Answer
Lower Bound = 8.59, Upper Bound = 20.63.
We observe that width of the interval decreased by an increase in sample size.
Work Step by Step
Here n = 30, df = n-1 = 29, $s^{2} = 12$, Confidence Interval = 90%
α = 1 - 0.90 = 0.10, α/2 = 0.05, 1 - α/2 = 0.95
$χ2_{α/2} = 42.557$, $χ2_{1-α/2} = 17.708$
$\frac{(n-1)s^{2}}{χ2_{α/2}} < σ^{2} < \frac{(n-1)s^{2}}{χ2_{1-α/2}}$
$\frac{29 \times 12.6}{42.557} < σ^{2} < \frac{29 \times 12.6}{17.708}$
$ 8.59 < σ^{2} < 20.63$
