Question

Recall that 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. Now 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 = 225 numerical entries from the file and r = 51 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.

Use the value of the sample test statistic to find the corresponding z value. (Round your answer to two decimal places.)


Find the P-value of the test statistic. (Round your answer to four decimal places.)
P-value =

Answer 1

We can use the formula for the test statistic for a hypothesis test of a single proportion:

z = (p-hat - p) / sqrt(pq/n)

where p-hat is the sample proportion, p is the hypothesized population proportion (0.301 according to Benford's Law), q = 1 - p, and n is the sample size.

Plugging in the values given, we get:

z = (0.2278 - 0.301) / sqrt(0.301*0.699/225) = -2.83

To find the P-value, we need to find the probability that a standard normal distribution is less than -2.83 (since this is a left-tailed test). Using a standard normal table or calculator, we find this probability to be 0.0023.

Therefore, the P-value is 0.0023.

Step-by-step explanation: