Answer
Confidence interval: $32.82\lt x ̅\lt37.38$
The margin of error has decreased.
Work Step by Step
$n=100$, so:
$d.f.=n-1=99$
$level~of~confidence=(1-α).100$%
$90$% $=(1-α).100$%
$0.9=1-α$
$α=0.1$
$t_{\frac{α}{2}}=t_{0.05}=1.660$
(According to Table VI, for d.f. = 100 and area in right tail = 0.05. Notice that there are no available values of $t$ for d.f. = 99, but the given value of $t$ is pretty close)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=35.1-1.660\times\frac{8.7}{\sqrt {40}}=32.82$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=35.1+1.660\times\frac{8.7}{\sqrt {40}}=37.38$
