Holt.Blue
Go Back

# Confidence Interval for a Population Proportion

When calculating a confidence interval for a proportion, you should keep the following in mind:
• In practice, we may trust this confidence interval when the number of successes is $15$ or greater and the number of failures is $15$ or greater. That is, when $np_0 \geq 15$ and $n(1 - p_0) \geq 15$.

• The confidence levels can be inaccurate unless your sample size sample is large. The actual confidence level can be less than the confidence level you specify.

• This page 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 $10.$

• When the guidelines for this interval are not met, you may use a non-parametric alternative: Bootstrap Interval for a Single Population Proportion.
 Number of Successes Sample Size Sample Data: $k=$ $n=$ 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: