Answer
$t_0\lt -t_{\frac{α}{2}}$: 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 $H_1:~µ_1\ne µ_2$
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(104.2-110.4)-0}{\sqrt {\frac{12.3^2}{24}+\frac{8.7^2}{27}}}=-2.054$
$n=24$ (use the smaller value of $n$), so:
$d.f.=n-1=23$
Two-tailed test:
$t_{\frac{α}{2}}=t_{0.05}=1.714$
(According to Table VI, for d.f. = 23 and area in right tail = 0.05)
Also, $-t_{\frac{α}{2}}=-1.714$
Since $t_0\lt -t_{\frac{α}{2}}$, we reject the null hypothesis.
