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Confidence Intervals

Definition

Confidence intervals are ranges of values calculated from sample data that are likely to contain an unknown population parameter with a certain level of confidence.

Analogy

Imagine you have a bag of marbles, but you don't know how many there are. You take multiple samples and calculate confidence intervals to estimate how many marbles are in the bag. The wider your interval, the less confident you can be about your estimate.

Related terms

Margin of Error: The margin of error is half the width of a confidence interval and represents how much we expect our estimate to vary from sample to sample.

Level of Confidence: The level of confidence determines how sure we want to be that our confidence interval contains the true parameter value. Common levels include 90%, 95%, and 99%.

Sample Size: Increasing sample size generally leads to narrower confidence intervals because more data reduces uncertainty.

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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.