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.
Activity: Is Mrs. Gallas a Good Free Throw Shooter?
Be sure to print off spinners for students to use 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 suggest working whole class on questions #1-3 and then letting students work in pairs or groups. Don’t worry too much that students are getting a specific wording of the conclusion. Instead, focus on them understanding the big ideas of significance testing. This activity is where student engage in the thinking, and then later we will give them the formulas and definitions (Experience First, Formalize Later).
Suggestion: Make the dotplot on a poster board or chart paper and save it for Lesson 9.2.
Mrs. Gallas really is an 80% free throw shooter, but this particular random sample of free throws shows less than 80% purely by chance to to the random selection.
Mrs. Gallas is less than 80% free throw shooter.
“Do we have some evidence that Mrs. Gallas is less than 80% free throw shooter?
Yes, her sample proportion is 0.64, which is less than 80%.
“Do we have convincing evidence that Mrs. Gallas is less than 80% free throw shooter?
Maybe. We need to find the probability of her results, assuming she really is an 80% free throw shooter.
For more discussion about “some” evidence versus “convincing” evidence, read this blog post from textbook author Josh Tabor.
Previewing Formal Inference
Don’t worry about vocab and formulas during this activity. But it is important for you as the teacher to know where we are headed:
Null Hypothesis: Mrs. Gallas is an 80% free throw shooter (p = 0.80)
Alternative Hypothesis: Mrs. Gallas is less than 80% free throw shooter (p < 0.80)
P-value: Number of dots less than or equal to 0.64 divided by the total number of dots.
Interpretation of P-value: Assuming Mrs. Gallas is an 80% free throw shooter, there is a (P-value) probability of getting a sample proportion of 0.64 or less purely by chance.
Formal Conclusion: Because (P-value) < alpha = 0.05, this provides convincing evidence that Mrs. Gallas is a less than 80% free throw shooter and we reject Ho.