Two Means Confidence Interval Calculator

For Independent Samples with Unknown but Equal Standard Deviations

Sample Group 1

Sample Mean (

x̄ 1

)

Sample Size (

n 1

)

Sample Standard Deviation (

s 1

)

Sample Group 2

Sample Mean (

x̄ 2

)

Sample Size (

n 2

)

Sample Standard Deviation (

s 2

)

Confidence Level (%)

Results

Confidence Interval: (, )

Visualization of Confidence Interval

Mean Difference

Lower Bound

Upper Bound

-5 -4 -3 -2 -1 0 1 2 3 4 5

Scale: Difference of Means

Understanding Confidence Intervals for Two Means

A confidence interval for the difference between two means estimates the range within which the true difference between the population means is likely to fall. This calculator is specifically for independent samples where the population standard deviations are unknown but assumed to be equal.

It uses the t-distribution and pooled standard deviation to account for the uncertainty introduced by estimating the population standard deviation from sample data. The inputs required are the sample means ( $x̄ 1$ , $x̄ 2$ ), sample sizes ( $n 1$ , $n 2$ ), sample standard deviations ( $s 1$ , $s 2$ ), and the desired confidence level.

The output is the confidence interval, presented as a lower and upper bound. This interval provides a range of plausible values for the difference between the two population means.