Testing a Claim About a Proportion (Lesson 9.3)

Chapter 9 - Day 3

Learning Targets
  • Check the Random and Large Counts conditions for performing a significance test about a population proportion.

  • Calculate the standardized test statistic for a significance test about a population proportion.

  • Find the P-value for a one-sided significance test about a population proportion using Table A or technology.

Activity: Is Mrs. Gallas a Good FT Shooter Part 2
Activity:
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Experience First

Before starting this lesson, there are a few items to have prepared:

  • Display the dotplot poster from Lesson 9.1, where students used spinners to simulate Mrs. Gallas taking free throws.

  • Make copies of Table A, or be sure students have access to Table A in the textbook.

  • Have students find their Chapter 7 Formula Review Sheet. This will be a helpful resource during the activity in this lesson.

 

This activity is an extension of the opening activity from Lesson 9.1, where students used a simulation to estimate the P-value for a significance test. In this lesson, students will use a normal distribution to calculate the P-value. 

As groups are working through questions #3-4 in the activity, be sure they are using the proportion from the null hypothesis (0.80), and not the sample proportion (0.64). This is because we assume the null hypothesis is true, which means we do know the true population proportion is 0.80. 

There is absolutely no new content in this activity. Students will be taking content from across the entire course and putting all the puzzle piece together today. It is our job to then formalize all of this learning with vocabulary, notation, and formulas. We are preparing students to do a full 4-step significance test in the next lesson. 

Formalize Later

The margin notes in red during the debrief are absolutely essential. This lesson is a perfect example of the Experience First, Formalize Later (EFFL) teaching model. 

 

Notice that we continue to practice the interpretation of the P-value. This is the holy grail of an intro stats class! It is what allows students to understand a significance test, rather than memorize a rule for significance tests (if the P is low, the null must go). During the debrief, we bring attention to the fact that the P-value is just the area of the shaded region in the normal distribution. 

In the QuickNotes, you will notice that we provide students with two formulas. We call these the GENERAL FORMULA and the specific formula. The GENERAL FORMULA will work for most significance tests we do in this course (chi-square tests are weird), while the specific formula changes from test to test. In the next lesson, students will be doing a full 4-step significance test, in which we will require them to provide both formulas.

We strongly suggest that students should not yet be made aware of calculator functions and applets that will perform entire significance tests yet. We save this reveal for after the Quiz 9.3 to 9.4.

Students should be ready for a full 4-step significance test in the next lesson!