Answer
We can say with 95% confidence that the population standard deviation of the age (in weeks) at which babies first crawl is between 7.08 and 16.98 weeks.
Work Step by Step
Here n = 12, df = n-1 = 11, $s^{2} = 100$, Confidence Interval = 95%
α = 1 - 0.905= 0.05, α/2 = 0.025, 1 - α/2 = 0.975
$χ2_{α/2} = 21.920$, $χ2_{1-α/2} = 3.816$
$\frac{(n-1)s^{2}}{χ2_{α/2}} < σ^{2} < \frac{(n-1)s^{2}}{χ2_{1-α/2}}$
$\frac{11 \times 100}{21.920} < σ^{2} < \frac{11 \times 100}{3.816}$
$ 50.18 < σ^{2} < 288.26$
7.08 < σ < 16.98
