Chapter 16: Confidence Intervals and Hypothesis Testing
This chapter shows how a single sample can be used to construct confidence intervals and test hypotheses about population parameters. Hypothesis testing, also known as testing for significance, is a fundamental part of inferential econometrics.
Statistical significance should not, however, be confused with practical importance. Just because we can reject a null hypothesis and claim a statistically significant result, does not mean that the result matters. In economics, many data sets are large n, which means it is easy to find statistically significant results that are not of practical importance. Tests of significance have a place in econometrics but are not the be all and end all of inference.
Hypothesis testing can be confusing, but it has a coherent, stable framework
that should help you organize the complicated details. The next section demonstrates
that there is a sampling distribution for each sample statistic that is a
random variable. Section 16.3 will explain how confidence intervals are constructed
and interpreted. We then turn to the logic of hypothesis testing (Section
16.4) and explain why the t distribution is so often used (Section 16.5).
The chapter’s last section puts the ideas into practice by working on
a real-world example.