Use the information below to answer Questions 1 and 2.

Use the information below to answer Questions 1 and 2.

Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way shown in the following table.

The owner of a small business would like to audit its account payable over the past year because of a suspicion of fraudulent activities. He suspects that one of his managers is issuing checks to non-existing vendors in order to pocket the money. There have been 790 checks written out to vendors by this manager. The leading digits of these checks are listed as follow:

1. Suppose you are hired as a forensic accountant by the owner of this small business, what statistical test would you employ to determine if there is fraud committed in the issuing of checks? What is the test statistic in this case?

1. What is the critical value for this test at the 5% significance level (95% confidence level)? Do the data provide sufficient evidence to conclude that there is fraud committed?

Hypothesis Test versus Confidence Interval – Questions 3 through 5

Random samples of size n1=55 and n2 = 65 were drawn from populations 1 and 2 , respectively. The samples yielded

Test Ho: (p1-p2) = 0 against Ha: (p1-p2) >0 using α = .05.

1. Perform a hypothesis test of p₁ = p₂with a 5% significance level (95% confidence level).

1. Obtain a 95% confidence interval estimate of p₁ - p₂.

1. Do you come up with the same conclusion for Question 19 and Question 20? Why or why not?

Hardness of Gem – Questions 22 and 23

 Listedbelow are measured hardnessindices from three different collections of gemstones.

You are also given that .

1. What is the test statistic?

1. Use a 5% significance level (95% confidence level) to test the claim that the different collections have the same mean hardness.

1. The probability that an individual egg in a carton of eggs is cracked is 0.03. You have picked out a carton of 1 dozen eggs (that’s 12 eggs) at the grocery store. Determine the probability that at most one of the eggs in the carton are cracked.

1. In a group lineup of 7 models in a commercial, 3 are male and 4 are female. In how many ways can you arrange 3 models in a lineup if the first and the third must be a male but the second one must be a female?