Lesson 27: Likelihood Ratio Tests

In this lesson, we'll learn how to apply a method for developing a hypothesis test for situations in which both the null and alternative hypotheses are composite. That's not completely accurate. The method, called the likelihood ratio test, can be used even when the hypotheses are simple, but it is most commonly used when the alternative hypothesis is composite. Throughout the lesson, we'll continue to assume that we know the the functional form of the probability density (or mass) function, but we don't know the value of one (or more) of its parameters. That is, we might know that the data come from a normal distrbution, but we don't know the mean or variance of the distribution, and hence the interest in performing a hypothesis test about the unknown parameter(s).