Answer
Confidence interval: $3.341\ltµ_{Highly~Selective}\lt 4.759$
We are 95% confident that the mean time to degree completion for students first attending highly selective institutions is between 3.341 and 4.759 years.
Work Step by Step
$x ̅_{Highly~Selective}=4.05$ (item (b))
$s ̅_{Highly~Selective}=0.991$ (item (c))
$n=10$, 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)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=4.05-2.262\times\frac{0.991}{\sqrt {10}}=3.341$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=4.05+2.262\times\frac{0.991}{\sqrt {10}}=4.759$
