ABSTRACT
The approach to computing a confidence interval for the mean, as described in Section 4.3, is a special case of a more general method developed by Laplace about two centuries ago. Two key components are the notion of a sampling distribution and the standard error of an estimator. About a century ago, Jerzy Neyman and Egon Pearson developed a new approach that dominates applied research today. They used Laplace’s notion of a sampling distribution and standard error, but they proposed an alternative framework for making inferences about the population mean (and other parameters) based on what is called hypothesis testing. Roughly, in the simplest case, some speculation is made about some unknown parameter, such as the population mean µ, and the goal is to determine whether the speculation is unreasonable based on the data available to us.
