Statistical Inference and Hypothesis Testing in Data Science Applications

In this module, we will define a hypothesis test and develop the intuition behind designing a test. We will learn the language of hypothesis testing, which includes definitions of a null hypothesis, an alternative hypothesis, and the level of significance of a test. We will walk through a very simple test.

In this module, we will expand the lessons of Module 1 to composite hypotheses for both one and two-tailed tests. We will define the “power function” for a test and discuss its interpretation and how it can lead to the idea of a “uniformly most powerful” test. We will discuss and interpret “p-values” as an alternate approach to hypothesis testing.

In this module, we will learn about the chi-squared and t distributions and their relationships to sampling distributions. We will learn to identify when hypothesis tests based on these distributions are appropriate. We will review the concept of sample variance and derive the “t-test”. Additionally, we will derive our first two-sample test and apply it to make some decisions about real data.

In this module, we will consider some problems where the assumption of an underlying normal distribution is not appropriate and will expand our ability to construct hypothesis tests for this case. We will define the concept of a “uniformly most powerful” (UMP) test, whether or not such a test exists for specific problems, and we will revisit some of our earlier tests from Modules 1 and 2 through the UMP lens. We will also introduce the F-distribution and its role in testing whether or not two population variances are equal.