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 $µ\ne25$.
Work Step by Step
$H_0:~µ=25$ versus $H_1:~µ\ne25$
Requirement:
The population from which the sample is extracted is normally distributed.
$n=15$, so:
$d.f.=n-1=14$
$t_0=\frac{x ̅-µ_0}{\frac{s}{\sqrt n}}=\frac{23.8-25}{\frac{6.3}{\sqrt {15}}}=0.738$
$t_{\frac{α}{2}}=t_{0.005}=2.977$
(According to Table VI, for d.f. = 14 and area in right tail = 0.005)
Since $-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$, we do not reject the null hypothesis.
