Answer
σ is between 30.9 and 67.5.
Work Step by Step
$\alpha=1-0.99=0.01.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=24-1=23$.
$X_{L}^2= X_{0.975}^2=9.26$
$ X_{R}^2= X_{0.025}^2=44.181$
Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(23)\cdot 42.8^2}{44.181}}=30.9$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(23)\cdot 42.8^2}{9.26}}=67.5.$
