Answer
Confidence interval: $45.5\lt x ̅ \lt54.5$
Work Step by Step
$n=20$, so:
$d.f.=n-1=19$
$level~of~confidence=(1-α).100$%
$98$% $=(1-α).100$%
$0.98=1-α$
$α=0.02$
$t_{\frac{α}{2}}=t_{0.01}=2.539$
(According to Table VI, for d.f. = 19 and area in right tail = 0.01)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=50-2.539\times\frac{8}{\sqrt {20}}=45.5$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=50+2.539\times\frac{8}{\sqrt {20}}=54.5$
