Answer
$t_0\lt -t_{\frac{α}{2}}$: null hypothesis is rejected.
There is enough evidence to conclude that the population means differ.
Work Step by Step
- Mean;
- Independent sampling.
$H_0:~µ_1=µ_2$ versus $H_1:~µ_1\ne µ_2$
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(125.3-130.8)-0}{\sqrt {\frac{8.5^2}{41}+\frac{7.3^2}{50}}}=-3.271$
$n=41$ (use the smaller value of $n$), so:
$d.f.=n-1=40$
Two-tailed test:
$t_{\frac{α}{2}}=t_{0.005}=2.704$
(According to Table VI, for d.f. = 40 and area in right tail = 0.005)
Also, $-t_{\frac{α}{2}}=-2.704$
Since $t_0\lt -t_{\frac{α}{2}}$, we reject the null hypothesis.
