Confidence Interval Calculator
Calculate the confidence interval for a population mean. Enter the sample mean, standard deviation, and sample size to determine the range and margin of error.
What is a Confidence Interval?
A Confidence Interval (CI) is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter (such as the mean).
For example, a 95% confidence interval means that if you were to take 100 different samples and calculate a confidence interval for each sample, approximately 95 of those intervals would contain the true population mean.
Components
- Sample Mean (x̄): The average of your data sample.
- Standard Deviation (s): A measure of how dispersed the data is.
- Sample Size (n): The number of observations in your sample.
- Confidence Level: The probability that the interval contains the true parameter (commonly 95% or 99%).
Formula
CI = x̄ ± Z * (s / √n)
This calculator uses the Z-score method, which assumes a normal distribution and is generally used when the sample size is large (n > 30) or the population standard deviation is known.
? Frequently Asked Questions
It means that we are 95% confident that the true population mean lies within the calculated interval. It does NOT mean there is a 95% chance the mean is in this specific interval (a common misconception), but rather reflects the reliability of the estimation method.
A T-score is typically used when the sample size is small (n < 30) and the population standard deviation is unknown. However, for large samples, Z and T scores converge.
Increasing the sample size narrows the confidence interval (makes it more precise) because the standard error decreases as 'n' increases.