Answer
Confidence interval: $44.6\lt x ̅\lt55.4$
The margin of error has increased.
Work Step by Step
$n=15$, so:
$d.f.=n-1=14$
$level~of~confidence=(1-α).100$%
$98$% $=(1-α).100$%
$0.98=1-α$
$α=0.02$
$t_{\frac{α}{2}}=t_{0.01}=2.624$
(According to Table VI, for d.f. = 14 and area in right tail = 0.01)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=50-2.624\times\frac{8}{\sqrt {15}}=44.6$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=50+2.624\times\frac{8}{\sqrt {15}}=55.4$
