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Confidence Intervals for Difference
of Proportions

Chapter 10 - Day 2 - Lesson 10.1

Learning Targets
  • Determine whether the conditions are met for doing inference about a difference between two proportions.

  • Construct and interpret a confidence interval for a difference between two proportions.

Activity: Which Gender Uses Twitter More? 
Answer Key:

The best part about this Activity and this lesson is that students have all of the pieces of the puzzle to put it together without the help of the teacher. They know the four step process. They know how to construct a confidence interval. They know the formulas for the sampling distribution of the difference of proportions. Here they put it all together. Be sure that students clearly show the direction of their subtraction (females – males) and notice the additional sentence we added to the conclusion. At the end of the Activity, you can preview significance tests (which students will do tomorrow) by asking if the confidence interval provides convincing evidence that there is a difference in Twitter use between the genders. The answer is yes, because the confidence interval of plausible values does not include 0.

General Formula, Specific Formula, Work, Answer.

This is where we start to reap the benefits of asking students to provide the General Formula and Specific Formula for every confidence interval and significance test. The General Formula for a confidence interval is always the same: point estimate +/- margin of error. This General Formula should help students to produce the Specific Formula without memorizing.

4-step White Board Critique

We used the Check Your Understanding to do a White Board Critique. Here is how it works:

  1. Assign students a 4-step problem to work on in pairs.

  2. Monitor the room to support student learning. As each pair finishes, send them to the white board to write up 1 of the steps STATE, PLAN, DO, or CONCLUDE. The first two pairs should handle the PLAN and the DO because they take the longest to write up.

  3. Once all 4 steps are on the board, call the class back together as a group. Ask them to critique the solution on the board as if it were a quiz or test question. Make any revisions with a red marker. This is your opportunity to make clear your expectations for a 4-step problem on an assessment.

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