Question

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 = 250 numerical entries from the file and r = 60 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 α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like?

The area in the right tail of the standard normal curve.

The area not including the right tail of the standard normal curve.

The area in the left tail and the right tail of the standard normal curve.

The area not including the left tail of the standard normal curve.

The area in the left tail of the standard normal curve.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.301
Alternative hypothesis: P < 0.301

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.02901
z = (p - P) / S.D

z = - 2.103

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than -2.103.

Thus, the P-value = 0.018.

The area in the left tail of the standard normal curve.

Interpret results. Since the P-value (0.018) is greater than the significance level (0.01), we have to accept the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that that p is less than 0.301.