To do this, we use what we know about the sampling distribution of xˉ1​−xˉ2​ and, in particular, its estimated standard deviation (the standard error). Recall from In-Class Activity 12.D that you learned that the difference in the sample means, xˉ1​−xˉ2​, also has an approximately normal distribution, centered at the difference of the population means, μ1​−μ2​. The standard deviation is given by the following formula:
√n1/​σ12​​+n2/​σ22​​​
In practice, we will have to estimate the standard deviation because it depends on the unknown population standard deviations. Replacing σ1​ and σ2​ by the sample standard deviations s1​ and s2​, we get the standard error of the difference: standard error of xˉ1​/−xˉ2​=√n1​/s1²​+n2/​s2²