Answer
σ is between 0.253 and 0.701.
Work Step by Step
The mean can be counted by summing all the data and dividing it by the number of data: $\frac{0.56+0.75+...+0.88}{7}=0.719.$
Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(0.56-0.719)^2+...+(0.88-0.719)^2}{6}}=0.366.$
$\alpha=1-0.9=0.1.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=7-1=6$.
$X_{L}^2= X_{0.95}^2=1.635$
$ X_{R}^2= X_{0.05}^2=12.592$
Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(6)\cdot 0.366^2}{12.592}}=0.253$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(6)\cdot 0.366^2}{1.635}}=0.701.$
