Test a claimed proportion using simple, structured inputs. Review z value, p value, and bounds. Export summaries quickly for reports, audits, and classroom practice.
| Case | Successes | Sample Size | Claimed Proportion | Alternative | Alpha | Summary |
|---|---|---|---|---|---|---|
| Website Conversion | 62 | 100 | 0.50 | p > 0.50 | 0.05 | Useful for testing whether a campaign improved conversion. |
| Defect Review | 18 | 250 | 0.10 | p < 0.10 | 0.05 | Useful for checking whether defects stayed below target. |
| Survey Agreement | 144 | 200 | 0.70 | p ≠ 0.70 | 0.01 | Useful for comparing observed support against a benchmark. |
Sample proportion: p̂ = x / n
Null standard error: SE₀ = √[ p₀(1 - p₀) / n ]
Test statistic: z = ( p̂ - p₀ ) / SE₀
Two-sided p value: 2 × [1 - Φ(|z|)]
Right-tailed p value: 1 - Φ(z)
Left-tailed p value: Φ(z)
Confidence interval: p̂ ± z* × √[ p̂(1 - p̂) / n ]
Here, x is the number of successes, n is the sample size, p₀ is the claimed proportion, and Φ is the standard normal cumulative distribution function.
A one sample proportion test checks whether an observed sample proportion matches a claimed population proportion. It is useful when outcomes have two categories, such as pass or fail, click or no click, or defect and nondefect. This calculator helps students, analysts, and researchers test a proportion quickly. It reports the sample proportion, standard error, z statistic, p value, and confidence interval. These outputs support faster interpretation and clearer reporting.
Use this tool when you have a sample size and a count of successes. Enter the hypothesized proportion from your null hypothesis. Then choose a significance level and the alternative hypothesis direction. The calculator is valuable for quality control, survey analysis, medical screening reviews, website conversion checks, and classroom exercises. It is most reliable when normal approximation conditions are satisfied. That means the expected counts under the null are large enough for z test assumptions.
The test first computes the sample proportion by dividing successes by sample size. Next, it builds the null standard error from the claimed proportion. The z statistic measures how far the sample result is from the claim after scaling for sampling variation. The p value then shows how surprising the sample would be if the null hypothesis were true. A small p value suggests strong evidence against the claim. The confidence interval adds another helpful view by showing a plausible range for the population proportion.
Statistical significance should be interpreted with context. A significant result does not always imply practical importance. Look at the sample proportion difference, the interval width, and the sample size together. Larger samples can detect smaller differences. Smaller samples may produce wide intervals and uncertain conclusions. This page supports sound interpretation by pairing formulas, usage steps, export tools, and example data in one place. It is designed for clean workflows, careful learning, and reliable decision support.
Before making decisions, confirm that the data are independent and coded. Also review whether the claimed benchmark is meaningful for your study. Good statistical practice combines correct calculation, reasonable assumptions, and plain language conclusions for readers.
It checks whether the proportion observed in one sample is consistent with a claimed population proportion. The test is commonly used for yes or no outcomes, defect rates, survey agreement, and conversion rates.
Use it when each observation falls into one of two categories and you want to compare the observed success rate against a benchmark. Examples include pass rates, click rates, approval rates, and defect proportions.
The null hypothesis states that the true population proportion equals the claimed value you entered as p₀. The calculator then tests whether your sample provides enough evidence to reject that claim.
The p value shows how unusual your sample result would be if the null hypothesis were true. Smaller p values indicate stronger evidence against the claimed proportion.
A confidence interval gives a plausible range for the true population proportion. It adds context to the hypothesis test and helps you judge the size and uncertainty of the estimated proportion.
Continuity correction slightly adjusts the test statistic when a discrete count is approximated with a continuous normal model. It can make the test more conservative in some settings.
You should have independent observations and a sample large enough for normal approximation. A common rule checks whether expected successes and failures are each at least five.
Yes. It works well for statistics homework, quality checks, polling summaries, A/B review, and reporting tasks. The export options also make it easier to share documented results.
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.