Lesson 8.1 –The Idea of a Significance Test
- State appropriate hypotheses for a significance test about a population parameter.
- Interpret a P-value in context.
Today we begin significance testing. We will continue this for the remainder of the year. Today’s lesson introduces the idea of a significance test. The goal is to get students thinking about how to test a claim and what would convince them that the claim is true. To do this, you will need to facilitate discussion and steer students with your questioning.
We begin by claiming Mrs. Gallas is an 80% free throw shooter. But when she went down to the gym and shot free throws, she only made 32 out of 50 free throws. Do you think Mrs. Gallas is really an 80% free throw shooter? Give students a minute to identify the population, sample, parameter and statistic. Make sure to use the proper notation and language for the parameter and statistic. This is a review from chapter 7.
Next we need to get students thinking about the two possible explanations for why Mrs. Gallas only made 32/50 free throws. This should be a class discussion, but wrap it up together in this order:
- Mrs. G. is an 80% free throw shooter and just had a streak of bad luck.
- Mrs. G. is not an 80% free throw shooter.
After discussing this, add into the margins that explanation #1 is the null hypothesis and explanation #2 is the alternative hypothesis. Explain that in order to test Mrs. Gallas’ claim, we will begin by assuming she is telling the truth but that she had an off day. To do this, we need to figure out the likelihood that an 80% shooter only makes 32/50. We are going to simulate this using a spinner. The spinner is made with the 10 section pie chart included and a paper clip. Discuss with students that in order to make the spinner an 80% shooter, they should label 8 out of 10 sections as a make and the remaining two are misses.
Students will need to take samples of 50 “free throws” and calculate the proportion of made free throws. We need lots of samples so each student is responsible for two samples. When they are done, they should add a dot to the dotplot you will draw on the board that is labeled from 0.50 to 1.
After collecting all samples, add to the dotplot a title. Identify that the dots are samples of 50 shot by an 80% shooter, not Mrs. Gallas! Now we can calculate the probability that an 80% shooter only makes 64% or less. Identify in the margin that this is the P-value. Depending on the class data, you may reject or fail to reject the null hypothesis. Whichever you do, add this into the margin.
We used a sentence frame for interpreting a P-value:
Assuming ___________________ (the null hypothesis context) there is a _________ (P-value) probability of getting _________ (given statistic) or lower/higher.