Answer
$t_0\lt -t_{\frac{α}{2}}$: null hypothesis is rejected.
There is enough evidence to conclude that a linear relation exists between commute time and the well-being index composite score.
Work Step by Step
$H_0: β_1=0$ versus $H_1: β\ne0$
$t_0=\frac{b_1}{s_{b_1}}=\frac{-0.0479}{0.00429}=-11.166$
$n=7$, so:
$d.f.=n-2=5$
$t_{\frac{α}{2}}=t_{0.025}=2.571$
(According to Table VI, for d.f. = 5 and area in right tail = 0.025)
Also, $-t_{\frac{α}{2}}=-2.571$
Since $t_0\lt -t_{\frac{α}{2}}$, we reject the null hypothesis.
