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# 2-9-09 - Economic Statistics 2 Class Notes X QUESTION What...

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Economic Statistics 2 – Class Notes – 2/9/09 X

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QUESTION : What do we see? ANSWER : The mean of all sample mean values (Xbar) equals the mean of the random variable X (the population mean, µ ) the population parameter we want to estimate. Also, the sampling distribution has a smaller VARIANCE than that of the parent population. If you took samples from a larger and larger population, the variance gets smaller TRUE FOR ALL DATA SETS The mean of all of the sample means is equal to the population mean. Also, when you form sample mean, it is unlikely that you will get all of the extreme values in any one sample. o QUESTION: So what does that do to the mean? The variance will always be smaller for the (larger) population! 2. The Actual Distribution of the Sample Mean (Xbar): 1. If the parent population is distributed normally , the sampling distribution of the Sample Mean (Xbar) is distributed normally.
2. For any parent population – regardless of its distribution – with finite mean ( µ ) and variance ( ), the

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