Easy-to-Use One Proportion Z Test Calculator

Our One Proportion Z Test Calculator can perform complete hypotheses testing and provides test statistic, degree of freedom, critical value, p-value, decision and conclusion.

Select null hypothesis:
\(\mathrm{H_0: p}\) \( \mathrm{ p_0} \)

Select alternative hypothesis:
\(\mathrm{H_a: p}\) \( \mathrm{ p_0} \)

Enter population proportion \( \mathrm{ p_0} \) value : Enter sample size \( \mathrm{ (n) }\) value :

Enter favourable cases \( \mathrm{ (x) }\) :

Enter sample proportion \( \mathrm{ \hat{p} }\) :

Enter Significance level \( ( \mathrm{ \alpha} )\) value : Round test statistic to: Round p-value to: Round critical value to:

How Does the Calculator Work?

Input Your Data: Enter the sample size (n), number of successes(x) or sample proportion \( \mathrm{\hat{p} } \) , and the hypothesized proportion \( \mathrm{p_0} \)

Choose Hypotheses: Select whether your hypothesis is one-tailed \( ( <,> ) \) or two tailed \( \ne \)

Specify Significance Level: Determine your desired \(\alpha\) level to set the threshold for statistical significance.

Get Results: Instantly receive critical values, test statistics, and p-values based on your inputs. The calculator helps you decide whether to accept or reject the null hypothesis

Why Use Our One Proportion Z Test Calculator?

Accuracy: To ensure that our calculator produces accurate answers, we apply exact statistical calculations.

Ease of Use: Simply enter your data and choices, and the program will perform the hard calculations for you.

Educational Tool: Ideal for studying and teaching hypothesis testing and statistical significance.

Applications of One Proportion Z Test:

Market Research: Analyze survey data to see if a fraction of respondents deviates considerably from the hypothesized value.

Quality Control: Evaluate product defect rates to verify they satisfy the required criteria.

Healthcare Studies: Assess therapy efficacy based on patient outcomes.

one proportion z test statistic

The One Proportion Z Test statistic is a statistical tool that determines whether the proportion of a single sample deviates considerably from a hypothesized value. It is especially important when we wish to determine whether an observed proportion in a sample is due to chance or an actual difference in the population.

Formula :

\( \mathrm{z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}} \)

Where:

\( \mathrm{\hat{p}} \) is the sample proportion
\( \mathrm{ p_0 } \) is the hypothesized proportion (null hypothesis)
n is the sample size.

Interpretation :

Z Score: The calculated Z score reflects how many standard deviations the sample percentage differs from the hypothesized proportion.

Significance: A high absolute value of z indicates a significant difference between \(\mathrm{\hat{p}} \) and \(\mathrm{ p_0 } \), resulting in the rejection of the null hypothesis.