Answer
$T\gt w_{1-α}$: null hypothesis is rejected.
There is enough evidence to conclude that offensive tackles are heavier than defensive tackles.
Work Step by Step
$H_0:M_{off}=M_{def}$ versus $H_1:M_{off}\gt M_{def}$
$Weight~~~~~~~~~Sample~~~~~~~~Rank$
$~~~250~~~~~~~~~~~defensive~~~~~~~~~~1$
$~~~278~~~~~~~~~~~defensive~~~~~~~~~~2$
$~~~289~~~~~~~~~~~defensive~~~~~~~~~~3$
$~~~295~~~~~~~~~~~defensive~~~~~~~~~4.5$
$~~~295~~~~~~~~~~~offensive~~~~~~~~~4.5$
$~~~300~~~~~~~~~~~defensive~~~~~~~~~~6$
$~~~305~~~~~~~~~~~defensive~~~~~~~~~~8$
$~~~305~~~~~~~~~~~offensive~~~~~~~~~~8$
$~~~305~~~~~~~~~~~offensive~~~~~~~~~~8$
$~~~309~~~~~~~~~~~offensive~~~~~~~~~10$
$~~~310~~~~~~~~~~~defensive~~~~~~~~~11$
$~~~313~~~~~~~~~~~offensive~~~~~~~~~12$
$~~~318~~~~~~~~~~~offensive~~~~~~~~~13$
$~~~320~~~~~~~~~~~offensive~~~~~~~~~14$
$~~~323~~~~~~~~~~~offensive~~~~~~~~~15$
$~~~328~~~~~~~~~~~offensive~~~~~~~~~16$
$~~~339~~~~~~~~~~~defensive~~~~~~~~~17$
$~~~380~~~~~~~~~~~offensive~~~~~~~~~18$
Small-sample case:
$S=4.5+8+8+10+12+13+14+15+16+18=118.5$
$T=S-\frac{n_1(n_1+1)}{2}=118.5-\frac{10(10+1)}{2}=118.5-55=63.5$
$w_α=w_{0.05}=21$
(According to table XIII, for $n_1=10$, $n_2=8$ and $α=0.05$)
Critical value:
$w_{1-α}=n_1n_2-w_α$
$w_{0.95}=10\times8-21=59$
Since $T\gt w_{1-α}$, we reject the null hypothesis.
