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Chapter 7

# Chapter 7

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University of Toronto St. George

Psychology

PSY201H1

Gillian Rowe

Fall

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Chapter 7Probability and Samples The Distribution of Sample Means 71 Samples and PopulationsSampling errornatural discrepancy or amount of error between a sample statistic and its corresponding population parameterIf you take two samples from the same population the samples will be different72 The Distribution of Sample MeansDistribution of sample meansthe collection of sample means for all the possible random samples of a particular size n that can be obtained from a populationprovides the ability to predict sample characteristics contains all possible samples ex if the entire set contains exactly 100 samples then the probability of obtaining any specific sample is 1 out of 100 p1100 Sampling distributiondistribution of statistics obtained by selecting all the possible samples of a specific size from a populationvalues in the distribution are not scores but statistics sample means stats obtained from samples so a distribution of stats is referred to as a sampling distribution distribution of sample means is an example of a sampling distribution To construct a distribution of sample meansselect a random sample of a specific size n from a population calculate the sample mean and place the sample mean in a frequency distribution Then select another random sample with the same number of scores and do the same Continue until you have the complete set of all the possible random samples General characteristics of the distribution 1 The sample means should pile up around the population mean Samples are not expected to be perfect but they are representative of the population As a result most of the sample means should be relatively close to the population mean 2 The pile of sample means should tend to form a normalshaped distribution Logically most of the samples should have means close toand it should be relatively rare to find sample means that are substantially different fromAs a result the sample means should pile up in the center of the distribution aroundand the frequencies should taper off as the distance between M and increases This describes a normalshaped distribution3 In general the larger the sample size the closer the sample means should be to the pop meanLogically a large sample should be a better representative than a small sample Thus the sample means obtained with a large sample size should cluster relatively close to the pop mean the means obtained from small samples should be more widely scatteredThe Central Limit TheoremCentral limit theoremfor any population with meanand standard deviationthe distribution of sample means for sample size n will have a mean ofand a standard deviation ofand will approach a normal distribution as n approaches infinityprovides a precise description of the distribution that would be obtained if you selected every possible sample calculated every possible sample mean and constructed the distribution of the sample means

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