One-Proportion z-Test
Computes the one-proportion z-test statistic, used to check whether the proportion observed in a sample differs from a hypothesized value. For example: out of 100 voters, 45 approve a measure — is that compatible with 50% in the population? The statistic divides the difference between the observed and hypothesized proportions by the standard error computed under the null hypothesis. It applies when the sample size is large enough for the normal approximation. Enter the successes, the total and the hypothesized proportion.
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One-Proportion z-Test
Computes the one-proportion z-test statistic, used to check whether the proportion observed in a sample differs from a hypothesized value. For example: out of 100 voters, 45 approve a measure — is that compatible with 50% in the population? The statistic divides the difference between the observed and hypothesized proportions by the standard error computed under the null hypothesis. It applies when the sample size is large enough for the normal approximation. Enter the successes, the total and the hypothesized proportion.
Does the sample match the proportion I expected?
There's a question that comes up constantly: is a proportion observed in a sample compatible with a reference value, or does it differ from it meaningfully? Election polls, defect rates on a production line, a product's approval percentage. The one-proportion z-test gives the formal answer.
The mechanics are straightforward. You have the proportion observed in the sample and the hypothesized proportion you want to test. The statistic measures the distance between the two in standard-error units, where the standard error is computed assuming the null hypothesis is true. A z value large in magnitude indicates the sample is far from what the hypothesis predicted.
Enter the successes, the total number of observations and the hypothesized proportion. The tool returns the z statistic, from which you obtain the p-value. Keep in mind this test relies on the normal approximation, which works well when the expected number of successes and failures is reasonably large, generally at least five on each side.
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