Significance Tests and Decision Making (Lesson 9.2)
Chapter 9  Day 2
Learning Targets

Make an appropriate conclusion in a significance test.

Interpret a Type I error and a Type II error in context.

Give a consequence of a Type I error and a Type II error in a given setting.
Experience First
This Flint water crisis is a real event that happened in a city in our home state. Statistical analysis was used extensively to expose the problem and city leaders often had to make decisions based on the data. In this activity, we illuminate some of the potential errors that can be made in this decision making process.
NOTE: This lesson can be moved to the end of the Chapter without any real disruption. The reason for this move would be to give students more time developing their thinking around conclusions for significance tests before presenting the idea of Type I and Type II errors. If you move this lesson to the end of the Chapter, we recommend two quizzes: one for 9.1, 9.3, 9.4 and the second for 9.5, 9.6, and 9.2.
While students are working on the activity in groups, we highly suggest checking on question #2. They must have the correct hypotheses here for the rest of the activity to go well. As part of your checkin, you might ask students "...so does the null hypothesis say the water is safe or dangerous?".
Formalize Later
An example that often helps students to understand these errors is the United States legal system, where a person is assumed to be innocent (null hypothesis) until proven guilty (alternative hypothesis). Here a Type I error is when an innocent person is convicted, while a Type II error is when a guilty person is set free. Another good example is the Toothpaste example.
This lesson is the appropriate time to inform students that the 5% cutoff for statistical significance is not set in stone. You can use the last question in the activity to open up this conversation. If we all agree that a Type II error is very dangerous in this context, we should feel comfortable increasing the probability of a Type I error if it allows us to decrease the probability of a Type II error. Because the P(Type I error) = alpha, we can increase our significance level alpha (to say 0.10) in order to decrease the chances of people drinking dangerous water.
In the QuickNotes, we provide a table with the 4 possibilities of what can happen when making a decision for a significance test. In a later course, students might learn about the power of a significance test (Ha is true and we correctly reject Ho).
Sometimes it is helpful for students to think of a Type I error as a false positive and at Type II error as a false negative.