ABSTRACT
The standard deviation of the sampling distribution of sample means would serve as a measure of “average” error. To recognize this fact, the standard deviation of the sampling distribution of a statistic has a special name: the standard error of the statistic. The logic of forming a confidence interval rests on the idea of a sampling distribution. Since the sample mean has a normal sampling distribution, all we need to know is how to find what k is for a given level of certainty—or, equivalently, what level of certainty we can have for a given k. So once we know the standard error of the sample mean, we are in a position to make statements about the population mean, with our level of confidence based on the normal distribution. The chapter discusses how this works in the context of two related types of inferential procedures: interval estimation and hypothesis testing. It also considers a slightly different problem involving confidence intervals.
