Question

In: Statistics and Probability

Recall that Benford's Law claims that numbers chosen from very large data files tend to have...

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 = 219 numerical entries from the file and r = 48 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. (i) Test the claim that p is less than 0.301. Use α = 0.10. (a) What is the level of significance?

State the null and alternate hypotheses. a) H0: p = 0.301; H1: p ≠ 0.301 b) H0: p < 0.301; H1: p = 0.301 c) H0: p = 0.301; H1: p > 0.301 d) H0: p = 0.301; H1: p < 0.301 I

Solutions

Expert Solution

Solution:-

The level of significance is 0.10.

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

d)

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 0.10. 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 = 0.030996
z = (p - P) / S.D

z = - 2.64

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 -2.64.

P-value = P(z < - 2.64)

Use the z-calculator to determine the p-value.

P-value = 0.0041

Interpret results. Since the P-value (0.0041) is less than the significance level (0.10), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that p is less than 0.301.

orchestra answered 1 year ago
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