Estimating a Difference Between Two Proportions (Lesson 10.1)
Chapter 10 - Day 1
Chapter 10
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
All Chapters
Learning Targets
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Check the Random and Large Counts conditions for constructing a confidence interval for a difference between two proportions.
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Calculate a C% confidence interval for a difference between two proportions.
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Use the four-step process to construct and interpret a confidence interval for the difference between two proportions.
Experience First
In Chapter 8, students learned how to construct and interpret confidence intervals for a proportion or a mean. In Chapter 9, students learned how to perform a significance test for a proportion or a mean. In Chapter 10, students will learn several more confidence interval and significance test procedures, in the following three categories:
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Difference of proportions (Lessons 10.1 and 10.2)
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Difference of means (Lessons 10.3 and 10.4)
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Mean of differences - Paired data (Lessons 10.5 and 10.6)
Of course, we will continue to use the same 4-step process (STATE, PLAN, DO, CONCLUDE) that we used in the previous two chapters. The big decision you will need to make as a teacher is around what you expect students to write for calculations (the DO step). It would be perfectly acceptable to continue the same expectations as in the previous chapters (General Formula, Specific Formula, Work, Answer). The challenge with maintaining this expectation in Chapter 10 is that the formulas get quite messy, and we don't want to distract students from what matters most here - the conclusions made in the context of the problem. For this reason, we have decided to instruct students to use technology for all calculations in this chapter. We will use the Traditional Inference applets at www.statsmedic.com/applets.
In this lesson, students will use the Two sample z interval for proportions applet. Notice that the data will need to be input into a two-way table.
Formalize Later
When debriefing the activity, here are a few items to highlight:
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When defining the parameter, it is important to include the word "difference" and to clearly indicate the order of subtraction.
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It is perfectly acceptable to subtract in the other order (Juniors - Seniors), as long as you are consistent with this choice throughout. The correct interval here would be (-28.1%, 11.2%).
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The Random and Large Counts condition now need to be checked for two samples (twice the work!).
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Remember that a confidence interval gives a list of plausible values for the parameter. In this activity, it is plausible that a higher percent of Juniors is going to prom (by as much as 11.2%) or that a higher percent of Seniors is going to prom (by as much as 28.1%).
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Because the confidence interval contains 0, it is plausible that there is no difference in the proportion of Juniors and Seniors going to prom.