Basic Framework of Hypothesis Testing and Its Application in Maximum Likelihood Function and Regression Models

The research field of this essay is probability and statistics, mainly focusing on the content of hypothesis testing. This paper discusses the most basic framework and mathematical explanation behind hypothesis testing by introducing the concept of sample space. It also discusses how to construct hypothesis testing. The two testing methods are the following: one is to calculate test statistics, and the other is to calculate the corresponding p-value. It then makes a judgment based on the calculated test statistics and p-value, whether null hypothesis need to be refused or not. The main aim is to solve problems of maximum likelihood estimation and how to reasonably test and summarize coefficients in linear regression models through the explanation and utilization of hypothesis testing. The comparative argumentation method is used. The conclusion of the paper is that through hypothesis testing and Lagrangian multiplier testing, it is possible to test whether there are specific constraints in the model and quickly test whether a certain term in the regression model is necessary or not. The F test can also be used to verify whether multiple coefficients can coexist.