Answer
σ is between 0.012 and 0.0225
Work Step by Step
The mean can be counted by summing all the data and dividing it by the number of data: $\frac{2.5113+...+2.5085}{25}=2.502.$ Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(2.5113-2.502)^2+...+(2.5085-2.502)^2}{24}}=0.0144.$ $\alpha=1-0.98=0.02.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=25-1=24$. $X_{L}^2= X_{0.99}^2=10.856$ $ X_{R}^2= X_{0.01}^2=42.98$ Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(24)\cdot 0.0144^2}{42.98}}=0.0124$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(24)\cdot 0.0144^2}{10.856}}=0.0225.$
