Answer
Lower Bound = 12.22, Upper Bound = 23.21
Work Step by Step
Here n = 15, df = n-1 = 14, $s^{2} = 252.81$, Confidence Interval = 90%
α = 1 - 0.90 = 0.10, α/2 = 0.05, 1 - α/2 = 0.95
$χ2_{α/2} = 23.685$, $χ2_{1-α/2} = 6.571$
$\frac{(n-1)s^{2}}{χ2_{α/2}} < σ^{2} < \frac{(n-1)s^{2}}{χ2_{1-α/2}}$
$\frac{14 \times 252.81}{23.685} < σ^{2} < \frac{14 \times 252.81}{6.571}$
$ 149.43 < σ^{2} < 538.63$
12.22 < σ < 23.21
