9

Hypothesis Testing

. . .the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation. Every experiment may be said to exist only to give the facts a chance of disproving the null hypothesis.

R. A. Fisher

The focus of this chapter is a discussion of testing of statistical hypotheses.

# Topics Covered:

- 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 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 errors, and determine the power of a test
- Understand the concept of the p-value, calculate it, and then use it to make the correct decision.
- Use appropriate confidence intervals to carry out various tests of hypotheses.