# Lecture 12. A) Statistical Tests

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# Statistical Tests

In the previous class we introduced hypothesis testing, and discussed how to set the critical value of a test. Here, we will discuss the selection of the test itself.

There are three main test statistics used in hypothesis testing. We will discuss their optimality later. The test statistics are

• Likelihood Ratio
• Lagrange Multiplier
• Wald Test

All of these tests reject when $T\left(X_{1}..X_{n}\right)\gt c$, where $T$ is the test statistic and $c$ is the critical value.