Continuing my new series of Statistics calculations by hand, I have released a "How To..." video Student's t test for unpaired (independent) samples with equal variance. This is one of three options when conducting a t test to compare the means of two samples to see of there is a significant difference between the samples (or not). It is slightly awkward in that you first have to determine if the variances of the two samples are equal or unequal with an F test before you can use the formula for t. In addition, if the variance is equal (as in the video below), you must pool the variance.
At 12 minutes and 6 seconds this is one of my longest videos, and it took a few takes to get it right. In my Statistics exams I set a problem similar to this, and it is a solution like this that I want students to provide in their answers.