Answer
Confidence interval: $1507.7\lt x ̅\lt1728.3$
Since the confidence interval does not contain the population mean, µ = $1493, in 2001, there is enough evidence to conclude that the mean household expenditure for energy has changed since then.
Work Step by Step
$n=35$, so:
$d.f.=n-1=34$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.032$
(According to Table VI, for d.f. = 34 and area in right tail = 0.025)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=1618-2.032\times\frac{321}{\sqrt {35}}=1507.7$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=1618+2.032\times\frac{321}{\sqrt {35}}=1728.3$
