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Confidence Interval for One Proportion

Created:December 20, 2024
Last Updated:March 25, 2025

This calculator will compute the confidence interval for a proportion with given sample size, number of successes, and confidence level. It will provide confidence intervals calculated using different methods, including the Normal approximation method, Wilson Score method, and Clopper-Pearson method.

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Confidence Interval for One Proportion with Normal Approximation

Definition: A confidence interval for a proportion provides a range of values that is likely to contain the true population proportion with a certain level of confidence.

Formula:p^±zα/2p^(1p^)n\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

Where:

  • p^\hat p is the sample proportion
  • zα/2z_{\alpha/2} is the critical value from the standard normal distribution
  • nn is the sample size
Example:

Suppose in a sample of 200 people, 30 are left-handed. To calculate a 95% confidence interval:

0.15±1.960.15(10.15)200(0.10,0.20)0.15 \pm 1.96 \sqrt{\frac{0.15(1-0.15)}{200}} \approx (0.10, 0.20)

We can be 95% confident that the true proportion of left-handed people in the population is between 10% and 20%.

Interpretation

Interpretation: We are 95% confident that the true population proportion lies within the calculated confidence interval.

Verification