Question

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 = 215 numerical entries from the file and r = 47 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?

What is the value of the sample test statistic? (Round your answer to two decimal places.)

Answer 1

Solution:

Claim: p is less than 0.301

i.e. p < 0.301

n = 215 (sample size)

r = 47 (No. of successes in the sample)

Let   be the sample proportion.

= x/n = 47/215 = 0.2186

Hypothesis can be written as

H₀ : p = 0.301

H₁ : p <  0.301

Use α = 0.10.

a)What is the level of significance?

Level of significance = = 0.10

What is the value of the sample test statistic?

The test statistic z is

z =   

= (0.2186 - 0.301)/[0.301* (1 - 0.301)/215]

= -2.59553570093

= -2.63

The value of the sample test statistic z = -2.63

Now , observe that ,there is < sign in H1. So , the test is left tailed.

p value = P(Z < z)

= P(Z < -2.63)

= 0.0043 (use z table)

p value is less than Level of significance 0.10

So , reject the null hypothesis and conclude that there is sufficient evidence to support the claim that  p is less than 0.301