Answer
Confidence interval: $35.44\lt x ̅\lt42.36$
Since the confidence interval contains the population mean, $µ=40.7~years$, in 2002, there is not enough evidence to reject that the mean age of an inmate on death row has changed since then.
Work Step by Step
$n=32$, so:
$d.f.=n-1=31$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.040$
(According to Table VI, for d.f. = 31 and area in right tail = 0.025)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=38.9-2.040\times\frac{9.6}{\sqrt {32}}=35.44$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=38.9+2.040\times\frac{9.6}{\sqrt {32}}=42.36$
