Elementary Statistics (12th Edition)

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

Chapter 7 - Estimates and Sample Sizes - 7-3 Estimating a Population Mean - Basic Skills and Concepts: 32

Answer

53, 34. 53 seems to be better because it uses both methods.

Work Step by Step

$\alpha=1-0.95=0.05.$ Using the table: $z_{\alpha/2}=z_{0.025}=1.96.$ Standard deviation=$\frac{range}{4}=\frac{2.95-0}{4}=0.7375.$ Hence the sample size this way:$\left (\frac{z_{\alpha/2}\cdot \sigma}{E}\right)^2=\left (\frac{1.96\cdot0.7375}{0.2}\right)^2\approx53$. Using the sample standard deviation:$\left (\frac{z_{\alpha/2}\cdot \sigma}{E}\right)^2=\left (\frac{1.96\cdot0.587}{0.2}\right)^2\approx34$. 34 seems to be better because it uses both methods.
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