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Use alpha = 0.05 for all problems. 1. BENFORD'S LAW: Our number system consists of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The rst significant digit must be 1-9 because we do not write numbers such as 12 as 012. Although we may think that each digit appears with equal frequency so that each digit has a 1/9 probability of being the first signicant digit, this is not true. In 1881, Simon Newcomb discovered that digits do not occur with equal frequency. The same result was discovered again in 1938 by physicist Frank Benford. After studying much data, he was able to assign probabilities of occurrence to the first digit in a number as shown. The probability distribution is now known as Benford's Law and plays a major role in identifying fraudulent data on tax returns and accounting books. Benford's Law: mum-Inn" mmm The following distribution represents the first digit in 200 randomly selected and allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. These data are ) l'neant to prove someone is guilty of fraud, so test if the proportions of the leading digits is different than Benford's Law for all allegedly fraudulent checks written to a bogus company. The data are also provided in BenfordLaw.mtw. mum-mum'- mmmmm