Applied Statistics and Probability for Engineers

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 theP-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.

278 CHAPTER 9 TESTS OF HYPOTHESES FOR A SINGLE SAMPLE

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

Definition

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