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 an individual’s height and arm span are not the same.
Work Step by Step
$d_i=(Height)_i-(Arm~span)_i$
$d_1=-2.5$
$d_2=3.5$
$d_3=1$
$d_4=-3.5$
$d_5=0.5$
$d_6=-3$
$d_7=0.5$
$d_8=-1.5$
$d_9=3$
$d_{10}=-2$
$d ̅=\frac{∑d_i}{n}=-0.4$
$s_d=\sqrt {\frac{∑(d_i-d ̅)^2}{n-1}}=2.47$
$H_0:~µ_d=0$ versus $H_1:~µ_d\ne0$
$t_0=\frac{d ̅ }{\frac{s_d}{\sqrt n}}=\frac{-0.4}{\frac{2.47}{\sqrt {10}}}=-0.512$
$n=10$, so:
$d.f.=n-1=9$
Two-tailed test:
$t_{\frac{α}{2}}=t_{0.025}=2.262$
(According to Table VI, for d.f. = 9 and area in right tail = 0.025)
Also, $-t_{\frac{α}{2}}=-2.262$
Since $-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$, we do not reject the null hypothesis.
