Confidence Interval Calculator for Two Means

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

Input Data

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

Sample Group 1

Sample Mean (

\bar{x}_1

)

Sample Size (

$$n_1$$

)

Sample Standard Deviation (

$$s_1$$

)

Sample Group 2

Sample Mean (

\bar{x}_2

)

Sample Size (

$$n_2$$

)

Sample Standard Deviation (

$$s_2$$

)

Confidence Level (%)

Results

Confidence Interval:

Lower Bound: , Upper Bound:

Visualization

Understanding Confidence Interval 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 uses Welch's t-test, suitable when population variances are unknown and potentially unequal.

Key Terms:

Sample Mean ( $\bar{x}$ ): The average value of a sample.
Sample Size ( $$$n$$$ ): The number of observations in a sample.
Sample Standard Deviation ( $$$s$$$ ): A measure of the dispersion of sample values.
Confidence Level: The probability that the confidence interval contains the true difference of means.

Formula: The confidence interval is calculated as: $(\bar{x}_1 - \bar{x}_2) \pm t \cdot SE$ , where $SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$ and $$$t$$$ is the t-value from the t-distribution for the given confidence level and degrees of freedom.

This tool is useful in various fields like healthcare, business, and research to compare the means of two independent groups.

Learn more about confidence intervals and hypothesis testing on resources like Khan Academy and StatTrek.