Standard Error: 0.0176

Critical Values of t: -1.96 to 1.96

Confidence Interval: 0.4254 to 0.4946

Critical Values of t: -1.96 to 1.96

Confidence Interval: 0.4254 to 0.4946

This confidence interval calculator is designed for sampling population proportions. To use it, enter the observed proportion, sample size, and alpha (half of the desired confidence level; so .0025 for a 95% confidence interval). The resulting confidence interval shows the expected range of the true value of the population proportion, within the margin of error set by the alpha value.

This tool uses Student's t-distribution to generate the expected range of error; it can work with relatively small sample sizes. In addition to a confidence interval, the calculator will also generate the standard error of the proportion and the critical values of t for that sample size (determines degrees of freedom). The degrees of freedom as always calculated as n-1, n being the sample size drawn from the population. For large sample sizes, the resulting critical values of t will converge on a standard normal distribution. This pattern becomes evident once your sample size exceeds 30 and gets very close for sample sizes over 100.

The instructions for this calculator assume you're looking for a two-sided confidence interval, where there is an equal probability of the error being above or below the range. Be sure to split your alpha value in two to reflect this. For a 95% confidence interval, set alpha at .025. For a 99% confidence interval, set alpha at .0005.