Confidence Intervals and Hypothesis Tests

This lecture covers the construction of confidence intervals based on pivots, using the central limit theorem to approximate the distribution of an estimator. It explains how to build confidence intervals and conduct hypothesis tests, illustrating with examples. The instructor discusses the importance of standard errors, unknown variances, and statistical models. The lecture also delves into the concepts of likelihood, Bayesian inference, and the ROC curve for tests. Additionally, it explores the Pearson statistic, goodness of fit tests, and the power of tests. The presentation concludes with a discussion on the null and alternative hypotheses, emphasizing the significance of the ROC curve in testing.