##
Overview
Section* *

#### Case-Study: Guilty

Jin and Carlos watching a recent T.V. show, and the episode concluded with a courtroom scene. In the scene, the judge handed down her conclusion. She said “I do not have enough evidence to conclude you are not guilty, therefore I can NOT conclude you are guilty” Carlos turned to Jin and said, “Isn’t this the same thing as being innocent?“. Let’s see if we can use the logic of hypothesis testing to help Jin respond to Carlos.

In lesson 4, we learned about constructing confidence intervals to estimate actual population values. In this unit, we extend this idea of estimation to testing specific (hypothesized) values. Much of our day to day lives involves hypothesizing about actual values. Does the average number of hours worked a week really equal 40? Is the average fish caught on a weekend fishing trip really equal 4 feet (Ok, that is an attempt at a fish story)? These are examples of hypothesis testing. In a courtroom in the U.S., the hypothesis test is about being innocent (remember innocent until proven guilty).

It is important to understand that confidence intervals and hypothesis tests are similar, but used for different purposes. Confidence intervals give us an estimate of a population value when we typically do not know what the population value is. On the other hand, hypothesis tests require us to start with a guess (hypothesis) about what we think the value is. For example, we may think the difference between groups is zero and we want to see our evidence supports this guess. However, in practice, most people put more emphasis on confidence intervals as opposed to hypothesis testing, because confidence intervals estimate of specific values, but hypothesis testing is still an integral part of what we do in research.

So what is hypothesis testing and how can it help Jin explain the judge’s ruling?

## Objectives

- Compute a hypothesis test for two groups
- Correctly identify elements of Z and T test
- Apply the appropriate test for quantitative versus categorical data
- Correctly interpret the results of a hypothesis test (including p values)
- Identify the similar elements between confidence intervals and hypothesis tests