Proportion Confidence Interval

Understand the proportion confidence interval result

Proportion Confidence Interval gives a focused calculation for reproducing a basic survey interval or checking an introductory statistics exercise. It asks for sample proportion, sample size, critical z value and reports lower bound and upper bound and margin. The Wald interval adds and subtracts z times the square root of p times one minus p divided by n. Bounds describe sampling uncertainty under the normal approximation, not certainty about an individual response. By exposing lower bound and upper bound and margin, Proportion Confidence Interval makes this specific arithmetic inspectable instead of presenting an unexplained number.

With the page defaults of Sample proportion 0.5, Sample size 100, Critical z value 1.96, the verified output is Lower bound 0.402, Upper bound 0.598, Margin 0.098. Enter a proportion such as 0.5, not the percentage number 50. In Proportion Confidence Interval, each labeled default remains visible while you edit, so you can change one assumption at a time and trace how lower bound responds.

Method, limits, and private processing

The Wald method behaves poorly with small samples or proportions near zero or one. Proportion Confidence Interval evaluates the entered values entirely in your browser, without sending the inputs to a server. When using its lower bound and upper bound and margin, retain the stated method and input units because this result is bounded by the assumptions of the Wald interval adds and subtracts z times the square root of p times one minus p divided by n.