Answer
$t_0\gt t_α$: null hypothesis is rejected.
There is enough evidence to conclude that the designated hitter result in more runs scored.
Work Step by Step
$x ̅_1,n_1~and~s_1$ refer to American League and $x ̅_2,n_2~and~s_2$ refer to National League.
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(6.0-4.3)-0}{\sqrt {\frac{3.5^2}{30}+\frac{2.6^2}{30}}}=2.136$
$n=30$, so:
$d.f.=n-1=29$
Right-tailed test:
$t_α=t_{0.05}=1.699$
(According to Table VI, for d.f. = 29 and area in right tail = 0.05)
Since $t_0\gt t_α$, we reject the null hypothesis.
