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Presidential elections are a great example of this. Election committees often put out surveys to see if citizens in a state will vote for a given candidate. Let’s say that in Utah, a survey to determine whether citizens vote republican or not shows a 99% confidence interval of (0.65, 0.8).
Since we are 99% confident that the overall proportion of Utah citizens that vote republican is between 0.65 and 0.80 (between 65% and 80%), then we are very confident that the state will vote republican.
Next presidential election, watch the news when polls close. You’ll see that they will declare Utah as republican before they count a single vote. This is because the confidence interval is so clearly in the majority.