Answer
Confidence interval: $2992.2\lt x ̅\lt3849.8$
We are 90% confident that the mean amount of additional tax owed is between $\$2992.$2 and $\$3849.8$.
Work Step by Step
We want to estimate the mean using a sample whose size is greater than 30.
$n=100$, 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, the closest value to 99, and area in right tail = 0.05)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=3421-1.660\times\frac{2583}{\sqrt {100}}=2992.2$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=3421+1.660\times\frac{2583}{\sqrt {100}}=3849,8$
