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Unformatted text preview: Sheet1 Page 1 AGENDA Populations and sample Sampling distribution of the mean (sigma known) Central Limit Theorem Sampling distribution of the mean (sigma unknown) Sampling distribution of the variance POPULATIONS AND SAMPLE Populations can be either Infinite Finite Samples are usually necessary Impossible to observe infinite population Impractical or uneconomical to observe finite population Random sample Representative of the population Unbiased Tables of random numbers, etc. Sampling distributions are what you get when you observe the random sample means and variances SAMPLING DISTRIBUTION OF THE MEAN (SIGMA KNOWN) Population Mean = u Variance = sigma^2 Sample of the population Mean of sample = x bar X bar is a random variable Every sample will be slightly different Mean of x bar = u Variance of x bar = (sigma^2) / n STANDARD ERROR OF THE MEAN The reliability of the sample mean is measured by the standard error of the mean STANDARDIZED SAMPLE MEAN CENTRAL LIMIT THEORM Regardless of the underlying population, the mean of a sample becomes normally distributed as n approaches infinity...
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- Fall '08