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1 A histogram of the average withdrawal amounts made daily

1. A histogram of the average withdrawal amounts made daily over the span of a month should cluster around $50.

2. A histogram of the daily standard deviations of the withdrawal amounts over the span of a month should cluster around $40.

3. It would be surprising to discover a transaction for more than $100.

4. The monitoring system will have a higher chance of detecting a change in transaction behavior if the control limits in the X-bar chart are moved closer to $50.

5. If the daily average withdrawal exceeds the upper control limit in the X-bar chart, then the procedure has committed a Type I error.

6. An upcoming holiday weekend increases the size of most withdrawals. If the average on such a day remains inside the control limits, then a Type I error has occurred.

7. By sampling 200 transactions daily, auditors can move the control limits in the X-bar chart closer to $50 without increasing the chance of a Type I error.

8. Control limits in an X-bar chart at $50 {3 × 40 > 1n based on samples of size n = 100 are more likely to produce a Type I error than control limits at $50 {3 × 40 / √n based on samples of size n = 200.

Auditors at a bank randomly sample 100 withdrawal transactions made at ATM machines each day and use video records to verify that authorized users of the accounts made the transactions. The system records the amounts withdrawn. The average withdrawal is typically $50 with SD $40. Deposits are handled separately.

2. A histogram of the daily standard deviations of the withdrawal amounts over the span of a month should cluster around $40.

3. It would be surprising to discover a transaction for more than $100.

4. The monitoring system will have a higher chance of detecting a change in transaction behavior if the control limits in the X-bar chart are moved closer to $50.

5. If the daily average withdrawal exceeds the upper control limit in the X-bar chart, then the procedure has committed a Type I error.

6. An upcoming holiday weekend increases the size of most withdrawals. If the average on such a day remains inside the control limits, then a Type I error has occurred.

7. By sampling 200 transactions daily, auditors can move the control limits in the X-bar chart closer to $50 without increasing the chance of a Type I error.

8. Control limits in an X-bar chart at $50 {3 × 40 > 1n based on samples of size n = 100 are more likely to produce a Type I error than control limits at $50 {3 × 40 / √n based on samples of size n = 200.

Auditors at a bank randomly sample 100 withdrawal transactions made at ATM machines each day and use video records to verify that authorized users of the accounts made the transactions. The system records the amounts withdrawn. The average withdrawal is typically $50 with SD $40. Deposits are handled separately.

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