Match each of the following flawed arguments to the abstract description that most accurately identifies its reasoning error concerning percentages and absolute numbers.
- Bicycle thefts accounted for 15% of all reported property crimes in the city this year, up from 5% a decade ago. Therefore, there are more bicycle thefts now than there were ten years ago.Takes an increase in a relative proportion to be sufficient evidence that an absolute quantity has grown.
- Hospital Alpha treated 400 patients for respiratory illness this month, while Hospital Beta treated only 80. Thus, a patient at Hospital Alpha is more likely to be treated for a respiratory illness than a patient at Hospital Beta.Infers a higher comparative rate based solely on a larger absolute number.
- Zeta Tech's share of the global smartphone market fell from 30% to 20% over the last three years. This shows that Zeta Tech is manufacturing fewer smartphones than it did three years ago.Presumes, without providing justification, that a decrease in a share of a whole must correspond to a decrease in absolute numbers.
- The city's public library received a record 10,000 new book donations this year. Consequently, donated books must represent a larger percentage of the library's total acquisitions this year than in previous years.Concludes that a relative proportion has grown merely because the absolute amount has reached a record high.
Answer
The bicycle theft argument pairs with the proportion-to-quantity increase flaw; the hospital argument pairs with the quantity-to-rate flaw; the smartphone argument pairs with the share-to-quantity decrease flaw; the library argument pairs with the quantity-to-proportion increase flaw.
Each argument represents one of four directional variations of the percentage vs. number flaw. By precisely identifying whether the premise offers absolute data or proportional data, and whether the conclusion claims an absolute result or a proportional result, you can map each argument to its abstract description.
Step-by-Step Solution
Key Concept
Percentages vs. Numbers Flaws
Estimated Time:1m 30s