Confidence Interval for Proportion Calculator

About Confidence Interval for Proportion Calculator

Welcome to our Confidence Interval for Proportion Calculator. This tool helps you find the confidence interval for a population proportion based on:

• The number of successes in a sample
• The total sample size
• Your desired confidence level

Use this calculator to get both the lower bound and the upper bound of your confidence interval, along with a detailed, step-by-step explanation.

Understanding Confidence Intervals for Proportions

A confidence interval provides a range of values within which the true population proportion is likely to lie. It's based on the sample proportion, sample size, and the desired confidence level.

Formula

For large samples, the approximate confidence interval (using the Normal approximation) for a proportion \( p \) is given by:

\[ \hat{p} \pm z_{\alpha/2} \sqrt{ \frac{\hat{p}(1 - \hat{p})}{n} } \] where:

• \(\hat{p} = \frac{\text{number of successes}}{n}\)
• \(n\) is the sample size
• \(z_{\alpha/2}\) is the critical value from the standard normal distribution for the chosen confidence level

Additional Resources

For more information on confidence intervals and their applications, check out the following resources:

• Confidence Interval - Wikipedia
• Confidence Intervals - Khan Academy

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