Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 12 - Section 12.1 - Assess Your Understanding - Explaining the Concepts - Page 598: 32

Answer

Because all the terms in $Σ\frac{(O_i-E_i)^2}{E_i}$ are positive, no matter the observed value is greater or less than the expected value. The larger is the difference between the observed and the expected values, the larger will be $(O_i-E_i)^2$ and, the larger will be $X^2=Σ\frac{(O_i-E_i)^2}{E_i}$. So, we will reject the null hypothesis only when $X^2$ is large enough, that is, when $X^2\gt X_α^2$ (right tailed test).

Work Step by Step

Given above.
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