Answer
$T\gt T_\frac{α}{2}$: null hypothesis is not rejected.
There is not enough evidence to conclude that aspirin affects the median time it takes for a clot to form.
Work Step by Step
$H_0:M_D=0$ versus $M_D\ne0$
Let the "before aspirin" values to be the X and the "after aspirin" values to be the Y.
$D_i=X_i-Y_i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Rank$
$D_1=X_1-Y_1=12.3-12.0=0.3~~~~~~~~~~~~~~~~~+2.5$
$D_2=X_2-Y_2=12.0-12.3=-0.3~~~~~~~~~~~~~~-2.5$
$D_3=X_3-Y_3=12.0-12.5=-0.5~~~~~~~~~~~~~~~-5$
$D_4=X_4-Y_4=13.0-12.0=1~~~~~~~~~~~~~~~~~~~~+7.5$
$D_5=X_5-Y_5=13.0-13.0=0~~~~~~~~~~~~~~~~~~~~discard$
$D_6=X_6-Y_6=12.5-12.5=0~~~~~~~~~~~~~~~~~~~~discard$
$D_7=X_7-Y_7=11.3-10.3=1~~~~~~~~~~~~~~~~~~~~+7.5$
$D_8=X_8-Y_8=11.8-11.3=0.5~~~~~~~~~~~~~~~~~~+5$
$D_9=X_9-Y_9=11.5-11.5=0~~~~~~~~~~~~~~~~~~~~discard$
$D_{10}=X_{10}-Y_{10}=11.0-11.5=-0.5~~~~~~~~~~~-5$
$D_{11}=X_{11}-Y_{11}=11.0-11.0=0~~~~~~~~~~~~~~~~discard$
$D_{12}=X_{12}-Y_{12}=11.3-11.5=-0.2~~~~~~~~~~~~-1$
$n=8$
Two-tailed test.
$T_+=2.5+7.5+7.5+5=22.5$
$|T_-|=|-2.5-5-5-1|=13.5$
$|T_-|\lt T_+$. So:
Test statistic: $T=|T_-|=13.5$
Critical value: $T_\frac{α}{2}=3$
(According to table XII, for $n=8$ and $\frac{α}{2}=0.025$)
Since $T\gt T_\frac{α}{2}$, we do not reject the null hypothesis.
