Introduction

This is a picture of a Dalmation dog covered in black spots. He is wearing a red color, appears to be in a nature setting, and there is a spout of water from a water fountain in the foreground.
Figure 9.1 You can use a hypothesis test to decide if a dog breeder’s claim that every Dalmatian has 35 spots is statistically sound. (credit: Robert Neff)

Chapter Objectives

By the end of this chapter, the student should be able to do the following:

  • Differentiate between Type I and Type II errors
  • Describe hypothesis testing in general and in practice
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation known
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown
  • Conduct and interpret hypothesis tests for a single population proportion

One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90 percent of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.

A statistician will make a decision about these claims. This process is called hypothesis testing. A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analyses of the data, to reject the null hypothesis.

In this chapter, you will conduct hypothesis tests on single means and single proportions. You will also learn about the errors associated with these tests.

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will do the following:

  1. Set up two contradictory hypotheses.
  2. Collect sample data. In homework problems, the data or summary statistics will be given to you.
  3. Determine the correct distribution to perform the hypothesis test.
  4. Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.
  5. Make a decision and write a meaningful conclusion.

Note

To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets. See Appendix E.