Singer 3 Sampling Distributions A sampling distribution is a probability distribution of all possible values of the sample statistic. Obtained from repeated sampling, or … Theoretical distribution of the sample statistic of interest calculated for all possible samples of the same size that can be drawn from the same population.
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© 2008 by Harvey A. Singer 4 Sampling Distributions Can have sampling distributions of the sample mean. sample median. sample variance. sample proportion. Here, focus attention on the sampling distribution of the sample mean x .
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© 2008 by Harvey A. Singer 5 Starting Point Need to bound the sampling error on the sample means. Find the maximum value of the sampling error possible at a given level of risk of being wrong. Margin of error, MoE . Think of the sample mean as a random variable. Sample mean varies randomly in value from one random sample to another. The starting point is the concept of the “sampling distribution of the sample mean.”
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© 2008 by Harvey A. Singer 6 Sampling Distribution of the Sample Mean The sampling distribution of the sample mean is the probability distribution of all possible values of the sample mean resulting from completely sampling a population for all possible samples of the same size. That is, the sampling distribution of the sample mean is a distribution of probability over all possible values of sample mean, calculated from all possible samples of the same number of observations drawn from the same population. Simply, it is the probability distribution of the sample means calculated for all possible samples.
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© 2008 by Harvey A. Singer 7 Sampling Distribution of x The sampling distribution of the sample mean is the probability distribution of the values of x from all possible samples of size n drawn from the same population. The sampling distribution of the sample mean is the listing for all possible means x of samples of size n . ( 29 [ ] x Prob , x
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© 2008 by Harvey A. Singer 8 Complete Sampling of a Population Start with a finite population of size N with mean μ and standard deviation σ . Select all possible random samples all of size n . There are k possible samples of size n that can be selected from a population of size N . Calculate the sample mean
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Section 7 Operation Management Statistics - Dr. Harvey A....

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