Answer
Confidence interval: $-2.17\lt µ_d\lt1.37$
We are 95% confident that the population mean difference between height and arm span is between -2.17 and 1.37 inches.
The interval includes $µ_d=0$. So, we can that there is not enough evidence to conclude that an individual’s height and arm span are not the same.
Work Step by Step
$n=10$, so:
$d.f.=n-1=9$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.262$
(According to Table VI, for d.f. = 9 and area in right tail = 0.025)
$Lower~bound=d ̅-t_{\frac{α}{2}}.\frac{s_d}{\sqrt n}=−0.4-2.262\times\frac{2.47}{\sqrt {10}}=-2.17$
$Upper~bound=d ̅+t_{\frac{α}{2}}.\frac{s_d}{\sqrt n}=−0.4+2.262\times\frac{2.47}{\sqrt {10}}=1.37$
