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Unformatted text preview: Sampling Distributions First... • Distribution of sample means –collection of sample means for all the possible random samples of a particular size ( n ) that can be obtained from a population •vs • Sampling distribution –distribution of statistics obtained by selecting all the possible samples of a specific size from a population First... • Distribution of sample means is a • Sampling distribution You should know everything there is to know about . . . • Sampling distribution of the mean –Its composition –Properties –Sample size –Central limit theorem Background • A basic goal in a lot of research is to describe populations – what are members of a population typically like? •Do depressed individuals have unusually high IQs? •How much do individuals with a B.A. make? • We want to know parameters — often µ One Approach • Hypothesize • Sample • Determine probability of sample given hypothesized population • Decide whether hypothesis is true 1 2 3 4 5 6 One Approach • Hypothesize about µ for the population of interest –For the population of all depressed people, we hypothesize that the mean IQ ( µ ) is 116 H: µ = 116 One Approach • Draw a sample from the population –say, 300 depressed individuals –Compute M (in this case, their mean IQ) •say, M = 100 One Approach • Determine probability of drawing a sample with a mean of M = 100 given the hypothesized population mean of µ = 116 • Hypothesize about µ for the population of interest –For the population of all depressed people, we hypothesize that the mean IQ ( µ ) is 116 H: µ = 116 Probability of M = 100? If it’s improbable , reject the hypothesis that µ = 116 • Hypothesize about µ for the population of interest –For the population of all depressed people, we hypothesize that the mean IQ ( µ ) is 116 H: µ = 116 Probability of M = 100? 7 8 9 10 11 One Approach • Hypothesize about µ for the population of interest –For the population of all depressed people, we hypothesize that the mean IQ ( µ ) is 116 H: µ = 116 One Approach • Draw a sample from the population –say, 300 depressed individuals –Compute M (in this case, their mean IQ) •say, M = 100 One Approach • Determine probability of drawing a sample with a mean of M = 100 given the hypothesized population mean of µ = 116 • Hypothesize about µ for the population of interest...
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 Fall '07
 Pfordesher
 Normal Distribution, Standard Deviation

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