Calculate point estimates and confidence intervals for population proportions.
Sample Data
Formulas
p-hatx / n
Standard Error√(p̂q̂/n)
Proportion Analysis
Sample Proportion (p̂)35.00%Estimated population proportion
Sample Size Sufficient
Standard Error0.0477
Margin of Error±9.35%
Confidence Interval
[25.65%44.35%]
Interpretation
We are 95% confident that the true population proportion lies between 25.65% and 44.35%.
Overview
The p-hat estimator (p̂) is the point estimate for a population proportion. Because it's based on a sample, we calculate a margin of error to provide a range (confidence interval) within which the true population proportion likely resides.
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Pro Tips
Ensure your sample is randomly selected for the most accurate estimation.
A 95% confidence level is the standard for most scientific research.
The largest possible margin of error occurs when p-hat is 0.5 (50%).
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Fun Facts
"Political polls use p-hat to estimate candidate support. A 'statistical tie' occurs when candidates' support levels are within each other's margins of error."
"The precision of p-hat increases with the square root of the sample size, meaning you need 4x the sample to double the precision."
"The Central Limit Theorem allows us to use Z-scores for proportions if the sample is large enough (np ≥ 10 and nq ≥ 10)."
