Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 499 numerical entries from the file and r = 131 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using $\alpha$ = 0.01. What is the value of the test statistic?
A)1.874
B)-41.856
C)-0.084
D)0.084
E)-1.874

Question

Quizplus · Accepted Answer

The test statistic for a proportion is calculated using the formula $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{131}{499}$, $p_0 = 0.301$, and $n = 499$. Plugging these values into the formula gives a test statistic of approximately -1.874, indicating the difference between the observed sample proportion and the hypothesized proportion.

Benford's Law Claims That Numbers Chosen from Very Large Data α\alphaα

Benford's Law Claims That Numbers Chosen from Very Large Data $\alpha$