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Unformatted text preview: Distribution of sample means the distribution of means (i.e., average values) for all the possible random samples of a particular size that can be obtained from a population theoretical distribution sampling with replacement ( i.e. there is a constant probability for each & every selection) All the possible samples of n=2 that can be obtained from the population of four scores: 2, 4, 6, 8. Random sampling = Sampling with replacement The distribution of 16 sample means The distribution of sample means for n=2 RANDOM SAMPLE: each individual in the population has an equal chance of being selected if more than one individual is selected the sampling with replacement is used (there is the same probability for each selected individual). Basic properties of the distribution of sample means are described by a mathematical proposition known as the Central Limit Theorem Shape Mean Standard deviation The Shape of the distribution of sample means is normal if: (1) the population from which the samples are selected is a normal distribution (2) the size of the sample is relatively large (the larger the sample the more the shape of distribution resembles normal) The mean of the distribution of sample means is called the expected value of M and it is equal to the population mean . The standard deviation of the distribution of sample means is called the standard error of M . The standard error of M measures the average amount of difference one should expect between a sample mean and the population mean due to chance (i.e., it measures a sampling error ). The size of standard error of M is determined by two factors: (1) the size of the sample The law of large numbers predicts that the larger the sample, the more likely it is that the sample mean...
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 Fall '08
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