You Might Think That If You Looked At The First Digit In Randomly Selected Numbers That The Distribution Would Be Unifor 1 (65.6 KiB) Viewed 29 times
You Might Think That If You Looked At The First Digit In Randomly Selected Numbers That The Distribution Would Be Unifor 2 (25.21 KiB) Viewed 29 times
You might think that if you looked at the first digit in randomly selected numbers that the distribution would be uniform. Actually, it is not! Simon Newcomb, and later Frank Benford, both discovered that the digits occur according to the following distribution. Digit Probability 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 1 2 3 4 5 6 7 8 9 The IRS currently uses Benford's Law to detect fraudulent tax data. Suppose you work for the IRS and are investigating an individual suspected of embezzling. Use a = 0.01. The first digit of 153 checks to a supposed company are as follows: Digit Observed Frequency 38 1 2 26 3 14 4 11 5 17 6 9 7 13 8 11 9 14 a. Choose the appropriate null hypothesis for this test. Ho: The individual has been caught embezzling. - Ho: PA / P2 / Pa | PA + Ps / Po | P7 P - TP O Ho: PP2 PPA Ho: Pi = 0.301, P2 = 0.176, p = 0.125, p = 0.007, p = 0.079, po - 0.067, p = 0.058, p = 0.051, po = 0.046 OH: At least one proportion is different.
b. What is the value of the test statistic. Round answer to at least 4 decimal places. c. What is the P.Value? Round answer to at least 4 decimal places. P.Value - d. What is your decision? Reject the Nutt Hypothesis O Fail to reject the Null Hypothesis e. Use the decision in part d to make a conclusion about whether the individual is likely to have embezzled. The evidence shows that the individual may be guilty of embezzling. There is no evidence that the individual is embezzling.
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