Match each statistical paradox scenario with the statement that most effectively resolves its apparent discrepancy.
- A renowned medical center reported that its overall patient survival rate improved this year compared to last year. Paradoxically, the survival rate within every individual ward of the medical center was actually lower this year than it was last year.This year, the medical center treated a vastly larger proportion of patients with minor ailments in its low-risk wards, and a much smaller proportion of patients in its high-risk intensive care wards.
- During the past five years, the total annual number of reported bicycle thefts in the city of Belmont has doubled. Nevertheless, local law enforcement accurately claims that the risk of a bicycle being stolen in Belmont is lower now than it was five years ago.The number of bicycles owned and actively ridden by Belmont residents has more than tripled over the past five years due to a massive expansion of the city's bike-lane network.
- A recent study found that adults who regularly take dietary supplements designed to boost immune function catch colds more frequently than adults who never take such supplements. Yet, immunologists maintain that these supplements actively help prevent colds.Individuals who have naturally weaker immune systems and are inherently more prone to catching colds are significantly more likely to purchase and take immune-boosting supplements.
- Data reveals that over 80 percent of fatal traffic accidents occur in clear weather conditions, while fewer than 20 percent occur during heavy precipitation. However, safety experts continue to warn that driving in heavy precipitation is statistically far more dangerous.The vast majority of total driving hours are logged during clear weather, meaning the accident rate per mile driven is actually much higher during heavy precipitation.
Answer
The correct pairings resolve each paradox by addressing its specific statistical mechanism: shifting subgroup weights for the hospital wards, expanding denominator sizes for bicycle thefts, self-selection bias for immune supplements, and differing base rates of exposure for driving conditions.
Each correct pair links a surface-level statistical contradiction with the hidden variable that mathematically resolves it: shifting subgroup weights, expanding denominator sizes, biased sample selection, and differing base rates of exposure.
Step-by-Step Solution
Key Concept
Resolving Statistical and Proportional Paradoxes
Estimated Time:2m 30s