Use the following company data and the PPS Sampling Tables 1 & 2:
• The recorded book value of these accounts is $3,460,000.
• The company has a tolerable error of $63,460.
• The anticipated error is $13,000.
• The risk of incorrect acceptance is 5%.
• The acceptable number of overstatements of misstatements is 2.
Use probability proportional to size (PPS) sampling to do the following:
A. Determine the reliability factor.
B. Determine the correct expansion factor.
C. Determine the sample size you should use.
D. Determine the sampling interval you should use.
Table: Reliability Factors for Misstatements of Overstatement
|
Number of Overstatement Misstatements
|
Risk of Incorrect Acceptance
|
|
1%
|
5%
|
10%
|
15%
|
20%
|
25%
|
30%
|
37%
|
50%
|
|
0*
|
4.61
|
3.00
|
2.31
|
1.90
|
1.61
|
1.39
|
1.21
|
1.00
|
0.70
|
|
1
|
6.64
|
4.75
|
3.89
|
3.38
|
3.00
|
2.70
|
2.44
|
2.14
|
1.68
|
|
2
|
8.41
|
6.30
|
5.33
|
4.72
|
4.28
|
3.93
|
3.62
|
3.25
|
2.68
|
|
3
|
10.05
|
7.76
|
6.69
|
6.02
|
5.52
|
5.11
|
4.77
|
4.34
|
3.68
|
|
4
|
11.61
|
9.16
|
8.00
|
7.27
|
6.73
|
6.28
|
5.90
|
5.43
|
4.68
|
|
5
|
13.11
|
10.52
|
9.28
|
8.50
|
7.91
|
7.43
|
7.01
|
6.49
|
5.68
|
|
6
|
14.57
|
11.85
|
10.54
|
9.71
|
9.08
|
8.56
|
8.12
|
7.56
|
6.67
|
|
7
|
16.00
|
13.15
|
11.78
|
10.90
|
10.24
|
9.69
|
9.21
|
8.63
|
7.67
|
|
8
|
17.41
|
14.44
|
13.00
|
12.08
|
11.38
|
10.81
|
10.31
|
9.68
|
8.67
|
|
9
|
18.79
|
15.71
|
14.21
|
13.25
|
12.52
|
11.92
|
11.39
|
10.74
|
9.67
|
|
10
|
20.15
|
16.97
|
15.41
|
14.42
|
13.66
|
13.02
|
12.47
|
11.79
|
10.67
|
|
*The 0 row is always used for the reliability factor in the sample size formula and for basic precision.
|
From the American Institute of Certified Public Accountants: Auditing Practice Release, Audit Sampling, 1999 (as cited in Whittington & Pany, 2006)
Table: Expansion Factors for Expected Misstatement
|
|
Risk of Incorrect Acceptance
|
|
1%
|
5%
|
10%
|
15%
|
20%
|
25%
|
30%
|
37%
|
50%
|
|
Factor
|
1.9
|
1.6
|
1.5
|
1.4
|
1.3
|
1.25
|
1.2
|
1.15
|
1.0
|