Confidence interval
Also known as: interval estimate, CI
A confidence interval is a range of values, built from sample data, that is likely to contain an unknown population parameter such as a mean or proportion. It takes the form point estimate ± margin of error at a stated confidence level, commonly 95%.
A confidence interval is an interval estimate for an unknown population parameter — a mean, a proportion, a difference between groups — computed from sample data. Instead of reporting a single number (a point estimate), it reports a range: point estimate ± margin of error. The margin of error equals a critical value (from the z or t distribution) multiplied by the standard error of the estimate.
The confidence level describes the long-run reliability of the method. If you took many random samples and built a 95% confidence interval from each, about 95% of those intervals would capture the true parameter. For example, if a sample of test scores has a mean of 78 and the 95% interval is (74, 82), the data are consistent with a population mean anywhere in that range. The correct interpretation is about the method, not any single interval — a common exam trap is the claim that "there is a 95% probability the parameter is in this interval."
Three factors control an interval's width: confidence level (higher confidence → wider interval), sample size (larger n → narrower interval), and variability in the data (more spread → wider interval). Confidence intervals also connect to hypothesis testing — a 95% interval that excludes the null value corresponds to rejecting that null at the 5% significance level.
Confidence intervals are tested across a striking range of exams. AP Statistics builds intervals for means and proportions and stresses interpretation; USMLE Step 1 tests confidence intervals in biostatistics, especially whether an interval for a risk ratio or odds ratio crosses 1; and the CMA Part 1 exam includes them in its regression and statistical methods coverage.
Key takeaways
- A confidence interval is point estimate ± margin of error, giving a range of plausible values for a population parameter.
- A 95% confidence level means the method captures the true parameter in about 95% of repeated samples.
- Higher confidence levels and more variability widen the interval; larger samples narrow it.
- If a 95% interval excludes the null value (e.g., a ratio interval excluding 1), the result is statistically significant at the 5% level.
- AP Statistics, USMLE Step 1, and CMA Part 1 all test constructing or interpreting confidence intervals.