In This Chapter

Testing differences between means of two samples

Testing means of paired samples

Testing hypotheses about variances

In business, in education, and in scientific research the need often arises to compare one sample with another. Sometimes the samples are independent, sometimes they're matched in some way. Each sample comes from a different population. The objective is to decide whether or not the populations they come from are different from one another.

Usually, this involves tests of hypotheses about population means. You can also test hypotheses about population variances. In this chapter, I show you how to carry out these tests. I also discuss useful worksheet functions and data analysis tools that help you get the job done.

As in the one-sample case (Chapter 10), hypothesis testing with two samples starts with a null hypothesis (H_{0}) and an alternative hypothesis (H_{1}). The null hypothesis specifies that any differences you see between the two samples are due strictly to chance. The alternative hypothesis says, in effect, that any differences you see are real and not due to chance.

It's possible to have a *one-tailed test*, in which the alternative hypothesis specifies the direction of the difference between the two means, or a *two-tailed test* in which the alternative hypothesis does not specify the direction of the difference.

For a one-tailed test, the hypotheses look like this:

H_{0}: μ_{1}- μ_{2} = 0

H_{1}: μ_{1}- μ_{2}

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