Understanding and Applying Basic Statistical Methods Using R

Chapter 5SAMPLING DISTRIBUTIONS

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 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, , is used to estimate the population mean . 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 . Consequently, an issue of fundamental importance is how well the sample mean estimates the population mean. If the sample mean is , we estimate that the population mean is 23, but can we be reasonably ...