Computational Details

The test statistic in this case is known as Welch's approximate t.

If the data are distributed normally, or the sample sizes $n_1$ and $n_2$ are at least 30, the following statistic

$$t\;=\;\frac{(\overline{x}_1-\overline{x}_2)-(\mu_1-\mu_2)}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$$

approximately follows a Student's $t$ -distribution. (This value is in cell B13)

The degrees of freedom are the largest integer less than or equal to

$$\left(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}\right)^2\div\left[\frac... ...2}{n_1}\right)^2}{n_1-1}+\frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2-1}\right]$$

(This value is in cell B12)