Stats.Blue

# Confidence Interval for a Population Proportion

When calculating a confidence interval for a proportion, you should keep the following in mind:
• The confidence levels can be very inaccurate unless your sample size sample is very large. The actual confidence level is often less than the confidence level you specify.

• This website also computes the "plus four" interval. Statistical literature suggests that the plus four interval yields better results than the usual large-sample interval. Experts in statistical practice recommend that you use the plus four interval for estimating a proportion when the confidence level at least 90% and the sample size is at least 10.
 Sample Size $n$: Sample Proportion $\hat{p}$: Confidence Level: 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9%

 Sample Size: $n=$ Sample Proportion: $\hat{p}=$ Standard Error: $\mbox{SE}_{\hat{p}}=$ Critical $z$ Value: $z^{*}=$ % Confidence Interval:

Plus Four Confidence Interval:
 Plus Four Sample Size: $n+4=$ Plus Four Proportion: $\tilde{p}=$ Plus Four Standard Error: $\mbox{SE}_{\tilde{p}}=$ Critical $z$ Value: $z^{*}=$ % Confidence Interval: