Logical Reasoning

PT131 · S3 · Q13 A recent study of 10,000

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A recent study of 10,000 people who were involved in automobile accidents found that a low percentage of those driving large automobiles at the time of their accidents were injured, but a high percentage of those who were driving small automobiles at the time of their accidents were injured.

Conclusion

One is less likely to be injured in a car accident if driving a larger car.

Evidence

A study of 10,000 people who were in an accident found that a much lower percentage of large-car drivers were injured than small-car drivers.

Evaluation

Does this statistic show that drivers of larger cars are less likely to be injured in a car accident? Not quite. As always, with statistics, we have to be cautious about what it slice of the story it's giving us.

To support the claim the conclusion is making, we would want to look at 10,000 drivers and then find out what percentage of large-car drivers have ever been injured in an accident, and what percentage of small-car drivers have ever been injured in an accident.

This stat, meanwhile, looks at 10,000 people who were in an accident, and then finds out what percentage of large/small was injured.

To put it another way, the conclusion is about all drivers of large/small cars, regardless of whether they've been in an accident. The evidence is only about drivers who have been in an accident. The correct conclusion we could draw would be,

Goal

Find an answer pointing out the statistical flaw that we're only looking at a subset of drivers (those who have been in an accident) but concluding something about all drivers. Or find an objection that would help us argue the anti-conclusion, that small car drivers are less likely to be injured in an accident.

13.

Which one of the following, if true, most seriously weakens the argument?

  1. Most of the accidents analyzed

    Irrelevant Distinction Too Weak

    The best case we could make for this answer choice is that it sounds like the study data might be skewed, by dealing with a potentially unrepresentative slice of driving situations: areas with very high speed limits. But that's a very weak attack. If this answer isn't cheapening the data, then it's doing nothing to address the difference between driving a large / small car.

    10% picked this

  2. Most people who own small

    Too Weak / Irrelevant

    "On occasion" is a pretty giveaway that this is too weak to have any significant impact. Also, it doesn't really matter if large car drivers sometimes drive small cars or vice versa. The conclusion isn't about a type of driver. It's about which type of car is more/less likely to end up being in an injured driver situation.

    3% picked this

  3. Half of the study participants

    Out of Scope: "medium-sized cars"

    We might think we're wriggling our way out of some False Choice between large and small cars, but the author never acted like large and small are the only two choices. The author has noticed a significant statistical difference between large and small and is trying to make a comparative conclusion based on that difference. The only way information about very-small / medium / very-large cars would affect this conversation is if we also had their injury rate, so that we could judge whether there seemed to be a smooth continuum of "the larger the car, the lower the injury rate".

    10% picked this

  4. Correct

    A large automobile is far

    Why this is right

    We like strong language on Strengthen/Weaken/Paradox, so far more likely is instantly attractive. This answer affects how we judge the conclusion. Maybe the study revealed that 10% of large car drivers were injured in their accidents whereas 20% of small car drivers were injured in their accidents. If large cars are far more likely to be in an accident than small cars, then the probability of getting injured in an accident might still be higher for large car drivers. If you like probability math, keep reading: Say that 10% of large car drivers are injured in accidents while 20% of small car drivers are. But also add the idea that 60% of large car drivers will get into an accident, whereas only 25% of small car drivers will. Probability of being injured in large car: 60% * 10% = 6/10 * 1/10 = 6/100 = 6% Probability of being injured in small car: 25% * 20% = 1/4 * 1/5 = 1/20 = 5/100 = 5%

    Skill tested: Weaken · how this choice captures the argument's function is the move to repeat next time.

    71% picked this

  5. Only a small percentage of

    Relative VS. Absolute

    It doesn't matter that the overall likelihood of people getting injured is small, an absolute term. This argument is about whether a likelihood is smaller, a relative term.

    6% picked this

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