Answer
$t_0\gt t_α$: null hypothesis is rejected.
There is enough evidence to conclude that the mean collision claim of a 20- to 24-year-old driver is greater than the mean claim of a 30- to 59-year-old driver.
So a 20- to 24-year-old driver must be charged a higher insurance premium.
Work Step by Step
$x ̅_1,n_1~and~s_1$ refer to 20- to 24-year-old drivers and $x ̅_2,n_2~and~s_2$ refer to 30- to 59-year-old drivers.
$H_0:~µ_1=µ_2$ versus $H_1:~µ_1\gt µ_2$
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(4586-3669)-0}{\sqrt {\frac{2302^2}{40}+\frac{2029^2}{40}}}=1.890$
$n=40$, so:
$d.f.=n-1=39$
Right-tailed test:
Let's use $α=0.05$ level of significance.
$t_α=t_{0.05}=1.685$
(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.
