**Overview**

Module 6 builds on Modules 4 and 5 on “Foundations for inference” by examining (univariate) hypothesis testing. We examine the t-distribution as a means of accounting for uncertainty in our estimates when our sample size is small or the population standard deviation is unknown. We then examine hypothesis tests for one and two populations using the t-distribution, and we begin to conduct such tests in R. Finally, we read and analyze one especially prominent and recent use of hypothesis testing in US politics.

**Objectives**

- Explain what a t-distribution is and why we use it.
- Define null hypothesis, alternative hypothesis, and type 1 and 2 errors.
- Explain and put to practice the steps in conducting hypothesis testing.
- State a null and alternative hypothesis
- Calculate appropriate tests statistics
- Calculate p-values
- Compare p-values against different significance levels and interpret the results

- Critically analyze real-life usages of hypothesis testing.

**Assignment**

Exercise 3 is due at 5pm CST on Monday, 2/22. The Exercise 2 RMD file is located at Canvas. Be sure to download and skim through the file early in the week so that you can plan your time accordingly.

**Mid-course feedback**

Please look for a Canvas announcement from me later in the week with a link to a Google Form that will allow you to provide me with anonymous, mid-course feedback. I am always looking for ways to improve my instruction and better meet your needs and aims, so please do take a moment to complete the Form once it is published.

**Module**

**t-distribution**

We’re going to begin by refining our grasp of standard errors and confidence intervals. In particular, we’re going to examine the t-distribution as a conservative alternative to the normal distribution that will allow us to account for additional uncertainty whenever our sample size is small or we estimate the *population* standard deviation using the *sample* standard deviation.

Now watch the video on the “t-distribution.”

**(Univariate) Hypothesis testing**

Now read OIS Sections 4.3 through 4.5. Note that the Syllabus lists some additional sections of OIS that are suggested but optional.

After you have completed the reading, watch the video on “Hypothesis testing 1.”

Now watch the video on “Hypothesis testing 2.”

I realize the the videos for this module are longer than usual, but I wanted to be sure to walk through some examples step-by-step so that you can begin conducting your own hypothesis tests in the practice questions and exercise.

**Hypothesis testing in the 2020 US presidential election**

I am now going to ask you to read an especially prominent and recent usage of hypothesis testing in US politics. Specifically, we are going to read excerpts from the *State of Texas v. the Commonwealth of Pennsylvania, the State of Georgia, and the State of Michigan*. If you are attentive to US politics and followed the aftermath of the most recent presidential election, you may already be somewhat familiar with this case.

I should state at the outset that I selected this reading for its relevance. (Indeed, what could possibly be *more* relevant? Here is a recent legal case that uses hypothesis tests to substantiate claims about fraud in a presidential race!) I realize that the reading centers on a sensitive political issue. Accordingly, as we analyze and discuss the text, let’s remember to do so critically but cordially. And, let’s be sure to limit our discussion to what is relevant to the course objectives.

Now read *State of Texas v. Pennsylvania, Georgia, and Michigan*.

Here are some discussion questions to accompany your reading. Please try to answer the questions upon completing the reading, and be prepared to discuss them when we meet in Week 7:

- What is the author’s main claim (i.e., the takeaway of the statistical test)?
- Describe the nature of the statistical tests conducted by the author:
- What are the null and alternative hypotheses for each test?

- Given what you learned about hypothesis testing above, and assuming that the author’s math is correct, what are the results of the tests? (Be precise here.)

- How do you you interpret the results of the tests? How does the author interpret them? What do you think about this interpretation?

**Practice Questions and Exercise**

Once you have worked through the videos and reading, complete the Module 6 Practice Questions, which guide you through several hypothesis tests in R. Once you have finished the Practice Questions, be sure to complete Exercise 3.