The sample mean is not the only point estimate for which the sampling distribution is nearly normal. For example, the sampling distribution of sample proportions closely resembles the normal distribution when the sample size is sufficiently large. In this section, we introduce a number of examples where the normal approximation is reasonable for the point estimate. Chapters 3 and 4 will revisit each of the point estimates you see in this section along with some other new statistics.
We make another important assumption about each point estimate encountered in this section: the estimate is unbiased. A point estimate is unbiased if the sampling distribution of the estimate is centred at the parameter it estimates. That is, an unbiased estimate does not naturally over or underestimate the parameter. Rather, it tends to provide a ‘‘good’’ estimate. The sample mean is an example of an unbiased point estimate, as are each of the examples we introduce in this section.
Finally, we will discuss the general case where a point estimate may follow some distribution other than the normal distribution. We also provide guidance about how to handle scenarios where the statistical techniques you are familiar with are insufficient for the problem at hand.