Last year, the total number of traffic accidents in the city of Oakhaven increased by 15 percent compared to the previous year. However, the mayor of Oakhaven accurately claimed during a press conference that the city's traffic accident rate—measured as the number of accidents per 10,000 residents—actually decreased over the same period.
Which one of the following, if true, most helps to resolve the apparent discrepancy described above?
- Oakhaven experienced a massive influx of new residents over the past year, increasing its total population by 30 percent.Answer
- BA new safe-driving initiative caused a significant drop in the number of accidents caused by speeding.
- CSevere winter weather conditions last year made driving in Oakhaven much more dangerous than in the previous year.
- DThe neighboring city of Mapleton saw a decrease in both its total number of traffic accidents and its accident rate.
- EThe percentage of Oakhaven residents who own cars remained exactly the same as the previous year.
Answer
The statement that Oakhaven's total population increased by 30 percent.
The correct answer perfectly resolves the paradox by manipulating the denominator of the rate equation. A rate per 10,000 residents is calculated by dividing total accidents by the population. If the total number of accidents goes up by 15 percent, the only mathematical way for the rate to go down is if the population (the denominator) grows by an even larger percentage. An influx of residents increasing the population by 30 percent mathematically guarantees that the per-capita rate drops despite the absolute number of accidents rising.
Step-by-Step Solution
Key Concept
Understanding the difference between absolute numbers (totals) and proportions/rates, specifically how changes in a population denominator affect a per-capita rate.