Question

Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the transactions to be sure they were processed properly. a) Propose a sampling strategy for the supervisor. b) How would you modify that strategy if the company makes both wholesale and retail sales, requiring different bookkeeping procedures?

Short answer

a) Use simple random sampling. b) Use stratified sampling by distinguishing wholesale and retail sales.

Step-by-step solution

Understand the Problem

The goal is to select a sample of 10 transactions from 120 processed orders to ensure accuracy. We need a sampling strategy that represents the population adequately.

Propose a Sampling Strategy for Part a

For part a, a simple random sampling method can be used. Assign each transaction a unique number from 1 to 120. Use a random number generator to select 10 distinct numbers from this range. These numbers correspond to the transactions that the supervisor will recheck.

Recognize the Need for Different Sampling Strategy for Part b

In part b, we consider that the company has both wholesale and retail sales, each needing different bookkeeping procedures. Therefore, the sample should reflect both transaction types.

Propose a Stratified Sampling Strategy for Part b

To account for both types of sales, use stratified sampling. First, divide transactions into two groups: wholesale and retail. Next, determine the proportion of each type in the day's transactions. Sample 10 transactions relative to these proportions, ensuring both categories are represented.

Key concepts

Simple Random Sampling

Simple Random Sampling (SRS) is a fundamental method of collecting a sample from a larger set, known as the population, where each member of the population has an equal chance of being selected. This method is straightforward and ensures that every possible sample has the same probability of being chosen. For example, if a supervisor wants to review 10 transactions out of 120 processed orders, assigning a unique number to each transaction and using a random number generator would be an effective approach. This randomness helps ensure that the sample is free from bias and reflects the diversity within the entire group.

When using SRS, it's important to ensure that the selection process is truly random. This might involve using a computer tool or random number table to pick your sample. The simplicity of the method doesn't require stratification or categorization, which is both its strength and limitation. While randomness is key, particular patterns or important sub-groups within the data may not be adequately represented.

Stratified Sampling

Stratified Sampling is a technique that involves dividing a population into subgroups, or "strata," that share similar characteristics. This method is particularly useful when a population is not homogeneous and consists of distinct segments. Each stratum is then sampled independently. If a company processes both wholesale and retail sales, stratifying these would ensure that both types of transactions are adequately represented in the sample.

To implement stratified sampling, start by categorizing the transactions into wholesale and retail groups. Determine the proportion of each category within the total transactions. Then, select samples from each group according to these proportions. For instance, if there are 80 retail transactions and 40 wholesale ones, you might choose to sample 7 from retail and 3 from wholesale to maintain the ratio in your 10-sample review. This approach allows for a more detailed and representative sample, reflecting the underlying distribution of the whole population.

Audit Sampling

Audit Sampling is a method used to draw conclusions about a set of financial transactions by examining a subset of those transactions. This is an essential part of financial auditing used to ensure accuracy within a company’s records. The goal is to identify errors or discrepancies without reviewing every transaction, which can be time-consuming.

In a situation where 10 out of 120 transactions are checked, this can help provide insights into the processing accuracy of those transactions. The sampling method chosen should aim to minimize risk and increase audit efficiency. Methods like simple random sampling or stratified sampling could be deployed depending on the requirement of the audit. By focusing on selected transactions, auditors can make informed judgments about the financial health of a company without needing to review every transaction.

Transaction Validation

Transaction Validation is a crucial process in auditing and accounting that ensures all transactions are complete, accurate, and properly authorized. This process helps maintain the integrity of financial statements by verifying that each transaction has been executed in accordance with the company policies and procedures.

During an audit, sampled transactions are typically subjected to validation. This might involve checking the correctness of amounts, verifying supporting documents, and ensuring the necessary approvals are in place. Proper validation helps in identifying errors or fraud at an early stage. When employing sampling methods like simple random or stratified sampling, transaction validation efforts are focused and strategically targeted, offering a balance between thoroughness and efficiency.

Ensuring validated transactions maintain the credibility of the financial reporting process, which is essential for internal decision-making and external financial credibility.