• Calculate a confidence interval for the difference in proportions of two groups.
• Make conclusions based on a confidence interval.

Confidence intervals for the difference in proportions

Our primary goal is to use the data to examine whether there’s a difference in the proportions of regular voters between eligible voters who said they affiliate with a major political party ([latex]p_{1}[/latex]) and those who said they don’t ([latex]p_{2}[/latex]).

Ideally, we would have complete data about the two populations of interest (eligible voters with and without a major party affiliation) so we could calculate [latex]p_{1} - p_{2}[/latex] directly. However, we don’t have complete data on each population, so we’ll use our samples to draw conclusions about the differences between these two groups.

Let’s analyze this data set using our statistical tool.

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Though we have a “best guess” for the difference in proportions of regular voters between the two groups, we expect there is some variability associated with that guess. In other words, if we calculated the difference in proportions of regular voters from two other random samples of [latex]3,594[/latex] eligible voters with a major party affiliation and [latex]2,242[/latex] eligible voters without an affiliation, we would expect to get a different (yet probably close) value of [latex]\hat{p}_{1} - \hat{p}_{2}[/latex] than we did in the previous question.