The Practice of Statistics for AP - 4th Edition
The Practice of Statistics for AP - 4th Edition
4th Edition
ISBN: 9781429245593
Author: Starnes, Daren S., Yates, Daniel S., Moore, David S.
Publisher: Macmillan Higher Education
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Chapter 11.1, Problem 11E

a.

To determine

To check: If the data is consistent with Benford’s law by conducting the significant test at % significance law.

a.

Expert Solution
Check Mark

Answer to Problem 11E

There is sufficient evidence to reject the claim of Benford’s claim.

Explanation of Solution

Given:

The data set is:

    First digit (X)ProbabilityCount
    10.30161
    20.17640
    30.12543
    40.09734
    50.07925
    60.06716
    70.0587
    80.0518
    90.0466

Formula used:

The formula to compute the chi-square statistic is:

  χ2=(Observed - Expected)2Expected

Calculation:

The hypotheses are:

  H0:p1=0.301,p2=0.176,p3=0.125....p9=0.046Ha:At least one of the pi is different

The calculation for test statistic is done as:

    Observed valueExpected value(OE)(OE)2(OE)2/E
    6175.25-14.2520.306252.6985
    50446360.8182
    4331.2511.75138.06254.418
    3424.259.7595.06253.9201
    2519.755.2527.56251.3956
    1616.75-0.750.56250.0336
    714.5-7.556.253.8793
    812.75-4.7522.56251.7696
    611.5-5.530.252.6304
    (OE)2/E=21.5633

The test statistic is:

  χ2=(OE)2/E=21.5633

The degree of freedom is calculated as:

  Degree of freedom =Number of categories - 1=91=8

The p-value using chi-square table at 8 degree of freedom is 0.005792

The p -value is below significance level. The null hypothesis gets rejected. Thus, there is sufficient evidence to reject the claim of Benford’s claim.

b.

To determine

To discuss: The Type I and Type II errors in the context of the problem. Also, explain the error that is more serious.

b.

Expert Solution
Check Mark

Answer to Problem 11E

Type I error.

Explanation of Solution

Type I error happenes if the null hypthesis is rejected even if it is correct. Here, type I error would occur if it is concluded that Benford’s law is not appropriate for the sample even it is.

On the other hand, type II error would occur if it is concluded that Benford’s law is appropriate for the sample even it is not.

Here, Type I error is more worst because it will accuse an innocent company to commit fraud.

Chapter 11 Solutions

The Practice of Statistics for AP - 4th Edition

Ch. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10ECh. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.2 - Prob. 1.1CYUCh. 11.2 - Prob. 1.2CYUCh. 11.2 - Prob. 1.3CYUCh. 11.2 - Prob. 2.1CYUCh. 11.2 - Prob. 2.2CYUCh. 11.2 - Prob. 2.3CYUCh. 11.2 - Prob. 3.1CYUCh. 11.2 - Prob. 3.2CYUCh. 11.2 - Prob. 3.3CYUCh. 11.2 - Prob. 4.1CYUCh. 11.2 - Prob. 4.2CYUCh. 11.2 - Prob. 6.1CYUCh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Prob. 46ECh. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Prob. 50ECh. 11.2 - Prob. 51ECh. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Prob. 54ECh. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.2 - Prob. 57ECh. 11.2 - Prob. 58ECh. 11.2 - Prob. 59ECh. 11.2 - Prob. 60ECh. 11.2 - Prob. 61ECh. 11.2 - Prob. 62ECh. 11.2 - Prob. 63ECh. 11.2 - Prob. 64ECh. 11 - Prob. 1CRECh. 11 - Prob. 2CRECh. 11 - Prob. 3CRECh. 11 - Prob. 4CRECh. 11 - Prob. 5CRECh. 11 - Prob. 6CRECh. 11 - Prob. 1PTCh. 11 - Prob. 2PTCh. 11 - Prob. 3PTCh. 11 - Prob. 4PTCh. 11 - Prob. 5PTCh. 11 - Prob. 6PTCh. 11 - Prob. 7PTCh. 11 - Prob. 8PTCh. 11 - Prob. 9PTCh. 11 - Prob. 10PTCh. 11 - Prob. 11PTCh. 11 - Prob. 12PTCh. 11 - Prob. 13PT
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