Confidence Interval
Calculate confidence intervals for means and proportions
How to use Confidence Interval
- 1Enter the sample mean, standard deviation and sample size.
- 2Select the confidence level (90%, 95% or 99%).
- 3Read the margin of error and the lower and upper bounds of the interval.
What a confidence interval tells you
CI = mean ± z × (s / √n); margin = z × s / √nA confidence interval gives a range that, under repeated sampling, would contain the true population parameter a set percentage of the time.
Wider intervals mean more uncertainty; larger samples or lower confidence shrink the margin of error.
Frequently asked questions
Does 95% mean 95% chance the true value is inside?
Not exactly; it means 95% of such intervals from repeated samples would capture the truth.
Why does n appear under a square root?
Precision improves with √n, so you need four times the sample for half the margin.
z vs t, which to use?
Use t when the population standard deviation is unknown and n is small; z for large n or known sigma.