#4 The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or
ID: 3229287 • Letter: #
Question
#4
The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 233 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Use data given below to solve a, b, & c.
Distribution of first digits (Benford's Law)
Digit
1
2
3
4
5
Probability
0.301
0.176
0.125
0.097
0.079
Digit
6
7
8
9
Probability
0.067
0.058
0.051
0.046
First digits in allegedly fraudulent checks
First digit
1
2
3
4
5
6
7
8
9
Frequency
36
32
45
26
23
36
9
17
9
a.) What is the test statistic?
b.) What is the P-value?
c.) Could we assume the employee is responsible for embezzlement?
Distribution of first digits (Benford's Law)
Digit
1
2
3
4
5
Probability
0.301
0.176
0.125
0.097
0.079
Digit
6
7
8
9
Probability
0.067
0.058
0.051
0.046
Explanation / Answer
H0: the employee is responsible for embezzlement
H1: the employee is not responsible for embezzlement
a)
Chisquare test:
chisquare test statistic = 59.517
b) P-value = 0.000
c) Here P-value < alpha 0.0, So we reject H0
Thus we conclude that the employee is not responsible for embezzlement
Observed Expected Digits prob. freq (Oi) freq(Ei) (Oi-Ei)^2/Ei 1 0.301 36 70.133 16.61217528 2 0.176 32 41.008 1.978737417 3 0.125 45 29.125 8.652896996 4 0.097 26 22.601 0.511180965 5 0.079 23 18.407 1.146066659 6 0.067 36 15.611 26.62938447 7 0.058 9 13.514 1.507784224 8 0.051 17 11.883 2.203457797 9 0.046 9 10.718 0.275380108 233 59.51706392Related Questions
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