Significance Test for a Proportion
Chapter 9 - Day 4 - Lesson 9.2
Learning Targets
-
State and check the Random, 10%, and Large Counts conditions for performing a significance test about a population proportion.
-
Calculate the standardized test statistic and P-value for a test about a population proportion.
Activity: Are You Sure Mrs. Gallas Isn’t a Good Free Throw Shooter?
Activity:
Answer Key:
This Activity is the formalization of the experience that students had in the Chapter 9 Intro. We are setting the stage for students to be able to produce a formal 4-step significance test.
Putting it All Together
The amazing part about this lesson is that students already have all of the pieces. They just need to put them together. Here is a list of all the pieces:
-
Normal distribution calculations – Lesson 2.2.
-
Random Condition – random sampling was introduced in Lesson 4.1 and random assignment was introduced in Lesson 4.2.
-
10% condition – Lesson 6.3
-
Large Counts Condition – Lesson 6.3.
-
Sampling distribution of a sample proportion – Lesson 7.2
-
Making conclusions based on P-value – Lesson 9.1.
Interpreting the P-value using the picture
Be sure that students recognize that the Normal distribution in this activity is really just a model for the sampling distribution of a sample proportion (hopefully you saved your dotplot from the Chapter 9 Intro). Properly labeling and shading the Normal distribution leads directly to the interpretation of the P-value:
P-value = shaded region
Interpretation: Assuming Mrs. Gallas is an 80% free throw shooter (p = 0.80), there is a 0.002 probability of her getting a sample proportion of 0.64 or less, purely by chance.