Statistical Hypothesis Testing: Concepts and Applications

This lecture covers the fundamentals of statistical hypothesis testing, including the definition and purpose of hypothesis tests. The instructor begins by discussing confidence intervals and their significance in estimating unknown parameters. The lecture then transitions to hypothesis testing, explaining the difference between estimation methods and hypothesis tests. Various examples illustrate how to formulate null and alternative hypotheses, such as testing the fairness of a coin or the effectiveness of a new treatment. The instructor emphasizes the importance of understanding Type I and Type II errors, as well as the significance level (alpha) in decision-making. The concept of p-values is introduced, clarifying its role in determining the strength of evidence against the null hypothesis. The lecture also touches on different types of tests, including tests of conformity, independence, and goodness of fit. Throughout the session, the instructor provides mathematical frameworks and practical examples to ensure a comprehensive understanding of hypothesis testing in statistics.