Answer
Confidence interval: $161.5\lt x ̅\lt194.5$
We are 95% confident that the mean total work for the placebo treatment is between 161.5 and 194.5 kilojoules.
Work Step by Step
$n=16$, so:
$d.f.=n-1=15$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.131$
(According to Table VI, for d.f. = 15 and area in right tail = 0.025)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=178-2.131\times\frac{31}{\sqrt {16}}=161.5$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=178+2.131\times\frac{31}{\sqrt {16}}=194.5$
