Using Benford's law According to Benford's law (Exercise 5,...

Using Benford's law According to Benford's law (Exercise $5,$ page 359$),$ the probability that the first digit of the amount on a randomly chosen invoice is a 1 or a 2 is $0.477 .$ Suppose you examine an SRS of 90 invoices from a vendor and find 29 that have first digits 1 or 2 . Do you suspect that the invoice amounts are not genuine? Compute an appropriate probability to support your answer.

Key Concepts

Benford's Law

Benford's Law is a statistical principle that predicts the frequency distribution of leading digits in many naturally occurring collections of numbers. According to this law, smaller digits appear as the first digit more frequently than larger ones. This counterintuitive distribution is often used as a tool for detecting anomalies or potential manipulations in datasets, such as financial records or accounting figures.

Binomial Distribution

The Binomial Distribution is a probability distribution that models the number of successes in a fixed number of independent and identical trials, each with the same probability of success. It is commonly used in situations where the outcome of interest is binary (for example, whether an invoice follows an expected pattern). The distribution can be used to compute the probability of observing a certain number of successes, which is essential in assessing deviations from expected results.

Hypothesis Testing

Hypothesis Testing is a statistical method used to decide whether observed data deviate significantly from a stated hypothesis. In this context, the null hypothesis might state that the observed digit frequencies conform to the expected distribution (as predicted by Benford's Law). By calculating the probability of observing an outcome as extreme as, or more extreme than, the one measured (a p-value), one can assess whether there is sufficient evidence to reject the null hypothesis and suspect that the dataset may be manipulated or unusual.

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