I teach the sections of Chapter 13 in a different order than they appear in your textbook. I explain why here, and I also review the basic steps you’ll need to cover for full marks on a hypothesis test.

# Chapter 13: Inference about Comparing Two Populations

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## Lessons

## 13.0 | Introduction (Preview)

## 13.4 | F-test & Estimate (Preview)

The F-test plays an important role in Chapter 13. It allows us to compare the variances of two populations (using samples from each one) to determine if one is bigger, smaller, or simply different from the other. This also allows us to properly choose which t-test is appropriate (equal or unequal variances t-test) when comparing two population means. **You’re not done studying this chapter until you’ve mastered the F-test and F-estimate!**

## 13.1 | Equal Variances t-Test

This is one of the most common types of questions you'll find on past exams. It involves most new aspects of this chapter: Comparing two populations, running an initial F-test to determine that the population variances can be assumed equal, and finally the t-test itself - accompanied by it's own specific formulas for the test statistic and degrees of freedom. You'll need to be good (and fast) at solving this type of problem.

## 13.1 | Unequal Variances t-Test

When comparing two population means, you need to first run an F-test to determine whether or not the population variances can be considered equal. If the results of that F-test of variances leads you to reject the null hypothesis, then you can assume the population variances differ. This t-test is the follow-up step where you can then compare the two population means (unequal variances assumed).

## 13.3 | Matched Pairs t-Test & Estimate

Studies done by testing the same group of subjects twice (before and after some event / treatment) can produce more useful results than comparing the responses of two independent groups. When repeatedly measureing the same group is not possible, then matching pairs of individuals across the independent groups can also increase the odds that a test can find significant results.

## 13.5 | z-Test of Proportions (CASE 1)

The CASE 1 z-test of proportion can check to see if the proportion of individuals who fit in a specific category is larger in one population than it is in another population, or if it's smaller in one population than it is in another population, or if it's different in one population than it is in another population.

## 13.5 | z-Test of Proportions (CASE 2)

The CASE 2 z-test of proportion can check to see if the proportion of individuals who fit in a specific category is larger ** by a defined amount** in one population than it is in another population, or if it's smaller

**in one population than it is in another population, or if it's different**

*by a defined amount***in one population than it is in another population.**

*by a defined amount*## Multiple Choice

Test your understanding of Chapter 13: Inference About Comparing two Populations . Each question is accompanied by a mini-video lecture showing you how I decided which solution was the correct one.