# Statistics > Confidence Intervals > 2-Population Means

This utility computes confidence intervals for the difference of two population means from two independent samples. The confidence interval estimate of μ1 - &mu2 is:

where E is the margin of error, is the sample mean.

If population standard deviations σ1 and σ2 are unknown and are not assumed equal, the margin of error is given by

where n is the sample size, s is the sample standard deviation, and tα/2 is the inverse cumulative probability of Student's t distribution at 1 - α/2. The degree of freedom is given by

where A = s12 / n1 and B = s22 / n2.

If population standard deviations σ1 and σ2 are unknown and are assumed equal, the margin of error is given by

where , and the degree of freedom is n1 + n2 - 2.

If population standard deviations σ1 and σ2 are known, the margin of error is

### Dialog Inputs

The sample data of the population must be of only two categories. They can be inputted in one of three ways:

- Samples in one column: The population labels of samples are in one column of the Datasheet, and the individual samples are in another column.
- Samples in two columns: The samples of the two population are in two separate columns.
- Summarized sample data: The sample size, mean, and standard deviation of each of the two populations are provided (instead of individual sample values).

If population standard deviations are known, check the appropriate check box and provide the standard deviations.

Check the Assume population variances are equal check box if the population variances are assumed equal.

The confidence level must be between 0 and 1. For example, enter 0.95 for a 95% confidence level.