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Difficulty: HardBridging Conflicting Premises

A regional hospital implemented a strict new triage protocol to reduce the burden on its emergency department. The protocol successfully redirects all patients with minor, non-critical injuries to an affiliated urgent care facility. A year after implementation, an internal audit confirmed that the emergency department had not treated a single non-critical patient. Nevertheless, the audit also revealed that the average cost of treatment per patient in the emergency department had risen by 35 percent compared to the year before the protocol was introduced.

Statement: The apparent discrepancy is successfully resolved if it is true that by removing the large volume of inexpensive, non-critical cases from the emergency department, the only cases remaining to be averaged were severe traumas and complex emergencies, which inherently require the most expensive medical interventions.

Answer: Answer

Answer

True. The statement successfully resolves the paradox by explaining how removing low-cost cases increases the average cost of the remaining patient pool.
The correct answer is True. The statement successfully bridges the conflicting premises by highlighting a shift in the composition of the patient population. The original average cost was a blend of many inexpensive treatments (minor injuries) and some expensive treatments (severe traumas). By effectively removing all the inexpensive treatments from the emergency department, the hospital ensured that the new average would be calculated exclusively from the highly expensive cases. This mathematical reality perfectly explains how the average cost per patient could rise by 35 percent even though the protocol worked exactly as intended.

Step-by-Step Solution

1
Analyze the conflicting premises presented in the scenario.
The hospital successfully eliminated minor, low-cost injuries from the emergency department, yet the average cost per patient treated there increased by 35 percent.
Understanding the exact nature of the discrepancy is required before evaluating potential resolutions.
2
Evaluate the mechanism proposed in the statement.
The statement suggests that the increase in average cost is a direct mathematical result of removing inexpensive cases, leaving only the most expensive, severe traumas to be calculated in the new average.
We must determine if this new information logically allows both original premises to coexist without contradicting either one.
3
Apply logical and statistical reasoning to the proposed mechanism.
If the lowest values (inexpensive cases) are removed from a dataset, the average of the remaining values (expensive cases) will inevitably be higher than the original combined average.
This confirms that the proposed mechanism perfectly explains the surprising statistical outcome.

Key Concept

Resolving Statistical Paradoxes Involving Averages

Alternative Method

You can verify the logic by substituting hypothetical numbers: Assume 100 minor cases cost 100each,and10severecasescost100 each, and 10 severe cases cost 10,000 each. The original average is 110,000/110patients=110,000 / 110 patients = 1,000 per patient. If the protocol removes all 100 minor cases, the new average is 100,000/10patients=100,000 / 10 patients = 10,000 per patient. The average increased drastically simply by removing the low-cost cases.
Estimated Time:1m 30s
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Bridging Conflicting Premises

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