Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 7 - Estimates and Sample Sizes - 7-4 Estimating a Population Standard Deviation or Variance - Basic Skills and Concepts: 13

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 $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(6)\cdot 0.366^2}{1.635}}=0.701.$
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