Z-Test for a Single Proportion Calculator
Test a sample proportion against a hypothesized value.
Enter your values
Enter the sample proportion you are working with.
Enter the hypothesized proportion you are working with.
Enter the sample size you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- z-statistic
- 1.6971
- Two-sided p-value
- 0.0897
- Standard error
- 0.03536
- Significant at 0.05?
- No
Quick answer
The z-statistic compares the observed proportion to the hypothesized proportion, scaled by the standard error under the null hypothesis.
z = (p̂-p0)/sqrt(p0(1-p0)/n)
At a glance
| What it does | Test a sample proportion against a hypothesized value. |
|---|---|
| Category | Statistics |
| Inputs needed | Sample proportion, Hypothesized proportion, Sample size |
| Main output | z-statistic |
| Formula | z = (p̂-p0)/sqrt(p0(1-p0)/n) |
| Cost | Free — no sign-up, no download |
How to use the Z-Test for a Single Proportion Calculator
- 1Enter your observed sample proportion.
- 2Enter the proportion you're testing against (the null hypothesis value).
- 3Enter the sample size — the tool computes the z-statistic and p-value.
Inputs explained
- Sample proportion
- Enter the sample proportion you are working with.
- Hypothesized proportion
- Enter the hypothesized proportion you are working with.
- Sample size
- Enter the sample size you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Sample proportion0.56
- Hypothesized proportion0.5
- Sample size200
Results
- z-statistic1.6971
- Two-sided p-value0.0897
- Standard error0.03536
- Significant at 0.05?No
Frequently asked questions
When can I use a z-test for proportions?
When np0 and n(1-p0) are both at least 5-10, so the normal approximation holds.
What does a small p-value mean?
Strong evidence that the true proportion differs from the hypothesized value.
What do I need to enter into the Z-Test for a Single Proportion Calculator?
Just 3 values: sample proportion, hypothesized proportion, sample size. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Z-Test for a Single Proportion Calculator work out the answer?
The z-statistic compares the observed proportion to the hypothesized proportion, scaled by the standard error under the null hypothesis. It applies the formula z = (p̂-p0)/sqrt(p0(1-p0)/n) and shows the working so you can check each step by hand.
Is the Z-Test for a Single Proportion Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.