Answer
We can say with 90% confidence that the standard deviation of the travel tax for a 3-day business trip is between 8.69 and 22.15 dollars.
Work Step by Step
Here n = 8, df = n-1 = 7, $s^{2} = 151.88$, Confidence Interval = 90%
α = 1 - 0.90 = 0.10, α/2 = 0.05, 1 - α/2 = 0.95
$χ2_{α/2} = 14.067$, $χ2_{1-α/2} = 2.167$
$\frac{(n-1)s^{2}}{χ2_{α/2}} < σ^{2} < \frac{(n-1)s^{2}}{χ2_{1-α/2}}$
$\frac{7 \times 151.88}{14.067} < σ^{2} < \frac{7 \times 151.88}{2.167}$
$ 75.58 < σ^{2} < 490.617$
8.69 < σ < 22.15
