The recorded accounts receivable balance for Warner Company was $ 500,000 — each following independent sets conditions determine appropriate sample size examination MUS Based
General StudiesGeneralCase Study
The recorded accounts receivable balance for Warner Company was $ 500,000.
Required:
For each of the following independent sets of conditions, determine the appropriate sample size for the examination of Warner’s accounts receivable in MUS. Based on the differences in your calculations, identify the general relationship between different factors and sample size. (RIA 5 risk of incorrect acceptance, TM 5 tolerable misstatement, EM 5 expected misstatement).
a. RIA 5 5 percent, TM 5 $ 50,000, EM 5 $ 10,000.
b. RIA 5 5 percent, TM 5 $ 50,000, EM 5 $ 25,000.
c. RIA 5 10 percent, TM 5 $ 50,000, EM 5 $ 10,000.
d. RIA 5 10 percent, TM 5 $ 50,000, EM 5 $ 25,000.
SOLUTION
The following calculations use the MUS sample size table in Exhibit G.2:
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Ratio of expected to tolerable misstatement = Expected Misstatement ÷ Tolerable Misstatement
Scenarios (a) and (c): $10,000 ÷ $50,000 = 0.20
Scenarios (b) and (d): $25,000 ÷ $50,000 = 0.50
Tolerable misstatement as a percentage of population = Tolerable Misstatement ÷ Population
All scenarios: $50,000 ÷ $500,000 = 0.10
Scenario
RIA
EM TM
TM Population
Sample size
a.
0.05
0.20
0.10
47
b.
0.05
0.50
0.10
116
c.
0.10
0.20
0.10
35
d.
0.10
0.50
0.10
80
Scenarios (a) and (b) differ only with respect to expected misstatement. As the expected misstatement increases from $10,000 [scenario (a)] to $25,000 [scenario (b)], the sample size increases from 47 items to 116 items. Therefore, expected misstatement has a direct relationship with sample size.
Scenarios (a) and (c) differ only with respect to the risk of incorrect acceptance. As the risk of incorrect acceptance increases from 5 percent [scenario (a)] to 10 percent [scenario (c)], the sample size decreases from 47 items to 35 items. Therefore, the risk of incorrect acceptance has an inverse relationship with sample size.
Scenarios (b) and (d) differ only with respect to the risk of incorrect acceptance. As the risk of incorrect acceptance increases from 5 percent [scenario (b)] to 10 percent [scenario (d)], the sample size decreases from 116 items to 80 items. Therefore, the risk of incorrect acceptance has an inverse relationship with sample size.