[6.5] how close are sample means to population means?
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Sample distribution: the probability distribution of a statistic
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Note: statistics are random variables; parameters are constants
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Sample distribution of the sample mean: a probability distribution of all
possible values of the sample mean computed from a sample size n from the
population with mean and standard deviation
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Ex 1: Draw all possible samples of size 2 with replacement from the
population {2,4,6}. Construct a sampling distribution of the mean
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Note: the standard error of the sample mean is the standard deviation of
the sample mean
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Impact of Sample size on sampling variability
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The law of large numbers:
as additional observations are added to the
sample, the difference between the sample mean and the population mean
approaches zero
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Ex: Suppose a simple random sample size of n=34 is obtained from a
population with mean=30 and SD=4
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Describe the sampling distribution of the sample mean

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normal
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What is the probability that the sample mean is greater than 30.2

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