Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of $36$ PlayStation users had an average age of $34\mathrm{.}2$ years while a random sample of $30$ Xbox users had an average age of $32\mathrm{.}7$ years. Assume that the population standard deviation for the age of PlayStation and Xbox users is $3\mathrm{.}9$ and $4\mathrm{.}0$ years, respectively. Sony would like to set $\backslash$alpha $=0\mathrm{.}10.$ If Population $1$ is defined as PlayStation users and Population $2$ is defined as Xbox users, the test statistic for this hypothesis test would be $\_\_\_\_\_\_\_\_.$