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 business travelers walk at a different speed from leisure travelers.
Work Step by Step
$x ̅_1,n_1~and~s_1$ refer to business and $x ̅_2,n_2~and~s_2$ refer to leisure.
$H_0:~µ_1=µ_2$ versus $H_1:~µ_1\ne µ_2$
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(272-261)-0}{\sqrt {\frac{43^2}{20}+\frac{47^2}{20}}}=0.772$
$n=20$, so:
$d.f.=n-1=19$
Two-tailed test:
$t_{\frac{α}{2}}=t_{0.025}=2.093$
(According to Table VI, for d.f. = 19 and area in right tail = 0.025)
Also, $-t_{\frac{α}{2}}=-2.093$
Since $-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$, we do not reject the null hypothesis.
