Handout_9 THE SAMPLING DISTRIBUTION

Handout_9 THE SAMPLING DISTRIBUTION - May 1709 THE SAMPLING...

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May 17’09 THE SAMPLING DISTRIBUTION. #9 THE CENTRAL LIMIT THEOREM By definition , statistical inference is a procedure by which we reach a conclusion about a population on the basis of the information contained in a sample drawn from that population . {Statistical inference includes two general areas: estimation and the hypothesis testing .} How can we make proper statistical inferences about a large population (of size N ) when the statistical data have been collected only for the samples of smaller size n derived from that population? _ We can’t expect that a sample mean, x 1 , obtained from a first sample will be exactly equal to the population mean µ , but we’ll be satisfied with our sample results if the sam ple mean is “close enough” to the population mean. Also, we can’t expect that a sample mean, x 2 , obtained from a second sample will be exactly equal to the population mean or to the mean for the first sample. Again, we’ll be satisfied with our sample results if the mean for the second sample is “close enough” to the population mean and the mean for the first sample. But what is the meaning of the words “close enough” with respect to the sample mean and other descriptive measures? How to determine (and measure) this closeness? To answer these questions we should consider a “ sampling distribution ”. Recall that a sample statistic is a descriptive measure, such as the mean, median, range, variance, or standard deviation that is computed from the data of a sample . By definition
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Handout_9 THE SAMPLING DISTRIBUTION - May 1709 THE SAMPLING...

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