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 $µ_1\ne µ_2$.
Work Step by Step
- Mean;
- Independent sampling.
$H_0:~µ_1=µ_2$ versus $H_1:~µ_1\ne µ_2$
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(45.3-52.1)-0}{\sqrt {\frac{12.4^2}{13}+\frac{14.7^2}{18}}}=-1.393$
$n=13$ (use the smaller value of $n$), so:
$d.f.=n-1=12$
Two-tailed test:
$t_{\frac{α}{2}}=t_{0.025}=2.179$
(According to Table VI, for d.f. = 12 and area in right tail = 0.025)
Also, $-t_{\frac{α}{2}}=-2.179$
Since $-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$, we do not reject the null hypothesis.
