Answer
Lower Bound = 12.07, Upper Bound = 38.32
The confidence interval decreases by an increase in sample size.
Work Step by Step
Here n = 25, df = n-1 = 24, $s^{2} = 19.8$, Confidence Interval = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, 1 - α/2 = 0.975
$χ2_{α/2} = 39.364$, $χ2_{1-α/2} = 12.401$
$\frac{(n-1)s^{2}}{χ2_{α/2}} < σ^{2} < \frac{(n-1)s^{2}}{χ2_{1-α/2}}$
$\frac{24 \times 19.8}{39.364} < σ^{2} < \frac{24 \times 19.8}{12.401}$
$ 12.07 < σ^{2} < 38.32$
