Hypothesis Testing: Q-Q Plots and Non-Parametric Tests

This lecture focuses on hypothesis testing, specifically the second part of hypothesis tests and the introduction of Q-Q plots. The instructor begins by revisiting the general framework of hypothesis testing, emphasizing the importance of determining the plausibility of a hypothesis based on observed data. The discussion includes both parametric and non-parametric tests, highlighting the significance of goodness-of-fit tests. The instructor explains how to assess whether observed data aligns with a proposed distribution, such as normal or exponential distributions. The lecture also covers the fundamental theorem of statistics, known as the Glivenko-Cantelli theorem, which states that as sample size increases, the empirical distribution function converges to the true distribution. The instructor introduces the Kolmogorov-Smirnov test for goodness-of-fit and discusses the Chi-squared test for independence, explaining how to construct test statistics and interpret results. The session concludes with a brief overview of Q-Q plots, which visually assess the fit of data to a theoretical distribution, reinforcing the concepts of hypothesis testing and statistical inference.