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278 CHAPTER 9 TESTS OF HYPOTHESES FOR A SINGLE SAMPLE

LEARNING OBJECTIVES

After careful study of this chapter, you should be able to do the following:
1. Structure engineering decision-making problems as hypothesis tests
2. Test hypotheses on the mean of a normal distribution using either a Z-test or a t-test procedure
3. Test hypotheses on the variance or standard deviation of a normal distribution
4. Test hypotheses on a population proportion
5. Use the P-value approach for making decisions in hypotheses tests
6. Compute power, type II error probability, and make sample size selection decisions for tests on
means, variances, and proportions
7. Explain and use the relationship between confidence intervals and hypothesis tests
8. Use the chi-square goodness of fit test to check distributional assumptions
9. Use contingency table tests
CD MATERIAL
10. Appreciate the likelihood ratio approach to construction of test statistics
11. Conduct small sample tests on a population proportion

Answers for many odd numbered exercises are at the end of the book. Answers to exercises whose
numbers are surrounded by a box can be accessed in the e-Text by clicking on the box. Complete
worked solutions to certain exercises are also available in the e-Text. These are indicated in the
Answers to Selected Exercises section by a box around the exercise number. Exercises are also
available for some of the text sections that appear on CD only. These exercises may be found within
the e-Text immediately following the section they accompany.

9-1 HYPOTHESIS TESTING

9-1.1 Statistical Hypotheses

In the previous chapter we illustrated how to construct a confidence interval estimate of a pa-
rameter from sample data. However, many problems in engineering require that we decide
whether to accept or reject a statement about some parameter. The statement is called a
hypothesis, and the decision-making procedure about the hypothesis is called hypothesis
testing. This is one of the most useful aspects of statistical inference, since many types of
decision-making problems, tests, or experiments in the engineering world can be formulated
as hypothesis-testing problems. Furthermore, as we will see, there is a very close connection
between hypothesis testing and confidence intervals.
Statistical hypothesis testing and confidence interval estimation of parameters are the funda-
mental methods used at the data analysis stage of a comparative experiment, in which the engi-
neer is interested, for example, in comparing the mean of a population to a specified value. These
simple comparative experiments are frequently encountered in practice and provide a good foun-
dation for the more complex experimental design problems that we will discuss in Chapters 13
and 14. In this chapter we discuss comparative experiments involving a single population, and our
focus is on testing hypotheses concerning the parameters of the population.
We now give a formal definition of a statistical hypothesis.

Definition
A statistical hypothesis is a statement about the parameters of one or more populations.