The Generalized Likelihood Ratio
We’ve already known that in hypothesis testing, we have a null hypothesis, where $ H_0: \theta = \theta_0$ versus alternative hypothesis $H_A: \theta \neq \theta_0$. We also have a presumed pdf function for the variables. Based on these information, we can construct a critical point/region when whatever level of significance $\alpha$ is given. Then if a sample of size $n$ comes in, we can use the sample mean to decide if we accept the null hypothesis or reject it based on whether it falls within the critical region or not.