Interactive confidence interval visualization showing the trade-off between interval width and confidence level
Your Confidence Interval Either Contains the True Mean or It Doesn't
A confidence interval is not a probability statement about one specific interval — it's a statement about the reliability of the method across repeated sampling. Once calculated, your interval either captures the parameter or it doesn't. Drag the slider to explore how confidence level changes precision.
Interval Simulator
95% Confidence
Drag to adjust confidence level
Width: 10.0 cm
80%90%99%
Confidence
95%
Precision
High
The 95% confidence level refers to the method, not the specific interval you calculated. If you repeated your sampling process many times and constructed a 95% confidence interval each time, about 95% of those intervals would contain the true population parameter. But for any single interval you compute, there's no probability — it either contains the true value or it doesn't. This is why we say "we are 95% confident" rather than "there is a 95% probability" — we're expressing confidence in the procedure, not making a probabilistic claim about this particular interval.
Know This
A 95% confidence interval of 165 to 175 cm for average height means we are 95% confident this specific interval contains the true population mean, not that there is a 95% probability the true mean lies within it.