Answer
We can say with 90% confidence that the standard deviation of the repair cost of a low-impact bumper crash on a mini- or micro-car is between 849.69 and 1655.34 dollars.
Work Step by Step
Here n = 14, df = n-1 = 13, $s^{2} = 1241914.106$, Confidence Interval = 90%
α = 1 - 0.90 = 0.10, α/2 = 0.05, 1 - α/2 = 0.95
$χ2_{α/2} = 22.362$, $χ2_{1-α/2} = 5.892$
$\frac{(n-1)s^{2}}{χ2_{α/2}} < σ^{2} < \frac{(n-1)s^{2}}{χ2_{1-α/2}}$
$\frac{13 \times 1241914.106}{22.362} < σ^{2} < \frac{13 \times 1241914.106}{5.892}$
$ 721978.507 < σ^{2} < 490.617$
849.69 < σ < 1655.34
