Chapter 9 - Section 9.3 - Assess Your Understanding - Vocabulary and Skill Building - Page 459: 9a

Lower Bound = 7.94, Upper Bound = 23.66

Here n = 20, df = n-1 = 19, $s^{2} = 12$, Confidence Interval = 90% α = 1 - 0.90 = 0.10, α/2 = 0.05, 1 - α/2 = 0.95 $χ2_{α/2} = 30.144$, $χ2_{1-α/2} = 10.117$ $\frac{(n-1)s^{2}}{χ2_{α/2}} < σ^{2} < \frac{(n-1)s^{2}}{χ2_{1-α/2}}$ $\frac{19 \times 12.6}{30.144} < σ^{2} < \frac{19 \times 12.6}{10.11}$ $ 7.94 < σ^{2} < 23.66$