Confidence interval for a sample mean or proportion.

What does a confidence interval actually tell you?

A confidence interval gives a range that's likely to contain the true population parameter at the stated confidence level. A common misconception is that a 95% confidence interval means "there's a 95% chance the true value is in this specific interval" — technically, the 95% describes the long-run reliability of the method (if you repeated the sampling many times, about 95% of the resulting intervals would contain the true value), not a probability statement about this one result.

How does sample size affect the interval width?

Larger samples produce narrower, more precise intervals. The margin of error shrinks in proportion to the square root of the sample size, so quadrupling your sample size only halves the margin of error.

How does confidence level affect the interval width?

Higher confidence requires a wider interval, all else equal, because capturing the true value more reliably requires casting a wider net — a 99% confidence interval is always wider than a 95% one built from the same data.

How is this related to your Sample Size Calculator?

The Sample Size Calculator works backward from a target margin of error to tell you how large a sample you need. This tool works forward from a sample you've already collected to compute the resulting confidence interval.

Worked example: a sample mean of 100, standard deviation of 15, n=30, at 95% confidence (z=1.96): margin of error = 1.96×(15/√30) ≈ 5.37, giving a confidence interval of roughly 94.63 – 105.37.