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Sampling Distribution of the Mean. is a random variable whose value depends on which members of the population are selected in the sample. Facts about the Sampling Distribution of the Mean. The average value of across all possible samples is , the population mean. Thus, .
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Sampling Distribution of the Mean is a random variable whose value depends on which members of the population are selected in the sample.
Facts about the Sampling Distribution of the Mean • The average value of across all possible samples is , the population mean. Thus, . • The standard deviation of the sampling distribution of is the population standard deviation divided by the .
is the standard error of • The sample to sample variability in decreases as n increases. • Large samples are more precise than small samples.
If our sample comes from a normal distribution with mean, , and standard deviation, , then has the standard normal distribution.
Central Limit Theorem • If we sample from a population with mean, , and standard deviation, , then is approximately standard normal for large n.
How large does n have to be? • If population is normal or near normal, n can be quite small. • If population is far from normal, the approximation is reasonably good for n=30, most of the time.
