## #13 - A recent study of 10,000 people who were involved in

rachue
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Hi there,

I'm having trouble understanding why D is solid here. I didn't like any of the other ACs so process of elimination brought me to it, but still, I want to understand why it's completely correct.

I know it has to be something with how the stimulus doesn't specify the total number of small and large cars involved in the study. The problem I have with D is that it only says that large cars are more likely to have accidents, but that doesn't necessarily mean that people won't get injured. What if larger cars have better airbags, seat belts, etc?
Steve Stein
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Let's start by focusing on the author's conclusion, which is that you are more likely to be injured in a small car than in a large car, based on a study that showed a smaller percentage of injuries among large car accident victims.

Since the stimulus is followed by a weaken question, the correct answer choice will be the one that calls into question the author's conclusion--the choice that will either suggest that people in smaller cars are better off (or that people in larger cars are worse off) than we might have thought.

Correct answer choice D provides this weakener: if large cars are more likely to be involved in an accident to begin with, then this weakens the conclusion that you'd be better off in a larger car--because even if injury is less likely for each accident, it appears that large car drivers experience more accidents overall. This doesn't completely crush the author's conclusion, but it does weaken the claim that people in big cars are safer overall.

Let me know if that makes sense--this can be a pretty tricky question.
Steve Stein
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cpassaro
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Can you please explain December 2009 LR sec. 2 Q 13 (car accidents)?

Thanks
Steve Stein
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Good question. Let's start by focusing on the author's conclusion, which is that you are more likely to be injured in a small car than in a large car, based on a study that showed a smaller percentage of injuries among large car accident victims.

Since the stimulus is followed by a weaken question, the correct answer choice will be the one that calls into question the author's conclusion--the choice that will either suggest that people in smaller cars are better off (or that people in larger cars are worse off) than we might have thought.

Correct answer choice D provides this weakener: if large cars are more likely to be involved in an accident to begin with, then this weakens the conclusion that you'd be better off in a larger car--because even if injury is less likely for each accident, it appears that large car drivers experience more accidents overall. This doesn't completely crush the author's conclusion, but it does weaken the claim that people in big cars are safer overall.

Let me know if that makes sense--this can be a pretty tricky question--thanks!

~Steve
Steve Stein
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cpassaro
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Thanks, that helps, but I guess I don't understand how D does more to weaken the conclusion than A? The conclusion is describing not just accidents, but injuries from accidents. It would seem to me that A - which describes how the study could have been skewed, would be the stronger answer?
Steve Stein
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Thanks for your response--this is a tricky question, in part because the author is discussing injuries following an accident.. Once an accident has occurred, the people in the small cars are more likely to be injured...

--but that doesn't mean that a small car injury is more likely in general than a large car injury.

This is tricky stuff! Perhaps an analogous argument might make the point more clearly:

A recent study of people involved in accidents found that a small percentage of those in car accidents were seriously injured, but a large percentage of those in airplane crashes were seriously injured. That shows that one is less likely to be seriously injured in a car accident than in a plane crash.

The correct answer choice D, in this case, would say that a car is far more likely to be involved in an accident than a plane. This would weaken the author's conclusion that one is more likely to suffer serious injury from a plane crash than from a car accident.

...again, once the accident happens, the plane makes injury more likely. But thankfully plane crashes are very rare, so as we know, you are much more likely to suffer serious injury in a car than in a plane.

I hope that's helpful--some of this stuff can be very challenging--some of the numbers and percentage questions in particular. Please let me know whether this clears that one up--thanks!

~Steve
Steve Stein
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cpassaro
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I think that helps...I just need to read more carefully. Thank you.
voodoochild
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Experts,
I went through this question and thought that D is an awesome strengthener. I didn't like A,B,C and E because of such bad answer choices.

Here's my reasoning why D could be a strengthener and a weakener. I realized about the weakening after a few hours.

Let's say L = probability that a large car is in accident; S = probability that a small car is in accident.

Now, let's say that the probability that a large car driver gets injured = Dl and the probability that a small car drivers gets injured = Ds

Given - D) L> S. Let L= 50% and S = 10%.
PRemise - low percentage of large car drivers get injured in an accident. Let Dl = 1%
PRemise - High percentage of small car drivers get injured in an accident. Let Ds = 90%

Thus L*Dl = .5 * .01 = .005
S*Ds = .01 * .9 = .009

Thus, D strengthens -- this is what my brain thought. Hence, I really struggled with this question.

On the other hand, if I choose other numbers, D could also weaken.

2 questions on this one:-
Question #1- How do I know, on such questions, whether a given answer is a strengthener or a weakener. It would be really difficult considering we have only 1:30 minutes (approx)

Question #2 - How do I write the conclusion of this question in a numerator/denominator form? I had a hard time decoding the conclusion in terms of "X/ Y is less likely than A / B." I am not sure exactly what "more likely" means and how it could be calculated, if I am asked to find such "likelihood."

Here are my thoughts about forming the conclusion. (I spent around 2 days on this problem. Still, I am not able to make any progress. )
Option 1
---( # of people driving large cars injured in an accident/ total number of people driving ALL cars) < (# of people driving small cars injured in an accident / total number of people driving ALL cars)
Option 2
---- ( # of people driving large cars injured in an accident/ total number of people driving large cars who met with an accident) < # of people driving smalls cars injured in an accident/ total number of people driving small cars who met with an accident)

Option 3
----- ( # of people driving large cars injured in an accident/10000) < ( # of people driving small cars injured in an accident/10000)

I was really lost. It will be great if you could provide a justification for why an option is actually possible or correct.

Any thoughts? On a side note, I liked this problem because it really gave a hard time to my nervous tissue.

Thanks
Nikki Siclunov
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Hey Voodoo,

I'm afraid you are over-thinking this problem, and, at the same time, not reading the stimulus carefully enough. I think the latter problem is causing the former, but then again I could be mistaken.

Here's how you should approach this question: the author concludes that large car drivers have a lower risk of injury than small car drivers. This is based on the premise that a relatively low percentage of large car drivers were injured at the time of their accident. This argument omits to take into account a crucial element: how likely is it that a given car (large or small) gets into an accident in the first place? If the likelihood were exactly the same, then the conclusion makes sense: indeed, large car drivers would have a lower risk of injury than small car drivers. Inversely, if large car drivers are generally more accident-prone than small car drivers are, then their overall risk of injury may be higher, even if comparatively fewer of them are injured once the accident occurs.

To put this in numerical terms, the study shows that the following ratio favors large car drivers:

#injuries
-----------
#accidents

The author takes that to mean that the following ratio also favors large car drivers:

#injuries
------------
#drivers

This is clearly a mistake, because the following ratio is unknown for each car type:

#accidents
------------
#drivers

Does this make sense? Let me know.
Nikki Siclunov
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voodoochild
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Hello Nikki,
Thanks for your reply. I have a math background and that's why I am asking these questions.

Nikki Siclunov wrote:Hey Voodoo,

the author concludes that large car drivers have a lower risk of injury than small car drivers.

How would you calculate this? I have provided three options above. I am not sure about the correct one.

Nikki Siclunov wrote: This is based on the premise that a relatively low percentage of large car drivers were injured at the time of their accident. This argument omits to take into account a crucial element: how likely is it that a given car (large or small) gets into an accident in the first place? If the likelihood were exactly the same, then the conclusion makes sense: indeed, large car drivers would have a lower risk of injury than small car drivers. Inversely, if large car drivers are generally more accident-prone than small car drivers are, then their overall risk of injury may be higher, even if comparatively fewer of them are injured once the accident occurs.

The bolded portion is factually incorrect, in my opinion, because of two reasons. (I could be wrong -- or I could have misunderstood the statements. Please help me.)
Reason#1 (I have already given numbers in my post above) Let's use our intuition for this. (I have given numbers in my post above) For instance, let's say that SUVs have a higher probability of accidents than say Corollas. (assume)
Now, if I am told that SUVs, on the other hand, also have the lowest probability of getting injured, that's awesome! Why? Because there is a good chance that I won't get injured at all! On the other hand, even though Corolla has lower probability of meeting an accident, but the chances of getting injured are high.....this is extremely bad. This definitely strengthens the argument.

Reason #2 - The author doesn't talk about "fewer of them are injured" -- but probabilities.

I also need to understand how one can calculate such probabilities. The author hasn't made a clear statement explaining what is the probability he is trying to calculate. "A high probability of meeting an accident" means nothing. It's a nonsensical statement. One has to define the denominator ...is it drivers, cars, small cars, large cars, vehicles....I simply cannot understand this.