Confidence Interval Calculator

Estimate the range for your population mean with known standard deviation.

Input Values

Sample Mean ($ \bar{x} $):

Sample Size (n):

Population Standard Deviation ($ \sigma $):

Confidence Level:

Results

Understanding Confidence Intervals

A confidence interval is a range of values that is likely to contain the true population mean. It is calculated from sample data and provides a level of confidence that the true mean falls within the interval.

For a known population standard deviation ($ \sigma $), the confidence interval for the population mean ($ \mu $) is given by:

$$ Confidence Interval = \bar{x} \pm Z_{\alpha/2} \frac{\sigma}{\sqrt{n}} $$

$ \bar{x} $: Sample Mean
$ Z_{\alpha/2} $: Z-score corresponding to the desired confidence level (e.g., 1.96 for 95% confidence)
$ \sigma $: Population Standard Deviation
$ n $: Sample Size

The confidence level indicates the probability that the interval contains the true population mean. For example, a 95% confidence level means that if we were to take many samples and calculate confidence intervals for each sample, approximately 95% of the intervals would contain the true population mean.

This calculator is useful in various fields like research, business analysis, and quality control to estimate population parameters from sample data when the population standard deviation is known.