## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 7 - Estimates and Sample Sizes - 7-4 Estimating a Population Standard Deviation or Variance - Basic Skills and Concepts - Page 370: 14

#### Answer

σ is between 2.9 and 6.9.

#### Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{62+61+...+67}{12}=60.67.$ Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(62-60.67)^2+...+(67-60.67)^2}{11}}=4.075.$ $\alpha=1-0.95=0.05.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=12-1=11$. $X_{L}^2= X_{0.975}^2=3.816$ $X_{R}^2= X_{0.025}^2=21.92$ Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(11)\cdot 4.075^2}{21.9}}=2.9$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(11)\cdot 4.075^2}{3.816}}=6.9.$

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