Answer
$t_0\gt -t_α$: null hypothesis is not rejected.
There is not enough evidence to conclude that $µ_d\lt0$.
Work Step by Step
$H_0:~µ_d=0$ versus $H_1:~µ_d\lt0$
$t_0=\frac{d ̅ }{\frac{s_d}{\sqrt n}}=\frac{−0.167}{\frac{0.4502}{\sqrt 6}}=-0.909$
$n=6$, so:
$d.f.=n-1=5$
Left-tailed test:
$t_α=t_{0.05}=2.015$
(According to Table VI, for d.f. = 5 and area in right tail = 0.05)
So, $-t_α=-2.015$
Since $t_0\gt -t_α$, we do not reject the null hypothesis.
