Answer
$T\gt T_α$: null hypothesis is not rejected.
There is not enough evidence to conclude that the exercise regimen the reduces the waistline.
Work Step by Step
$H_0:M_D=0$ versus $M_D\gt0$
Let the "Before" values to be the X and the "After" values to be the Y.
$D_i=X_i-Y_i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Rank$
$D_1=X_1-Y_1=23.5-19.75=3.75~~~~~~~~~~~~+9$
$D_2=X_2-Y_2=18.5-19.25=-0.75~~~~~~~~-4.5$
$D_3=X_3-Y_3=21.5-21.75=-0.25~~~~~~~~-1.5$
$D_4=X_4-Y_4=24-22.5=1.5~~~~~~~~~~~~~~~~~~+7.5$
$D_5=X_5-Y_5=25-25=0~~~~~~~~~~~~~~~~~~~~~~~discard$
$D_6=X_6-Y_6=19.75-19.5=0.25~~~~~~~~~~~+1.5$
$D_7=X_7-Y_7=35-34.25=0.75~~~~~~~~~~~~~~+4.5$
$D_8=X_8-Y_8=36.5-35=1.5~~~~~~~~~~~~~~~~~~+7.5$
$D_9=X_9-Y_9=52-51.5=0.5~~~~~~~~~~~~~~~~~~~+3$
$D_{10}=X_{10}-Y_{10}=30-31=-1~~~~~~~~~~~~~~~~~~-6$
$n=9$
Right-tailed test.
Test statistic: $T=|T_-|=|-4.5-1.5-6|=12$
Critical value: $T_α=8$
(According to table XII, for $n=9$ and $α=0.05$)
Since $T\gt T_α$, we do not reject the null hypothesis.
