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Auditing sampling methods. Traditionally, auditors have
Chapter 6, Problem 89E(choose chapter or problem)
Auditing sampling methods. Traditionally, auditors have relied to a great extent on sampling techniques, rather than 100% audits, to help them test and evaluate the financial records of a client firm. When sampling is used to obtain an estimate of the total dollar value of an account—the account balance—the examination is known as a substantive test (Audit Sampling—AICPA Audit Guide, 2012). In order to evaluate the reasonableness of a firm’s stated total value of its parts inventory, an auditor randomly samples 100 of the total of 500 parts in stock, prices each part, and reports the results shown in the next table.
a. Give a point estimate of the mean value of the parts inventory.
b. Find the estimated standard error of the point estimate of part a.
c. Construct an approximate 95% confidence interval for the mean value of the parts inventory.
d. The firm reported a mean parts inventory value of $300. What does your confidence interval of part c suggest about the reasonableness of the firm’s reported figure? Explain.
Questions & Answers
QUESTION:
Auditing sampling methods. Traditionally, auditors have relied to a great extent on sampling techniques, rather than 100% audits, to help them test and evaluate the financial records of a client firm. When sampling is used to obtain an estimate of the total dollar value of an account—the account balance—the examination is known as a substantive test (Audit Sampling—AICPA Audit Guide, 2012). In order to evaluate the reasonableness of a firm’s stated total value of its parts inventory, an auditor randomly samples 100 of the total of 500 parts in stock, prices each part, and reports the results shown in the next table.
a. Give a point estimate of the mean value of the parts inventory.
b. Find the estimated standard error of the point estimate of part a.
c. Construct an approximate 95% confidence interval for the mean value of the parts inventory.
d. The firm reported a mean parts inventory value of $300. What does your confidence interval of part c suggest about the reasonableness of the firm’s reported figure? Explain.
ANSWER:Solution :
Step 1 of 4:
Given the total number of parts is N.
We know that N = 500.
Then the sample size n=100.
The table is given below.
Part Number |
Part Price |
Sample |
2 |
108 |
3 |
101 |
55 |
2 |
832 |
500 |
1 |
77 |
73 |
10 |
688 |
300 |
1 |
910 |
54 |
4 |
839 |
92 |
6 |
121 |
833 |
5 |
271 |
50 |
9 |
399 |
125 |
12 |
761 |
1000 |
2 |
93 |
62 |
8 |
505 |
205 |
7 |
597 |
88 |
11 |
830 |
100 |
19 |
Our goal is:
a). We need to find a point estimate of the mean value of the parts inventory.
b). We need to find the estimated standard error of the point estimate of parts (a).
c). We need to construct an approximately 95% confident interval for the mean value of the parts inventory.
d). We need to write what does your confidence interval of part (c) suggest about the reasonableness of the firm’s reported figure and explain.
a). Now we have to find a point estimate of the mean value of the parts inventory.
Now we need to find calculate the sample mean.
The formula of the sample mean is
We know that n=100.
156.46
Therefore, the point estimate of the mean value of the parts inventory is 156.46