# 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 ...

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