5. 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 = 397 numerical entries from the file and r = 110 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 What is the value of the test statistic?

To test the claim that the population proportion (p) is less than 0.301, we will perform a hypothesis test using the given sample data.

Let's define the null hypothesis (H0) and the alternative hypothesis (Ha):

H0: p ≥ 0.301
Ha: p < 0.301

We will use a one-sample proportion test to compare the observed proportion (r/n) to the claimed proportion (p).

The test statistic for this hypothesis test is calculated as:

z = (observed proportion - claimed proportion) / sqrt((claimed proportion * (1 - claimed proportion)) / sample size)

In this case:
observed proportion = r/n = 110/397
claimed proportion = 0.301
sample size = n = 397

Now let's calculate the value of the test statistic:

z = (110/397 - 0.301) / sqrt((0.301 * (1 - 0.301)) / 397)

After plugging in the values and performing the calculations, the value of the test statistic (z) will be obtained.