Answer
$r_s\lt 0.643$: null hypothesis is not rejected.
There is not enough evidence to conclude that states with higher population densities have higher crime rates.
Work Step by Step
$H_0: X~and~Y~are~not~associated$ versus $H_1: X~and~Y~are~positively~associated$
See the picture.
$∑d_i^2=0+1+0+16+1+1+0+25=44$
$r_s=1-\frac{6∑d_i^2}{n(n^2-1)}=1-\frac{6\times44}{8(8^2-1)}=0.476$
Critical value = 0.643
(According to Table XIV, for n = 8 and α(1) = 0.05)
Since $r_s\lt 0.643$, we do not reject the null hypothesis.
