Confidence Interval Calculator for Two Means

Estimate the range for the true difference between two population means.

Input Data

Enter the sample statistics for both populations and the desired confidence level to calculate the confidence interval for the difference in means.

Sample 1

Sample Mean (

\bar{x}_1

)

Sample Size (

$$n_1$$

)

Population Standard Deviation (

\sigma_1

)

Sample 2

Sample Mean (

\bar{x}_2

)

Sample Size (

$$n_2$$

)

Population Standard Deviation (

\sigma_2

)

Confidence Level (%)

Confidence Interval Result

Lower Bound:

Upper Bound:

Visualization

Confidence Interval Range

Understanding Confidence Intervals

A confidence interval is a range of values that estimates an unknown population parameter. For two means, it estimates the difference between the average values of two groups. For example, if we calculate a 95% confidence interval for the difference in average test scores between two teaching methods, and the interval is [2, 8], it suggests that we are 95% confident that the true difference in average scores lies between 2 and 8 points. A wider interval indicates more uncertainty, while a narrower interval suggests a more precise estimate. The confidence level (e.g., 95%) reflects how sure we are that the interval contains the true difference.