\[CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}\]
Variables
CI1lower confidence limit
CI2upper confidence limit
xbsample mean
zcritical z value
sigmapopulation standard deviation
nsample size
Description
What is this formula?
This formula calculates the confidence interval for a population mean when the population standard deviation is known.
When to use it
Use this formula to estimate the range where the true population mean is likely to be located with a specified confidence level.
Example
If the sample mean is 50, the standard deviation is 8, the sample size is 100, and z=1.96, the formula estimates the 95% confidence interval.
Applications
Statistical inference, quality control, scientific research, engineering measurements, surveys, and process analysis.