A random sample is a set of values drawn independently from a larger population. A (uniform) random sample has the characteristic that all members of the population have an equal chance of being drawn. In the previous chapter, we discussed the implications of drawing repeated random samples from a normally distributed population, where the probability that a value lies in a given interval is governed by the normal density. This chapter will expand upon that discussion by using the idea of a sampling distribution, with its associated standard error, to assess estimation accuracy. Confidence intervals and tests of hypotheses offer a formal basis for inference, based on the sampling distribution. We will comment on weaknesses in the hypothesis testing framework.

Basic concepts of estimation

This section will introduce material that is fundamental to inference.

Population parameters and sample statistics

Parameters, such as the mean (μ) or standard deviation (σ), numerically summarize various aspects of a population. Such parameters are usually unknown and are estimated using statistics calculated using a random sample taken from the population. The sample mean is an example of a statistic, and it is used to estimate the population mean.

Other commonly used statistics are the proportion, standard deviation, variance, median, the quartiles, the slope of a regression line, and the correlation coefficient. Each may be used as an estimate of the corresponding population parameter.