Interpreting Confidence Intervals

Statistics · Axiom Academy

LESSON Interpreting Confidence Intervals Understanding what confidence intervals really tell us—and what they don't 1. What Confidence Intervals Really Mean A 95% confidence interval is constructed using a procedure that, if repeated many times with different samples, will produce intervals that contain the true parameter in 95% of cases. Watch how different samples from the same population produce different intervals: 2. The Most Common Misconception Why is this wrong? Once you've calculated a specific interval from your data, that interval either contains the true parameter or it doesn't. The true parameter is a fixed value—it's not moving around randomly. Visualize why probability doesn't apply to a specific interval: Here are several correct ways to interpret a 95% confidence interval: 4. Other Common Misconceptions Reality: The confidence interval is for the parameter (like the population mean μ), not for individual data values. You're thinking of a prediction interval or the spread of data. Reality: A wider interval means more uncertainty about where the parameter lies. Wider = less precise. A 99% CI is wider than a 95% CI because we're demanding higher confidence in the procedure. 5. Putting It All Together: A Real Example Suppose we survey 100 voters and find that 52% support a candidate. We calculate a 95% confidence interval: [42%, 62%].

This is the written version of the interactive lesson above. See the full Statistics course.