Answer
$t_0\lt t_α$: null hypothesis is rejected.
There is enough evidence to conclude that community college transfer students take longer to attain a bachelor’s degree.
Work Step by Step
$x ̅_1,n_1~and~s_1$ refer to community college to 4-year transfer and $x ̅_2,n_2~and~s_2$ refer to no transfer.
$H_0:~µ_1=µ_2$ versus $H_1:~µ_1\gt µ_2$
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(5.43-4.43)-0}{\sqrt {\frac{1.162^2}{268}+\frac{1.015^2}{1145}}}=12.977$
$n=268$ (use the smaller value of $n$), so:
$d.f.=n-1=267$
Right-tailed test:
$t_α=t_{0.01}=2.364$
(According to Table VI, for d.f. = 100, the closest value to 267, and area in right tail = 0.01)
Since $t_0\gt t_α$, we reject the null hypothesis.
