Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 9

Hypothesis Testing

The focus of this chapter is a discussion of testing of statistical hypotheses. The topics covered are:

• Basic concepts of testing of statistical hypotheses
• Tests concerning the mean of a normal distribution when variance is known
• Tests concerning the mean of a normal distribution when variance is unknown
• Tests concerning population means when sample size is large
• Tests concerning the difference of means of two populations with known variances
• Tests concerning the difference of means of two populations with unknown variances
• The paired t-test
• Testing concerning the one and two population proportions when sample size is large
• Tests concerning the variance of a normal distribution
• Tests concerning the ratio of variances of two normal populations
• Sequential tests of hypotheses

Learning Outcomes

After studying this chapter, the reader will be able to

• Construct null and alternative hypotheses.
• Determine an appropriate test statistic and use it to carry out a hypothesis test.
• Understand the concepts of type I and type II error, and determine the power of a test
• Understand the concept of p-value, calculate it, and then use it to make the correct decision.
• Use appropriate confidence intervals to carry out various tests of hypotheses.

9.1 Introduction

In our discussion in earlier chapters we noted that one of the aims of statistics is to make inferences about the unknown parameters of a population, based upon the information contained in a sample that is ...