Hypothesis Testing and Confidence Intervals: An Overview

This lecture introduces the fundamental concepts of hypothesis testing and confidence intervals in statistics. It begins with an overview of the course organization and a review of the Central Limit Theorem (CLT), emphasizing its importance in statistical inference. The instructor explains the five steps involved in hypothesis testing, including formulating null and alternative hypotheses, computing test statistics, and determining p-values. The relationship between hypothesis tests and confidence intervals is highlighted, illustrating how they are dual concepts. Several examples are provided, including hypothesis tests for population means and proportions, demonstrating the application of these concepts in real-world scenarios. The lecture also discusses the implications of type I and type II errors, emphasizing the importance of understanding statistical significance versus practical significance. The session concludes with a brief introduction to one-sided confidence intervals and the conditions under which the t-test should be used instead of the z-test, particularly in small sample sizes. Overall, this lecture lays a solid foundation for further exploration of probability and statistics.