Answer
$-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$: null hypothesis is not rejected
There is not enough evidence to conclude that the length of rhythm & blues songs is different from the length of alternative songs.
Work Step by Step
$x ̅_1,n_1~and~s_1$ refer to Rhythm & Blues and $x̅_2,n_2~and~s_2$ refer to Alternative.
$H_0:~µ_1=µ_2$ versus $H_1:~µ_1\ne µ_2$
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(242.7-238.3)-0}{\sqrt {\frac{26.9^2}{30}+\frac{28.9^2}{30}}}=0.610$
$n=30$, so:
$d.f.=n-1=29$
Two-tailed test:
$t_{\frac{α}{2}}=t_{0.05}=1.699$
(According to Table VI, for d.f. = 29 and area in right tail = 0.05)
Also, $-t_{\frac{α}{2}}=-1.699$
Since $-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$, we do not reject the null hypothesis.
