Z Tests
One Proportion Z Test Calculator
One Proportion Z Test Calculator test a single population proportion.
Z Tests
One Proportion Z Test Calculator
Test a single population proportion.
Formula
One-proportion z test: z = (p-hat - p0) / sqrt(p0(1-p0)/n), where p-hat = successes / sample size.
About the One Proportion Z Test Calculator
Test a single population proportion. Z procedures compare a standardized estimate with a normal reference distribution when their known-variance or large-sample conditions are satisfied.
How the One Proportion Z Test Calculator Works
One-proportion z test: z = (p-hat - p0) / sqrt(p0(1-p0)/n), where p-hat = successes / sample size.
The calculation runs in your browser. Submitted values are validated for the required numeric range, data shape, units, and method-specific restrictions before a result is shown.
Required Inputs
- Successes (required)
- Sample size (required)
- Null proportion (required)
- Alpha (required)
- Alternative hypothesis (required) Options: Two-tailed, Greater than, Less than
Results Reported
The result panel shows the final answer together with the intermediate quantities needed to audit the calculation. Depending on this method, reported values include:
methodsuccessesfailuressample_sizesample_proportionnull_proportiondifferencenull_standard_errorz_statisticp_valueexpected_successes_under_nullexpected_failures_under_nullnormal_approximation_warningalphatail_typedecision
One Proportion Z Test Calculator Example
Use the example data button to load a known sample, then calculate and review the statistic, p-value or estimate, and interpretation.
| Input | Example value |
|---|---|
| Successes | 56 |
| Sample size | 100 |
| Null proportion | 0.5 |
| Alpha | 0.05 |
| Alternative hypothesis | two |
How to Use the Calculator
- Confirm that the calculator title and method match the quantity, test, conversion, or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date, or option format.
- Select Example Data to inspect a valid input layout, or enter your own values and select Calculate.
- Review the result table, formula, worked substitutions, warnings, and interpretation rather than using only the headline number.
- Use Copy Result or Download CSV when you need a reusable record of the displayed calculation.
Understanding the Result
Confirm independence, the correct null value, suitable expected counts for proportions, and whether population standard deviations are genuinely known for mean tests.
Keep the entered values, units, selected options, and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size, and decision. For an estimate or conversion, report the formula convention and final unit.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods, or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the One Proportion Z Test Calculator calculate?
Test a single population proportion.
Which formula does the One Proportion Z Test Calculator use?
One-proportion z test: z = (p-hat - p0) / sqrt(p0(1-p0)/n), where p-hat = successes / sample size.
What input does this calculator need?
The calculator form shows the required values and validates them before calculating.
Are the formulas visible?
Yes. Each calculator displays its method, assumptions, and interpretation unless disabled by the site administrator.