Answer
We can say with 90% confidence that the population standard deviation of the number of ounces of peanuts is between 0.261 and 0.541 ounces.
Work Step by Step
Here n = 12, df = n-1 = 11, $s^{2} = 0.1219 $, Confidence Interval = 90%
α = 1 - 0.90 = 0.10, α/2 = 0.05, 1 - α/2 = 0.95
$χ2_{α/2} = 19.675$, $χ2_{1-α/2} = 4.575$
$\frac{(n-1)s^{2}}{χ2_{α/2}} < σ^{2} < \frac{(n-1)s^{2}}{χ2_{1-α/2}}$
$\frac{11 \times 0.1219}{19.675} < σ^{2} < \frac{11 \times 0.1219}{4.575}$
$ 0.068 < σ^{2} < 0.293$
0.261 < σ < 0.541
