\[CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\]
Variables
CI1lower confidence limit
CI2upper confidence limit
phsample proportion
zcritical z value
nsample size
Description
What is this formula?
This formula calculates the confidence interval for a population proportion using the normal approximation method.
When to use it
Use this formula when estimating the uncertainty range of a proportion obtained from sample data.
Example
If 60 out of 100 tested products are acceptable, the formula can estimate the confidence interval for the true acceptance proportion.
Applications
Survey analysis, quality control, polling statistics, biomedical studies, manufacturing analysis, and statistical inference.