• Calculate a confidence interval and explain what it means.
• Recognize common misinterpretations of confidence intervals.

Simulation of finding confidence intervals

Let’s continue exploring the data from a national survey of college students conducted by the American College Health Association. One of the questions posed to the participants was, “On how many of the last 7 days did you take a nap?”

Suppose we knew that the population proportion of college students who did not take a nap in the last week was [latex]0.40[/latex], or [latex]40\%[/latex]. Of course, in reality, we wouldn’t know the population proportion, but let’s assume that we did.

If we wanted to, we could simulate taking an even larger number of samples from this population and constructing a confidence interval for each one. Feel free to explore this further using the tool below:

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If we were to continue to repeatedly take more and more samples from the population and construct a confidence interval for each one, we would expect the proportion of confidence intervals containing the population proportion to be equal to the chosen confidence level.

Put another way, if we were constructing [latex]95\%[/latex] confidence intervals, then in the long run, we would expect [latex]95\%[/latex] of the intervals to contain the population proportion.

An important takeaway is that the chosen confidence level is associated with the method used to create the interval and not the likelihood that an individual interval contains the population proportion.