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 - Applying the Concepts - Page 596: 18a

Answer

$X^2\lt X_α^2$: the null hypothesis is not rejected. There is no sufficient evidence of racial profiling in Mundelein.

Work Step by Step

$H_0:$ race is independent of fault in a crash $H_1:$ race is not independent of fault in a crash Expected count of White: $9868\times0.719=7095.092$ Expected count of African American: $9868\times0.028=276.203$ Expected count of Hispanic: $9868\times0.207=2042.676$ Expected count of Asian: $9868\times0.046=453.928$ $X^2=Σ\frac{(O_i-E_i)^2}{E_1}=\frac{(7079-7095.092)^2}{7095.092}+\frac{(273-276.203)^2}{276.203}+\frac{(2025-2042.676)^2}{2042.676}+\frac{(491-453.928)^2}{453.928}=3.254$ $k=4$. So, $d.f.=4-1=3$ $X_α^2=X_{0.05}^2=7.815$ (According to Table VII, for d.f. = 3 and area to the right of critical value = 0.05) Since $X^2\lt X_α^2$, we do not reject the null hypothesis.
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