Answer
(a) See the picture.
(b) $r_s=-0.957$
(c) $r_s\lt -0.886$: null hypothesis is rejected.
There is enough evidence to conclude that X and Y are associated.
Work Step by Step
(a) See the picture.
(b) See the picture.
$∑d_i^2=25+9+1+1+20.25+12.25=68.5$
$r_s=1-\frac{6∑d_i^2}{n(n^2-1)}=1-\frac{6\times68.5}{6(6^2-1)}=-0.957$
(c) $H_0: X~and~Y~are~not~associated$ versus $H_1: X~and~Y~are~associated$
Critical values = 0.886 and -0.886
(According to Table XIV, for n = 6 and α(2) = 0.05)
Since $r_s\lt -0.886$, we reject the null hypothesis.
