Chapter 9, Problem 30QRA

a.

To determine

Suggest the type of sampling plan that should be considered by the auditor in the given case.

Explanation of Solution

Attributes sampling:

Attributes sampling helps the auditor to assess a specific rate of (deviation rate) occurrence for a specific characteristic of the audit population. It is helpful in finding the estimate related to a particular transaction or activity in the system.

Suggest the type of sampling plan that should be considered by the auditor in the given case:

The auditor should use attributes sampling that should be considered by the auditor in the given case.

In the given case, the auditor has a test of control for the sales order approvals. Attributes sampling is an ideal technique for the given purpose because attributes sampling assess the deviation rate for a specific characteristic. Sales order approvals is a specific characteristic. 

Thus, the auditor should opt the attribute sampling.

b.

To determine

Calculate the required sample size using the appropriate table or formula.

Explanation of Solution

Sample size:

The sample size is the portion of the total population that represent the total population. The auditor conducts sampling test on the selected sample. Large sample size would represent the population more accurately but considering a large sample size would be a complex and expensive process. The auditor should select the sample size that would represent the entire population precisely and accurately.

Calculate the required sample size using the appropriate table or formula:

The required sample size can be calculated with the help of the table provided in figure 9.4 of the chapter.

Statistical Sample Sizes for Tests of Controls at 5 Percent Risk of Assessing Control Risk Too Low (with Allowable Number of Deviations in Parentheses) shows the required sample size of 77 units at the tolerable deviation rate of 8 percent and anticipated deviation of 2%.

Thus, the required level of sample size is 77 units.

c.

To determine

Comment whether CPAs should conclude with a 5 percent risk of assessing control risk too low that the population deviation rate does not exceed the tolerable rate of 8 percent.

Explanation of Solution

Expected population deviation rate:

Expected population deviation rate is the estimated failure rate of control in the population. This prediction is done by the auditor. The estimation is based on the results of the primary sampling, last year’s sample testing, inquiry by the client and process observation. It is required to determine the level of sample size needed in the audit sampling process.

Comment whether CPAs should conclude with a 5 percent risk of assessing control risk too low that the population deviation rate does not exceed the tolerable rate of 8 percent:

No, the given statement is not correct. The CPAs should not conclude with the allowable deviation of 4.

The allowable deviation is 2 as described in the table Statistical Sample Sizes for Tests of Controls at 5 Percent Risk of Assessing Control Risk Too Low (with Allowable Number of Deviations in Parentheses of figure 9.4.

Figure 9.5 shows the Statistical Sampling Results Evaluation Table for Tests of Controls: Achieved Upper Deviation Rate at 5 Percent Risk of Assessing Control Risk Too Low table. This table can be used to calculate the upper limit at a deviation of 4. Which is 11.8. It states that the deviation can go up to 11.8%.

Thus, the allowable deviation should be 2.

d.

To determine

Use ACL to compute the required sample size for the test where the population size consists of 10,000 items.

Explanation of Solution

Sample size:

The sample size is the portion of the total population that represents the total population. The auditor conducts sampling test on the selected sample. Large sample size would represent the population more accurately but considering a large sample size would be a complex and expensive process. The auditor should select the sample size that would represent the entire population precisely and accurately.

Expected population deviation rate:

Expected population deviation rate is the estimated failure rate of control in the population. This prediction is done by the auditor. The estimation is based on the results of the primary sampling, last year’s sample testing, inquiry by the client and process observation. It is required to determine the level of sample size needed in the audit sampling process.

Compute the required sample size for the test:

Input in ACL software:

$\begin{array}{c}Population=10,000\\ Confidence=95\%\\ \mathrm{Pr}ecision=8.00\%\\ Errorrate=2.00\end{array}$

Output in ACL software:

$\begin{array}{c}Samplesize=79\\ Intervalsize=1,265.82\\ Numberoftolerableerrors=2\end{array}$

Thus, the required sample size for the test where the population size consists of 10,000 items is 79.

e.

To determine

Explain whether the CPAs can conclude with a 5 percent risk of assessing control risk too low that the population deviation rate does not exceed the tolerable rate of 8 percent.

Explanation of Solution

Control risk:

Inherent risk is a risk of misstatement of the financial statements due to the factors the failure of internal control. Company establishes an internal control department to detect the misstatement in the financial statements of the company due to error or fraud. When the internal control of the company is not able to find out the mistaken then it is known as control risk because company has control effectiveness issues.

Explain whether the CPAs can conclude with a 5 percent risk of assessing control risk too low that the population deviation rate does not exceed the tolerable rate of 8 percent:

Input in ACL software for computing the deviations:

$\begin{array}{c}Samplesize=79\\ Confidence=95\%\\ Numberoferrors=4\end{array}$

Output in ACL software:

$Uppererror\lim it=11.59\%$

The CPAs can conclude with a 5 percent risk of assessing control risk too low that the population deviation rate does not exceed the tolerable rate of 11.59% percent and not 8%.