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STATS 2B03 (25)
Chapter 5

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Aaron Childs

Stats 2B03: Statistical Methods for Science Chapter 5: Some Important Sampling Distributions 5.3 Distribution of the Sample Mean - Sample distribution of X avg– functional form: radial difference in appearance between the histogram of population and the histogram of the sampling distribution of X avghereas the former is uniformly distributed, the latter gradually rises to a peak and then drops off with perfect symmetry - Sampling distribution of X – mean: ∑ avg - Sampling distribution of X – variance: ∑ , variance of avg sampling distribution is not equal to the population variance; however, the variance of the sampling distribution is equal to the population variance divided by the size of the sample used to obtain the sampling distribution - Standard error of the mean: - Sampling distribution of X avg– sampling from normally distributed populations:  Distribution of Xavgwill be normal  The mean of the distribution of Xavgill be equal to the mean of the population from which the samples were drawn  The variance, of the distribution of avgwill be equal to the variance of the population divided by the sample size - Sampling from nonnormally distributed populations:  Central limit theorem: given a population of any nonnormal functional form with a mean μ and finite variance , the sampling distribution of , computed from samples of siz
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