This chapter deals with the notion of a sampling distribution, which plays a fundamental role when trying to generalize from a sample to a population of individuals or things. Sampling distributions also provide perspective on the relative merits of the location estimators introduced in Chapter 2.

As previously explained, the population mean c05-math-0001 represents the average of all individuals or things that are of interest in a particular study. But typically not all individuals of interest can be measured, in which case the sample mean, c05-math-0002, is used to estimate the population mean c05-math-0003. The sample mean is the average based on a subset of the population of interest, and so it will generally be the case that the sample mean is not equal to the population mean. That is, generally c05-math-0004. Consequently, an issue of fundamental importance is how well the sample mean estimates the population mean. If the sample mean is c05-math-0005, we estimate that the population mean is 23, but can we be reasonably ...

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