The Idea of a Significance Test (Lesson 9.1)
Chapter 9 - Day 1
State appropriate hypotheses for a significance test about a population parameter.
Interpret a P-value in context.
Make an appropriate conclusion for a significance test based on a P-value.
In this lesson, students will be introduced to the idea of a significance test using a simulation. Later in Lesson 9.3, students will use this same scenario to prepare for writing up full 4-step significance tests in Lesson 9.4.
You will want to make copies of the spinner (1 for each student) and change the name of the teacher on the Activity (unless your class already knows Mrs. Gallas…she is kind of a big deal). We highly suggest using large paper or a poster for the dotplot in the activity, so that you can refer back to it when you get to Lesson 9.3.
We suggest that you go through question #1 as a whole group, then let the students work in groups on the remainder of the activity.
Guiding Questions to use during the activity and debrief:
What title should we put on the dotplot?
Do we have some evidence that Mrs. Gallas is exaggerating? Do we have convincing evidence?
While this activity is meant to be an introduction to the P-value and the idea of a significance test, it is NOT the first time students will be doing inferential thinking. In fact, they calculated a P-value on the first day of class (Can Joy Smell Parkinson's?). They did similar thinking in the Is Anchored Putting Better? in Chapter 4. It is in this lesson that we really start to formalize with the vocabulary and notation around hypotheses, P-value, and making a formal conclusion for a significance test.
To extend the simulation to many more trials, use the 1 Categorical Variable, Single Group applet. Use Variable Name: Mrs. Gallas Free Throws, with two categories (yes = 32, no = 18). Click "Begin Analysis", then scroll down to the Perform Inference section, where you will "Simulate Sample Percent" with the hypothesized percent set to 80%.
While the activity utilizes an alternative hypothesis that is one-sided (p < 0.80), we introduce the idea of a two-sided test in the QuickNotes. Students will get more practice with this later. Also in the QuickNotes, we leave the vague idea that the "P-value is small" or the "P-value is large". You may want to discuss the commonly used cutoff of 5% to make this determination, but students will get the formal introduction to significance level in the next lesson.
In the QuickNotes, we also introduce students to the concept of "fail to reject the null" rather than accepting the alternative. To help students understand, we give the example of the United States legal system, where defendants are assumed to be innocent (null hypothesis) until convincing evidence is presented to deem them guilty (alternative hypothesis). The courts final ruling at the end of a trail is guilty (reject the null) or not guilty (fail to reject the null). Stating that a person is "not guilty" is not the same as saying they are "innocent"; it's just that there was not convincing enough evidence that they are guilty.