Hypothesis testing refers to the process of choosing between competing hypotheses about a probability distribution, based on observed data from the distribution. It is a core topic in mathematical statistics, and indeed is a fundamental part of the language of statistics. In this chapter, we study the basics of hypothesis testing, and explore hypothesis tests in some of the most important parametric models: the normal model and the Bernoulli model.

- Introduction
- Tests in the Normal Model
- Tests in the Bernoulli Model
- Tests in the Two-Sample Normal Model
- Likelihood Ratio Tests
- Chi-Square Tests

- Mean Test Experiment
- Proportion Test Experiment
- Variance Test Experiment
- Dice Goodness of Fit Experiment
- Sign Test Experiment
- Probability Plot Experiment
- Special Distribution Calculator

- Introduction to Probability and Mathematical Statistics. Lee J Bain and Max Engelhardt
- Statistical Inference. George Casella and Rober L Berger
- Statistics. David Freedman, Robert Pisani and Robert Purves
- An Introduction to Mathematical Statistics and Its Applications. Richard J Larsen and Morris L Marx
- Elementary Statistics. Mario Triola
- Introductory Statistics. Neil A Weiss
- Wikipedia statistics portal
- Wolfram MathWorld articles on probability and statistics

We must be careful not to confuse data with the abstractions we use to analyze them.

—William James