What Is a Confidence Interval? (With Examples)
What a confidence interval means, the correct way to interpret 95% confidence, how the interval is built, and what makes it wider or narrower.
6 min read · Reviewed August 2026
What a confidence interval means
A confidence interval is a range of plausible values for an unknown quantity — like a population mean — estimated from a sample. Instead of reporting a single number, you report a range, along with a confidence level (usually 95%) that reflects how the method performs over the long run.
For example, “the average commute is 34 minutes, 95% CI [31, 37]” says your best estimate is 34 minutes, and the data is consistent with a true average anywhere from about 31 to 37.
The correct interpretation of “95% confident”
The correct reading: if you repeated the whole study many times and built an interval each time, about 95% of those intervals would contain the true value. The 95% describes the reliability of the method, not this one interval.
How a confidence interval is built
Most confidence intervals for a mean have the same shape: a point estimate plus or minus a margin of error.
Here x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and t* is the critical value from the t-distribution for your confidence level. (For known population variance or large samples, a z critical value is used instead.)
What makes an interval wider or narrower
| Factor | Effect on width |
|---|---|
| Larger sample size (n) | Narrower — more data, more precision |
| Higher confidence level (99% vs 95%) | Wider — more certainty needs more room |
| More variable data (larger s) | Wider — noisier data, less precision |
This is why bigger samples are so valuable: they shrink the margin of error and give you a tighter, more useful interval.
Confidence intervals and hypothesis tests
Confidence intervals and hypothesis tests are two sides of the same coin. If a 95% confidence interval for a difference excludes 0, the corresponding two-tailed test is significant at α = 0.05. The interval adds something the p-value alone cannot: the size and direction of the effect.
Frequently asked questions
What does a 95% confidence interval actually mean?
It means the method used to build the interval captures the true value about 95% of the time over many repeated samples. It does not mean there is a 95% chance the true value is in this specific interval.
Why would I use a wider confidence level like 99%?
A higher confidence level gives you more assurance that the interval contains the true value, at the cost of a wider (less precise) interval. Choose based on how costly it would be to miss the true value.
How do I make a confidence interval narrower?
Increase the sample size, reduce the variability in your measurements, or accept a lower confidence level. Sample size is usually the most practical lever.