C.39.QR:5.3 - Obtain a warranted population claim and use it for the agreed decision

An audit lead is asked whether this month’s completed records meet an agreed criterion for commissioning a cause investigation. The criterion is a defect proportion above 5%, supported by a two-sided 95% confidence interval whose lower limit exceeds 5%. The commissioned decision concerns that population and criterion.

An analyst supplies a correct calculation: 40 defective inspections among 400, or 10%. Before returning it to the decision, the audit lead establishes what the inspected records represent. The register is reconciled with all completed records for the month. The selection log shows 400 independent uniform draws with replacement from that register. Every selected record was accessible. Inspectors applied the agreed defect definition, resolving ambiguous classifications against the records. In this constructed case these conditions are established; together they supply the sampling and measurement grounds that the ratio alone did not carry.

Each draw therefore has the same defect probability: the unknown fraction of defective records in the fixed target population. The analyst applies the Wilson interval for a binomial proportion. For 40 of 400, its nominal 95% interval is approximately 7.43%–13.33%. The returned population claim is an estimate with that qualification, supported by the selection process and measurement. The confidence qualification belongs to the statistical procedure’s repeated-sampling performance.

The audit lead then makes the second judgement. The agreed criterion compares the interval’s lower limit with 5%; 7.43% exceeds it. The owner receives the population, estimate, interval, sampling basis and criterion comparison, and commissions the investigation under the existing authority. The statistical result and the task’s decision rule have supplied different contributions to this completed answer.

Changing the decision rule would leave the population inference intact while changing its use for the task. For example, a rule requiring the same interval’s lower limit to exceed 8% would not authorize commissioning on this evidence: 7.43% is below that threshold. The estimate and interval would remain the same. Conversely, a selection log covering only one office would change the population inference itself and require a return to the sample design. The two returns have different objects and useful continuations. The established relation, the permissible inference and the receiving requirement determine which work to retain and which to reopen.