Answer
$w_{\frac{α}{2}}\lt T\lt w_{1-\frac{α}{2}}$: null hypothesis is not rejected.
There is not enough evidence to conclude that $M_x\ne M_y$.
Work Step by Step
Two-tailed test.
Small-sample case:
$T=S-\frac{n_1(n_1+1)}{2}=170-\frac{12(12+1)}{2}=170-78=92$
Critical values:
$w_{\frac{α}{2}}=w_{0.025}=50$
$w_{1-\frac{α}{2}}=n_1n_2-w_{\frac{α}{2}}$
$w_{0.975}=12\times15-50=130$
Since $w_{\frac{α}{2}}\leq T\leq w_{1-\frac{α}{2}}$ we do not reject the null hypothesis.
