Problem:
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.
Probability Proportional to Size (PPS) Sampling Tables
Table 1: 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 2: 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
|