In a probability$-$proportional$-$to$-$size sample with a sampling interval of $$20,000,$ an auditor

discovered that a selected account receivable with a recorded amount of $$10,000$ had an audit

amount of $$2,000.$ Calculate the projected misstatement for this one item.

Chris York, CPA, is considering the use of probability$-$proportional$-$to$-$size sampling in examining

the sales transactions and accounts receivable of Carter Wholesale Company.

a$.$ How does the defi nition of the items in an accounts receivable population vary between

probability$-$proportional$-$to$-$size sampling and mean$-$per$-$unit sampling?

b$.$ Should a population of accounts receivable be stratifi ed by dollar value before applying

probability$-$proportional$-$to$-$size sampling procedures? Discuss.

The auditors of Dunbar Electronics want to limit the risk of material misstatement in the

valuation of inventories to $2$ percent. They believe that there exists a $50$ percent risk that

a material misstatement could have bypassed the client$$s internal control and that the

inherent risk of the account is $80$ percent. They also believe that the analytical procedures

performed to test the assertion have a $40$ percent risk of failing to detect a material

misstatement.

a$.$ Briefly discuss what is meant by audit risk, inherent risk, control risk, and the risk that

analytical procedures might fail to detect a material misstatement.

b$.$ Calculate the maximum allowable risk of incorrect acceptance for the substantive test of

details.

c$.$ What level of detection risk is implicit in this problem?