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:
$T=S-\frac{n_1(n_1+1)}{2}=100-\frac{10(10+1)}{2}=100-55=45$
Critical values:
$w_{\frac{α}{2}}=w_{0.025}=18$
(According to table XIII, for $n_1=10$, $n_2=8$ and $\frac{α}{2}=0.025$)
$w_{1-\frac{α}{2}}=n_1n_2-w_{\frac{α}{2}}$
$w_{0.975}=10\times8-18=62$
Since $w_{\frac{α}{2}}\lt T\lt w_{1-\frac{α}{2}}$ we do not reject the null hypothesis.
