Measure sample proportion uncertainty with practical interval methods. Review reliable bounds, margin estimates, and interpretation steps for survey decisions.
| Survey | Sample Size | Successes | Sample Proportion | Confidence Level |
|---|---|---|---|---|
| Product Approval | 200 | 120 | 0.6000 | 95% |
| Voter Support | 500 | 265 | 0.5300 | 99% |
| Quality Pass Rate | 80 | 70 | 0.8750 | 90% |
Sample proportion: p̂ = x / n
Wald interval: p̂ ± z × √[p̂(1 − p̂) / n]
Wilson interval center: (p̂ + z² / 2n) / (1 + z² / n)
Wilson adjustment: z / (1 + z² / n) × √[p̂(1 − p̂) / n + z² / 4n²]
Agresti-Coull adjusted proportion: p̃ = (x + z² / 2) / (n + z²)
Finite population correction: √[(N − n) / (N − 1)]
Wilson and Agresti-Coull often give more stable intervals than the basic Wald method.
A confidence interval for proportion estimates the likely range of a true population share. It starts with sample data. Then it adds statistical uncertainty. This helps you avoid overreading one sample result. The calculator is useful for surveys, audits, experiments, and quality checks.
A single sample proportion gives only one point estimate. That value can shift from sample to sample. An interval shows the expected variation around that estimate. Wider intervals mean less precision. Narrower intervals mean more precision. Decision makers use this range to judge reliability before acting.
This calculator compares Wald, Wilson, and Agresti-Coull methods. Wald is simple and familiar. However, it can be weak for small samples or extreme proportions. Wilson usually performs better. Agresti-Coull is also strong and practical. Seeing all three methods helps you compare interval behavior quickly.
Larger samples usually shrink the margin of error. That produces tighter bounds. Smaller samples create wider intervals. Confidence level matters too. A 99% interval is wider than a 95% interval. This is because higher confidence needs a larger critical value. Better precision often needs more observations.
Finite population correction matters when your sample is large relative to the total population. In that case, uncertainty falls slightly. The correction adjusts the standard error downward. This makes the interval narrower. It is common in internal audits, class surveys, and inventory quality studies.
If a 95% interval runs from 0.53 to 0.66, the true population proportion is plausibly inside that range. It does not mean every future sample will land there. It means the method captures the true value in repeated sampling about 95% of the time.
It is a range that estimates the true population proportion using sample data. The range reflects sampling uncertainty and a selected confidence level.
Wilson is often preferred because it behaves better for small samples and proportions near 0 or 1. It is usually more stable than the simple Wald interval.
A 95% confidence level means the method would capture the true population proportion in about 95% of repeated samples built the same way.
Wide intervals usually happen with small samples, extreme proportions, or high confidence levels. Each factor increases uncertainty or demands stronger coverage.
Use it when your sample is taken from a limited population and the sample size is a noticeable share of that population.
Yes. The calculator accepts both cases. Wilson and Agresti-Coull are especially helpful when proportions are near the boundaries.
No. Margin of error is half the full interval width when the interval is symmetric. It measures how far bounds extend from the center estimate.
Yes. It works well for polls, defect rates, approval studies, pass rates, and any binary outcome measured with sample counts.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.