# 8

# HYPOTHESIS TESTS

In this chapter, we move from confidence intervals to hypothesis tests, which are used in *research community* mainly because peer reviewers and regulators typically require evidence of statistical significance prior to publishing or approving results. *Data scientists* will encounter them in what marketers call A–B testing. After completing this chapter, you should be able to

- describe the difference between a hypothesis test and a confidence interval,
- correctly use the vocabulary of hypothesis testing,
- test hypotheses for
- a single proportion
- two proportions
- two means

- distinguish when to use one-way and two-way hypothesis tests.

## 8.1 REVIEW OF TERMINOLOGY

Previously, we introduced these two concepts:

- A study or an experiment to compare one treatment with another.
- Effective design of sample surveys to accurately reveal characteristics of populations.

We also saw that variation comes from two random sources:

- Which subjects get assigned to which treatments, and
- Which individuals or elements get selected for the sample.

We saw that resampling methods, or the corresponding formulas, could be used to quantify this random variability.

*Definition:* Statistical inference

Statistical inference is the process of accounting for random variation in data as you draw conclusions.

### Confidence Intervals and Hypothesis Tests

Inference procedures, which are designed to protect you from being fooled by random variation, fall into two categories.

*Confidence Intervals* Confidence ...