Answer
Confidence interval: $16.32\lt x ̅\lt20.48$
Compared to the results obtained in part (a), the margin of error has increased.
Work Step by Step
$n=35$, so:
$d.f.=n-1=34$
$level~of~confidence=(1-α).100$%
$99$% $=(1-α).100$%
$0.99=1-α$
$α=0.01$
$t_{\frac{α}{2}}=t_{0.005}=2.728$
(According to Table VI, for d.f. = 34 and area in right tail = 0.005)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=18.4-2.728\times\frac{4.5}{\sqrt {35}}=16.32$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=18.4+2.728\times\frac{4.5}{\sqrt {35}}=20.48$
