Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 7 - Confidence Intervals and Sample - 7-2 Confidence Intervals for the Mean When σ Is Unknown - Exercises 7-2 - Page 387: 13

Answer

$17.87\lt\mu\lt20.53$ this range is higher than the national average of $15.9$

Work Step by Step

Given $n=12, \bar X=19.2, s^2=4.41$, we have $s=2.1$ and at a 95% confidence and $df=11$, the critical t-value is $t_{\alpha/2}=2.2 $ (use table F) The margin of error can be found as $E=2.2\times\frac{2.1}{\sqrt {12}}=1.33$ Thus, the interval of the true mean can be estimated as $\bar X-E\lt\mu\lt\bar X+E$ which gives $17.87\lt\mu\lt20.53$ It appears that this range is higher than the national average of $15.9$
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