Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Two-Sample t-Test - Large Samples

We define a new variable: the difference,

between the means and  of the two samples. The mean of this variable d is . Its standard deviation is given by:

which is also called the standard error. For large samples (n1, n2) the distribution of the differences d is approximately normal. So we can apply the same methods as for the one-sample t-test for large samples, but now using the new variable d.