# Standard Error of the Proportion Calculator

Calculate the standard error of a sample proportion.

## Understanding the Standard Error of the Proportion

The standard error of the proportion estimates how much a sample proportion \( \hat{p} \) would vary if multiple samples were drawn from the same population. It’s used to construct confidence intervals and test hypotheses about proportions.

### Formula for Standard Error of the Proportion

The standard error \( SE \) is calculated using the following formula:

$$ SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}} $$

where:

- \( \hat{p} \): Sample proportion
- \( n \): Sample size

### Example Calculation

Suppose a survey finds that 60% of respondents support a new policy. With a sample size of 150, the standard error is calculated as follows:

**Step 1:**Set \( \hat{p} = 0.6 \) and \( n = 150 \).**Step 2:**Substitute values into the formula: \[ SE = \sqrt{\frac{0.6 \times (1 - 0.6)}{150}} = 0.039 \]

This means the standard error of the proportion is approximately 0.039, giving an idea of the sampling variability.

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.