Answer
$t_0\gt t_{\frac{α}{2}}$: null hypothesis is rejected.
There is enough evidence to conclude that $µ_1\ne µ_2$.
Work Step by Step
$H_0:~µ_1=µ_2$ versus $H_1:~µ_1\ne µ_2$
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(32.4-28.2)-0}{\sqrt {\frac{4.5^2}{13}+\frac{3.8^2}{8}}}=2.290$
$n=8$, so:
$d.f.=n-1=7$
Two-tailed test:
$t_{\frac{α}{2}}=t_{0.05}=1.895$
(According to Table VI, for d.f. = 19 and area in right tail = 0.05)
Since $t_0\gt t_{\frac{α}{2}}$, we reject the null hypothesis.
