Answer
$r_s\gt -0.600$, we do not reject the null hypothesis.
There is not enough evidence to conclude that as the per capita personal incomes of states increase the birthrates decrease.
Work Step by Step
$H_0: X~and~Y~are~not~associated$ versus $H_1: X~and~Y~are~negatively~associated$
See the picture.
$∑d_i^2=2.25+25+1+6.25+1+9+25+36+9=114.5$
$r_s=1-\frac{6∑d_i^2}{n(n^2-1)}=1-\frac{6\times114.5}{9(9^2-1)}=0.046$
Critical value = -0.600
(According to Table XIV, for n = 9 and α(1) = 0.05)
Since $r_s\gt -0.600$, we do not reject the null hypothesis.
