Analyze the four brief arguments below. Pair each argument with the abstract description that best characterizes its flaw in reasoning regarding numerical or proportional evidence.
- Ten years ago, 5% of patients discharged from Valley Hospital were readmitted within a month. This year, the readmission rate is 8%. Therefore, Valley Hospital is readmitting more patients this year than it did a decade ago.Infers an increase in absolute numbers solely from an increase in a percentage, ignoring a potential change in the total baseline population.
- Last year, the state recorded 400 fires in electric vehicles and over 10,000 fires in gas-powered cars. Clearly, any given electric vehicle is far less likely to catch fire than a gas-powered car.Inappropriately concludes a lower probability of an event based solely on a smaller raw number of occurrences, failing to account for disparities in group sizes.
- In 2015, popcorn accounted for 60% of snack bar revenues at the cinema. Today, popcorn accounts for only 40% of snack revenues. Thus, the cinema's total sales volume of popcorn must have declined since 2015.Presumes, without providing justification, that a decline in a proportion guarantees a decline in the absolute quantity.
- Since introducing the new pest-resistant seeds, the total number of crops lost to insects in the region has doubled. This proves the new seeds are less effective at preventing insect damage per acre planted than the previous seeds.Derives a claim about a proportional rate of failure based entirely on an increase in an absolute number, overlooking a potential increase in overall volume.
Answer
The correct pairings match the specific numerical or proportional shift in each argument to its abstract logical flaw description.
Each correct pairing accurately identifies whether the specific argument is flawed by improperly moving from a percentage to a raw number (as seen in the Hospital and Cinema arguments) or by improperly moving from a raw number to a percentage/rate (as seen in the Electric Vehicles and Farming arguments).
Step-by-Step Solution
Key Concept
Percentages vs. Numbers Flaws
Estimated Time:2m 0s