To determine the projected misstatement for the population using ratio estimation, the following calculation can be used:
Projected Misstatement=(Sample MisstatementSample Book Value)
×Population Book ValueProjected Misstatement=(Sample Book ValueSample Misstatement)
×Population Book Value
Given:
* Sample Misstatement = $420,000
* Sample Book Value = $12,000,000
* Population Book Value = $20,000,000
Projected Misstatement=(420,00012,000,000)×20,000,000Projected Misstatement=(12,000,000420,000)×20,
000,000
Projected Misstatement=0.035×20,000,000=700,000Projected Misstatement=0.035×20,000,000=700,000 Therefore, the projected misstatement is $700,000.
IIA Standards: 2320 - Analysis and Evaluation
IIA Practice Guide: Statistical Sampling

According to the IIA guidance, reviewing and approving payroll timesheets by the timekeeper before processing is considered least effective in managing the risk of payroll fraud. While this procedure might detect some errors or irregularities, it does not provide a robust control against fraud because the timekeeper can collude with employees or fail to review timesheets adequately. On the other hand, procedures such as comparing payroll lists to personnel records, deactivating payroll database access upon termination, and validating changes to payroll by the personnel department involve checks and balances that are more effective at preventing or detecting fraudulent activities.
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IIA Practice Guide: Managing the Business Risk of Fraud: A Practical Guide IIA Standards and Guidance: IPPF - Practice Guide

Detective controls are designed to identify and detect errors or fraud after they have occurred. Receipts for employee expenses serve as a detective control by providing evidence of transactions, enabling verification and review of expenses to identify any fraudulent or unauthorized activities. Awareness of prior incidents of fraud (Option A) is more of a preventive control, contractor non-disclosure agreements (Option B) are preventive controls to mitigate risks of information leakage, and verification of currency exchange rates (Option C) is more of a transaction control. Reference: IIA Glossary - Detective Controls, COSO Framework