Answer
$-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$: null hypothesis is not rejected.
There is not enough evidence to conclude that $µ\ne600$
Work Step by Step
$H_0:~µ=600$ versus $H_1:~µ\ne600$
Requirement:$-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$, we do not reject the null hypothesis.
$n\geq30$
$n=65$, so:
$d.f.=n-1=64$
$t_0=\frac{x ̅-µ_0}{\frac{s}{\sqrt n}}=\frac{583.1-600}{\frac{114.9}{\sqrt {65}}}=-1.186$
$t_{\frac{α}{2}}=t_{0.05}=1.671$
(According to Table VI, for d.f. = 60, the closest value to 64, and area in right tail = 0.05)
Since $-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$, we do not reject the null hypothesis.
