# Chapter 7 - Estimates and Sample Sizes - 7-4 Estimating a Population Standard Deviation or Variance - Basic Skills and Concepts: 17

σ is between 0.0108 and 0.0214.

#### 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 $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(24)\cdot 0.0144^2}{42.98}}=0.0108$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(24)\cdot 0.0144^2}{10.856}}=0.0214.$

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