Answer
We can say with 95% confidence that the population standard deviation of the rate of return is between 2.11 and 5.06 percent.
Work Step by Step
Here n = 12, df = n-1 = 11, $s^{2} = 8.875$, Confidence Interval = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, 1 - α/2 = 0.975
$χ2_{α/2} = 21.920$, $χ2_{1-α/2} = 3.816$
$\frac{(n-1)s^{2}}{χ2_{α/2}} < σ^{2} < \frac{(n-1)s^{2}}{χ2_{1-α/2}}$
$\frac{11 \times 8.875}{21.920} < σ^{2} < \frac{19 \times 8.875}{3.816}$
$ 4.45 < σ^{2} < 25.58$
2.11 < σ < 5.06
