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 = 275 numerical entries from the file and r = 67 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$\alpha$ = 0.1. What does the area of the sampling distribution corresponding to your P-value look like?
A)The area not in the left tail and the right tail of the standard normal curve.
B)The area not including the left tail of the standard normal curve.
C)The area not including the right tail of the standard normal curve.
D)The area in the left tail and the right tail of the standard normal curve.
E)The area in the left tail of the standard normal curve.

Question

Quizplus · Accepted Answer

We are testing the claim that p < 0.301, which means our alternative hypothesis is Ha: p < 0.301. Since we do not know the population proportion, we will use a one-sample proportion test. We can use the normal approximation to the binomial distribution since n = 275 is large enough and the success-failure condition is met (67 successes and 208 failures). The test statistic is given by:

z = (p-hat - 0.301)/sqrt(0.301*0.699/275)

where p-hat = 67/275 is the sample proportion.

Using a significance level of alpha = 0.1, the critical value for a one-tailed test is z = -1.28.

Calculating the test statistic, we get:

z = (67/275 - 0.301)/sqrt(0.301*0.699/275) = -3.140

Since -3.140 is less than -1.28, we reject the null hypothesis and conclude that there is evidence to support the claim that p < 0.301.

The P-value is the area in the left tail of the standard normal distribution corresponding to z = -3.140. Therefore, the area of the sampling distribution corresponding to the P-value is in the left tail of the standard normal curve.

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

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