The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9.

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 206 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Complete parts (a) and (b) below. LOADING... Click the icon to view the tables. (a) Using the level of significance alpha equals 0.05 , test whether the first digits in the allegedly fraudulent checks obey Benford's Law. What is the null hypothesis? A. H0: The distribution of the first digits in the allegedly fraudulent checks obey Benford's Law. Your answer is correct. B. H0: The distribution of the first digits in the allegedly fraudulent checks do not obey Benford's Law. C. None of these. What is the alternative hypothesis? A. H1: The distribution of the first digits in the allegedly fraudulent checks do not obey Benford's Law. Your answer is correct. B. H1: The distribution of the first digits in the allegedly fraudulent checks obey Benford's Law. C. None of these. What is the test statistic? chi Subscript 0 Superscript 2 equals52.875 (Round to three decimal places as needed.) What is the P-value of the test? P-valueequals nothing (Round to three decimal places as needed.)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 28 20 23 36 9 16 7

Explanation / Answer

applying chi square goodness of fit test:

  test statistic =52.875

p value =0.0000

observed Expected Chi square x Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei 1 0.301 42.000 62.0 6.45 2 0.176 25.000 36.3 3.49 3 0.125 28.000 25.8 0.20 4 0.097 20.000 20.0 0.00 5 0.079 23.000 16.3 2.78 6 0.067 36.000 13.8 35.70 7 0.058 9.000 11.9 0.73 8 0.051 16.000 10.5 2.87 9 0.046 7.000 9.5 0.65 total 1 206 206 52.875

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.