# 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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