Statistics
Activity:
Difference Between Two Proportions
Posted on May 26, 2008
Topic: Sampling Distributions
In this activity, students use confidence intervals to estimate the difference of two population proportions. First they find the intervals by calculating the critical value and the margin of error. Last, they determine the sample size when given a confidence interval and margin of error.
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Activity Key Steps:
In Problem 1, students estimate the true difference between two population proportions in order to introduce the formulas for the margin of error and confidence interval.
The scenario students use describes the numbers of men and women that used coupons at a grocery store. They are to use the Calculator application to find each sample proportion and the difference between them.
Students will find the margin of error, but first they will use the invNorm command to calculate the z-score. After doing so they will store the value.
They construct the confidence interval by subtracting from and adding to the difference of the sample proportions. Students can also enter the z-score themselves, shown to the right.
Students will state their findings as a statement, a sample is below:
We are 95% certain that the difference in proportion of men and women who use coupons at that store is between 1.5% and 31.2%.
Problem 2 is a set of problems for students to practice. They can then move on the Problem 3, which investigates Sample Size.
At the end of this activity, students use the fact that the sampling distribution of the difference is approximately a normal distribution with mean p1 – p2 and standard deviation
to calculate a confidence interval for p1 – p2.