The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9.
ID: 3050308 • Letter: T
Question
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 212 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Complete parts (a) and (b) below. =0.01
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
42
25
45
20
24
17
15
17
7
A. Calculate the test statistic 20 using technology, rounding to three decimal places.
B. P-value rounding three decimal places?
=
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
Excel formulation
Please rate
Oi Ei (Oi-Ei)^2/Ei 0.301 42 63.812 7.455703379 0.176 25 37.312 4.062643225 0.125 45 26.5 12.91509434 0.097 20 20.564 0.015468586 0.079 24 16.748 3.140166229 0.067 17 14.204 0.550381301 0.058 15 12.296 0.594633702 0.051 17 10.812 3.541559748 0.046 7 9.752 0.776610336 TS 1 212 212 33.05226085 p-value 6.02671E-05Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.