Question

A random sample of 20 binomial trials resulted in 8 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.

(1) Compute p̂.

(2) Compute the corresponding standardized sample test statistic. (Round your answer to two decimal places.)

(3) Find the P-value of the test statistic. (Round your answer to four decimal places.)

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 = 218 numerical entries from the file and r = 52 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. Use α = 0.05.

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


(5) Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer 1

a)

1

sample proportion p̂ = x/n=

0.4000

2)

test stat z =(p̂-p)/√(p(1-p)/n)=

-0.89

3)

p value                          =

0.3734

4)

sample success x   =		52
sample size          n    =		218
std error   se =√(p*(1-p)/n) =		0.0311
sample proportion p̂ = x/n=		0.2385
test stat z =(p̂-p)/√(p(1-p)/n)=		-2.01

5)

p value                          =

0.0222