Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 12 - Statistics - 12.4 The Normal Distribution - Exercise Set 12.4 - Page 814: 72

Answer

$0.4\%$

Work Step by Step

The margin of error of a sample size $n$ is a $95\%$ probability that a sample lies within the margin of error which is $\pm\frac{1}{\sqrt n}\cdot 100\%$ Hence here the margin of error: $\pm\frac{1}{\sqrt {10000}}\cdot 100\%=\pm1\%$. Thus it improved the margin of error by $1.4\%-1\%=0.4\%$
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