A confidence interval gives a range produced by a sampling method. It communicates uncertainty around an estimate, but it is not a promise that a particular future value will fall inside the range.
The estimate and the margin
An interval is commonly written as an estimate plus or minus a margin of error. The margin reflects variability, sample size, and the selected confidence procedure.
What confidence means
In repeated sampling, a method designed for 95% confidence will capture the true parameter about 95% of the time under its assumptions. It is not accurate to say there is a 95% probability that one fixed parameter is moving between this one interval's endpoints.
Check the assumptions
Independence, sample design, distribution shape, standard error, and measurement quality matter. A larger sample often narrows the interval, but a biased sample can remain misleading.
A worked example
Worked example: an estimate of 50 with a margin of 4 creates an interval from 46 to 54 under the selected method. The width communicates sampling uncertainty, not every possible source of error.
Report the sample, method, confidence level, and assumptions with the interval. A precise-looking interval from biased data can still be misleading.
When comparing two intervals, overlap alone is not a complete significance test. State the comparison, sample design, and statistical method instead of turning a visual rule into a universal conclusion.
Read a confidence interval as an estimate paired with uncertainty and assumptions, not as a guarantee of precision.
COMMON QUESTIONS
Frequently asked questions
Does higher confidence make an interval wider?
Usually. Holding other inputs constant, a higher confidence level uses a larger critical value and produces a wider interval.
Does a narrow interval prove the estimate is correct?
No. It may be precise under the model while still reflecting biased data or an unsuitable method.