Understand the hypothesis test
Read the test as a model-based comparison
One-Proportion z-Test. The observed effect is scaled by its null-model uncertainty and located on a reference distribution selected before looking at the result.
1State H₀, the effect, and direction2Calculate the statistic under H₀3Report p-value with effect and interval
Test statistic and reference model
z=(p̂−p₀)/√[p₀(1−p₀)/n].
Show the observed proportion and effect difference with the p-value; statistical and practical significance are separate.
Responsible interpretation
A p-value is not the probability that the null is true, the chance the result occurred ‘by luck,’ or a measure of effect size, importance, replication, bias, or causation.
Required assumption: The normal approximation requires enough expected successes and failures under the null, plus independent stable-probability trials.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the one-proportion z-test calculator works
z=(p̂−p₀)/√[p₀(1−p₀)/n].
Show the observed proportion and effect difference with the p-value; statistical and practical significance are separate.
Worked example
One-Proportion z-Test example
60 successes in 100 trials tested against p₀=0.5 gives z=2.
z=(p̂−p₀)/√[p₀(1−p₀)/n].
Supported inputs
Precision and limits
Model and design
The normal approximation requires enough expected successes and failures under the null, plus independent stable-probability trials.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Show the observed proportion and effect difference with the p-value; statistical and practical significance are separate.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
Continue calculating
Related calculators
