Answer
a)σ is between 7.87 and 14.14.
b)σ is between 8.87 and 15.92.
c)There seems to be no difference in the variation.
Work Step by Step
a)$\alpha=1-0.99=0.01.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=40-1=39$.
$X_{L}^2= X_{0.975}^2=20.707$
$ X_{R}^2= X_{0.025}^2=66.766$
Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(39)\cdot 10.3^2}{66.766}}=7.87$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(39)\cdot 10.3^2}{66.766}}=14.14.$
b) $\alpha=1-0.99=0.01.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=40-1=39$.
$X_{L}^2= X_{0.975}^2=20.707$
$ X_{R}^2= X_{0.025}^2=66.766$
Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(39)\cdot 11.6^2}{66.766}}=8.87$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(39)\cdot 11.6^2}{66.766}}=15.92.$
c)There seems to be no difference in the variation because the intervals in a) and b) overlap.
