The following facts relative to a variables sampling plan are presented in random order: 1. Combined reliability

Question:

The following facts relative to a variables sampling plan are presented in random order:

1. Combined reliability is 95 percent.

2. Materiality is $\$ 80,000$.

3. Audited value of sample items is $\$ 371,250$.

4. The preliminary estimated population standard deviation is $\$ 200$.

5. Effectiveness of internal control and other audit procedures are judged to be 80 percent and 10 percent, respectively.

6. Population of accounts receivable is 4,000 .

7. Book value of accounts receivable is $\$ 2.65$ million.

8. Objective is to determine whether book value is fairly stated.

9. Alpha risk is 5 percent.

10. Planned precision is $\$ 61,540$ (rounded).

11. Sample size is 558 (rounded).

12. The estimated population standard deviation determined from the sample is $\$ 210$.

Required:

a. Reperform the steps up to and including the calculation of sample size.

b. What $\beta$ risk is implicit in the sample design?

c. Compute achieved precision. Is this consistent with the planned $\beta$ risk? If not, compute adjusted precision.

d. Is book value fairly stated?

e. Assume that instead of being $\$ 2.65$ million, the book value of accounts receivable is $\$ 2.75$ million. Would your conclusion differ from your answer to $d$ above? What course of action would you take?

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