Answer
$t_0\gt t_α$: null hypothesis is rejected.
There is enough evidence to conclude that $µ\gt100$.
Work Step by Step
$H_0:~µ=100$ versus $H_1:~µ\gt100$
Requirement:
$n\geq30$
$n=40$, so:
$d.f.=n-1=39$
$t_0=\frac{x ̅-µ_0}{\frac{s}{\sqrt n}}=\frac{108.5-100}{\frac{17.9}{\sqrt {40}}}=3.003$
$t_α=t_{0.05}=1.685$
(According to Table VI, for d.f. = 39 and area in right tail = 0.05)
Since $t_0\gt t_α$, we reject the null hypothesis.
