Answer
Confidence interval: $31.76\lt x ̅\lt38.44$
Compared to the results obtained in part (a), the margin of error has increased.
Work Step by Step
$n=40$, so:
$d.f.=n-1=39$
$level~of~confidence=(1-α).100$%
$98$% $=(1-α).100$%
$0.98=1-α$
$α=0.02$
$t_{\frac{α}{2}}=t_{0.01}=2.426$
(According to Table VI, for d.f. = 39 and area in right tail = 0.01)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=35.1-2.426\times\frac{8.7}{\sqrt {40}}=31.76$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=35.1+2.426\times\frac{8.7}{\sqrt {40}}=38.44$
