Hypothesis Tests Comparing Two Means

Overview of Mean Comparison Formulas (lots of Student t-Tests)

Hypothesis testing of two sample means is so confusing because there are four sets of formulas! This video just gives you an overview of how to approach these problems: paired (dependent) samples, samples where you know sigmas, samples where you don't know sigmas but assume they're equal, and samples where you don't know sigmas nor assume they're equal.

Comparing Means When You Know Sigmas of the Populations

This video covers the type of problem where you're testing a hypothesis about the means of two samples when somehow you magically know the two samples' population standard deviations. This is not a very realistic scenario, because if you don't know the populations' means how would you know their standard deviations, but most classes cover it anyways as a way to introduce hypothesis testing of means. Also included: doing these on your calculator.

Means of Independent Samples-Sigmas Unknown & Assumed Unequal (Student t-Test)

This video covers hypothesis tests of the means of two samples where you make no assumptions at all - all you have to work with are the means and standard deviations of your samples. This is what happens in real life when you're analyzing data, so this is the one that's most important for you to know for tests and future math classes. Student t-distribution, here we come! Also included: doing these on your calculator.

Means of Independent Samples-Sigmas Unknown But Assumed Equal (Pooled Variance)

Stay with me: When you compare two samples, you're trying to figure out something about the populations from which those samples were drawn, right? In this particular type of hypothesis test, even though you don't know the standard deviations of those two populations, we will nonetheless assume that the two standard deviations are equal so that we can "pool" their variances. Why? The reasons are subtle, but they have to do with getting to use more degrees of freedom.

Comparing Sample Means with Matched Pairs (Dependent)

Yet another type of Student t-Test, this is a fun type of hypothesis test because it's what you see all the time in real life, especially in before-and-after infomercials! It's also good for stats students because: 1) the formulas are a lot simpler than the crazy ones comparing other types of means; and 2) the problems are pretty easy to spot. Also included: doing these on your calculator.

Confidence Intervals Comparing Means of Two Samples

This video shows you how to create a confidence interval comparing two sample means, based on looking at the formulas for hypothesis testing two means.

Mean Comparisons On Your Calculator

There are so many types of sample mean hypothesis tests, it's hard to keep track! I put the calculator how-to's in the previous videos about each type of problem, but in this video I just jump through them real quick and show you the menu picks for each of the types of problems, so you can review them quickly before a test. Add this to your playlist!