Answer
Confidence interval: $2.648\lt x ̅\lt3.852$
Work Step by Step
We want to estimate the mean using a sample whose size is less than 30, but that was obtained from a population that is normally distributed.
$n=17$, so:
$d.f.=n-1=16$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.120$
(According to Table VI, for d.f. = 16 and area in right tail = 0.025)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=3.25-2.120\times\frac{1.17}{\sqrt {17}}=2.648$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=3.25+2.120\times\frac{1.17}{\sqrt {17}}=3.852$
