# 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.

## 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.