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 597: 24

Answer

$X^2_0\lt X_α^2$: null hypothesis is not rejected. There is not enough evidence to conclude that the first digit of the Fibonacci numbers does not follow the Benford distribution.

Work Step by Step

$H_0:$ the first digit of the Fibonacci numbers follows the Benford distribution versus $H_1:$ the first digit of the Fibonacci numbers does not follow the Benford distribution In MINITAB, enter the observed frequencies in C1 and the probabilities of occurrence (problem 13) in C2. Select Stat -> Tables -> Chi-square Goodness-of-Fit Test (One Variable) Select Observed counts and enter C1. Select specific proportions and enter C2. Click OK. $X^2_0=1.20082$ $k=9$. So, $d.f.=9-1=8$ $X_α^2=X_{0.05}^2=15.507$ (According to Table VII, for d.f. = 8 and area to the right of critical value = 0.05) Since $X^2_0\lt X_α^2$, we do not reject the null hypothesis. Also, P-value $=0.997\gtα$
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