Question

Benford's Law claims that numbers chosen from very large data files tend to have "l" 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 "l" 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 = 402 numerical entries from the file and r = 107 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 a = 0.01 Are the data statistically significant at the significance level? Based on your answers, will you reject or fail to reject the null hypothesis? The P-value is greater than the level of significance so the data are not statistically significant. Thus, we fail to reject the null hypothesis. The P-value is greater than the level of significance so the data are not statistically significant. Thus, we reject the null hypothesis. The P-value is less than the level of significance so the data are not statistically significant. Thus, we reject the null hypothesis. The P-value is greater than the level of significance so the data are statistically significant. Thus, we fail to reject the null hypothesis. The P-value is less than the level of significance so the data are statistically significant. Thus, we reject the null hypothesis.

Answer 1

Null and alternative hypotheses

Ho : p = 0.301

Ha : p < 0.301

Test statistic

Z = p^ - p / sqrt[ p^ * (1-p^)/n]

Where p^ = r/n = 107/402

p^ = 0.266

Z = (0.266-0.301)/sqrt[0.266*0.734/402]

Z = -1.59

P-value for Z = -1.59 and left tailed test

Using Z table

P-value = P( Z < -1.59)

p-value = 0.056

Decision rule : if p-value < $\alpha$ we Reject the null hypothesis otherwise we fail to reject the null hypothesis

Our p-value = 0.056 > 0.01

The p-value is greater than the level of significance so the data are not statistically significant. Thus we fail to reject the null hypothesis.