Slides-07 - ECON1203/ECON2292 Business and Economic...

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Click to edit Master subtitle style ECON1203/ECON2292 Business and Economic Statistics Week 7

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22 Week 7 topics l Sampling distribution of sample mean l Central limit theorem l Concept of a confidence interval l Interval estimation of population mean when population variance is known l Selecting sample size l Key references l Keller 9.1-9.2, 9.4, 10.1-10.3
Process of inference l Recall previous discussion of inferential statistics l Parameters describe key features of populations l In practical situations parameters are unknown because they are difficult or impossible to determine l Instead a sample is drawn from the population to provide basic data l These data are used to calculate various sample statistics l Sample statistics used as estimators for population parameters 33

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Process of inference… l Now need to relate population parameters to properties of the distribution of the sample statistics l Key concept here is the sampling distribution of a sample statistic l Have previously asked what a sample mean tells us about the population mean? l To answer this need to know about the sampling distribution of the sample mean 44
Sampling distributions l Sampling distribution of a sample statistic, is the distribution of all possible values that can be assumed by that statistic, computed from samples of the same size drawn from the same population l Assume random sampling from the population distribution of a rv X l Thus a sample of size n , X 1, X 2,…, X n constitutes a sequence of iid random variables 55

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66 Sampling distributions… l Assume population distribution of a rv has some mean, μ & variance, σ 2 l In any particular sample the sample mean (or sample variance) will (almost certainly) not equal (or 2) l Indeed, if the sample statistics equalled the population values, this would be happy coincidence l As we move from one sample (of size n ) to another we would expect the sample mean (or variance) to differ between samples l Quantifying this variability yields a sampling distribution
Sampling distributions . .. l

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Slides-07 - ECON1203/ECON2292 Business and Economic...

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