CHAPTER 11 - Testing Statistical Hypotheses: Simple Hypothesis vs. Simple Alternative

Abstract

This chapter focuses on testing statistical hypotheses—simple hypothesis and simple alternative. Hypothesis testing is one of the principal branches of mathematical statistics. The chapter presents an introduction to a few of the basic principles of testing statistical hypotheses. A distinguishing feature of hypothesis testing in the field of mathematical statistics is that there is always one particular state of nature that one does not wish to eliminate unless there is overwhelming evidence or reason for doing so. The two states of nature imply that there are two distinct probability distributions of the random variables. When distinguishing between two states of nature, the statistician identifies with each state of nature a probability distribution function of some random variables. The chapter explains how a best critical region can be obtained by the means of a very important theorem of J. Neyman and E. S. Pearson, a theorem which is basic to the problems of statistical inference. Neyman–Pearson fundamental lemma is fundamental to a great deal of statistical inference.