Techniques of Hypothesis Testing

Techniques of Hypothesis Testing
Dr. Scott Stevens

Objectives

When you finish reading this article, you should be able to

• Determine the appropriate null and alternate hypotheses for your hypothesis test • Determine if your test is one- or two- tailed • Conduct an appropriate test using Excel in any of three ways o Using the critical score approach o Using the non-rejection region approach (for a two-tailed test) o Using the P-value approach

Selecting the Right Null Hypothesis

There are four ideas to keep in mind when creating the null and alternative hypotheses :

• The null and alternative hypotheses always talk about population characteristics, never sample characteristics. In our course, this means that null and alternative hypotheses will always be about μ and π, never about or p. (In Chapter 10, we’ll be dealing with more than one population, but the null will still be about population parameters.)

• The null and alternative hypotheses are complementary events. Said less formally, the null and alternative hypotheses “cover all of the bases”. If the null says “μ < 6”, then the alternative has to be everything that’s left — “μ > 6”.[1]

• The null hypothesis always contains the “=” part of the hypotheses; that is, our null hypotheses will always be “>”, “ 0.5. This means my null hypothesis must be H0: π < 0.5.

One-Tailed and Two Tailed Tests

Here’s an easy rule of thumb:

• If the null hypothesis is an equality (“=”), you’re doing a two-tailed test • If the null hypothesis is parameter > number, you’re doing a lower-tail test • If the null hypothesis is parameter < number, you’re doing an upper-tail test

What does the “tail of the test” mean? It’s specifying what kind of sample statistic will lead to rejection of the null hypothesis. If the null hypothesis is that a population’s mean is 100, then a sample mean that’s a lot bigger than