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Chapter 7

Ch. 7 - Probability and Samples.docx

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PSYC 2530
Anne Russon

Ch. 7 - Probability & Samples Sunday, November 11, 2012 5:54 PM PSYC 2530 Introductory Statistics Chapter 7: Probability and Samples: The Distribution of Sample Means  Sample error is the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.  The distribution of sample means is the collection of sample means for ALL of the possible random samples of a particular size (n) that can be obtained from a population.  A sampling distribution is a distribution of statistics obtained by selecting all of the possible samples of a specific size from a population.  Characteristics of a distribution of all sample means: o 1) The sample means should pile up around the population means o 2) The pile of sample means should tend to form a normal-shaped distribution o 3) In general, the larger the sample size, the closer the sample means should be to the population mean, μ  In a distribution of sample means: o Mean = μ o  Central Limit Theorem: For any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will have a mean of μ and a standard deviation of nand will approach a normal distribution as n approaches infinity. o 1) The central limit theorem describes the distribution of sample means for any population, no matter what shape, mean, or standard deviation. o 2) The distribution of sample means “approaches” a normal distribution very rapidly. By the time the sample size reaches n = 30, the distribution is almost perfectly normal.  According to the central limit theorem, the parameters of the distribution of sample means are as follows: o a. Shape. The distribution of sample means is normal if EITHER of the following is satisfied:  1) The population from which the samples are selected is a normal distribution  2) The number of scores (n) in each samp
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