The following material is from section 10.2 in the textbook.

Introduction

As with single samples and populations, we can ask questions and test hypotheses to compare two population parameters, such as two population means, using sample statistics. This simply require a different type of test, but overall the procedure is the same. Two notes:

two sample tests can be completed with either the p-value method or the rejection region method
we must consider whether the samples we take are independent vs dependent before deciding the correct procedure
we will not use a 2-sampleZtest in general, since these are not realistic in applications.

Independent vs. Dependent Samples

In independent samples, the two samples have nothing to do with each other. They are chosen completely independently of each other.

In dependent, or paired samples, there is a connection between the two samples. Often, these are before and after values for some type of experiment.

The two-sample t-test

When comparing the means of two populations using two independent samples, you will use a 2-sample t-test. This is located on your calculator under [STAT]->Tests. The hypotheses will look like the following:

Notice again that the overall idea from 1-sample tests is the same, the notation is just different to account for two populations.

Do you pool or not?

You may notice in this test, that you are asked whether or not to pool (in the calculator and in other software). Looking in the textbook, you will see that the formulas for the degrees of freedom and the test statistic are quite different in each case. The rule is:

If variances are assumed to be equal, pool. (This means that we make one estimate for the shared variance).
If variances are assumed to be unequal, do not pool. (This means two separate estimates are made).

Example video

The following video will walk you through an example problem that uses a 2-sample t-test. Use the following calculator guide as you watch the video: 2 Sample ttest.pdf

Click NEXT to continue to the dependent samples t-test.