litesee - CR - test 2 Q 14

[stormier]

A recent survey of all auto accident victims in Dole County found that, of the severely injured drivers and front-seat passengers, 80 percent were not wearing seat belts at the time of their accidents. This indicates that, by wearing seat belts, drivers and front-seat passengers can greatly reduce their risk of being severely injured if they are in an auto accident.
The conclusion above is not properly drawn unless which of the following is true?


A Of all the drivers and front-seat passengers in the survey, more than 20 percent were wearing seat belts at the time of their accidents.
B Considerably more than 20 percent of drivers and front-seat passengers in Dole County always wear seat belts when traveling by car.
C More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured.
D More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.
E Most of the auto accidents reported to police in Dole County do not involve any serious injury.

Is there a mathematical way to the solution ?

[pradeepkaushal9518]

i think its knewton question

imo D

More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.

if it is true than the conclusion can be drawn that wearing seat belt can reduce the risk of severely injured

[fitzgerald23]

The important things to note:

1. This was a survey of all accident victims
2. 80% of severely injured victims did not wear seat belts in the front seat
3. By wearing seat belts they can avoid serious injury

They basically want to know the assumption made in order for point 3 to be true. In order for 3 to be true then people in non-serious accidents must also have worn seatbelts. If they were not wearing seatbelts and not seriously injured then there would be no real correlation between wearing safety belts or not wearing them.

Lets go through POE and get rid of (what I think) the easy ones

E. Incorrect. This does not matter in the conclusion. We dont care that only serious injuries are reported. We just want proof that they can be prevented.

C. Incorrect. This is only about front seat people. Rear seat passengers play no role in the conclusion

B. Incorrect. We need only know about people in the survey. What the population does is not applicable to the situation.

That brings us to A & D

D. Incorrect. What does D tell us. More than half the front seat people were not wearing seat belts. That actually could weaken the conclusion. Why is that the case? Lets say there were 100 accidents. At least 51 would not have on safety belts while at most 49 would. Now go back to the passage. Does the passage tell us how many were serious accident victims? No. What if there are 98 drivers without a safety belt and only 2 drivers with a safety belt in the accident survey? Lets say there are 10 seriously injured people in the accidents. 8 would have no seat belt while 2 would. The conclusion there would be that 100% of seat belt wearing people were seriously injured and thus is worse for a person in an accident since only 8 of 98 were hurt.

A. Correct. This lets us know that more than 20% of the people were wearing seat belts at the time of the accident. If we know that 80% of all serious injury involved no safety belt that means 20% did. By telling us that the entire population contains more than 20% with a safety belt we can safely say that there are drivers who wore a seat belt and were not seriously injured. Lets do the math. Assume 101 drivers. At least 21 must have worn a safety belt. If there are 100 serious accidents then 80 did not have one on and 20 did. All those without seatbelts were hurt while there was at least 1 safe with it. Thus its better. Lets say there are 10 accidents. 8 without, 2 with. That means 8/80 non seat belt wearers were injured while 2/21 seatbelt wearers were injured. Thats a 10% chance of being hurt without a seatbelt and a 9.5% chance of being seriously hurt with one. Thus wearing the seatbelt must reduce the risk of injury.

[pradeepkaushal9518]

yes i think i should change to A as in the question it is told about 80% hence we should see the option in which rest 20 % of the drivers is mentioned not about 50%.

[stormier]

The important things to note:

1. This was a survey of all accident victims
2. 80% of severely injured victims did not wear seat belts in the front seat
3. By wearing seat belts they can avoid serious injury

They basically want to know the assumption made in order for point 3 to be true. In order for 3 to be true then people in non-serious accidents must also have worn seatbelts. If they were not wearing seatbelts and not seriously injured then there would be no real correlation between wearing safety belts or not wearing them.

Lets go through POE and get rid of (what I think) the easy ones

E. Incorrect. This does not matter in the conclusion. We dont care that only serious injuries are reported. We just want proof that they can be prevented.

C. Incorrect. This is only about front seat people. Rear seat passengers play no role in the conclusion

B. Incorrect. We need only know about people in the survey. What the population does is not applicable to the situation.

That brings us to A & D

D. Incorrect. What does D tell us. More than half the front seat people were not wearing seat belts. That actually could weaken the conclusion. Why is that the case? Lets say there were 100 accidents. At least 51 would not have on safety belts while at most 49 would. Now go back to the passage. Does the passage tell us how many were serious accident victims? No. What if there are 98 drivers without a safety belt and only 2 drivers with a safety belt in the accident survey? Lets say there are 10 seriously injured people in the accidents. 8 would have no seat belt while 2 would. The conclusion there would be that 100% of seat belt wearing people were seriously injured and thus is worse for a person in an accident since only 8 of 98 were hurt.

A. Correct. This lets us know that more than 20% of the people were wearing seat belts at the time of the accident. If we know that 80% of all serious injury involved no safety belt that means 20% did. By telling us that the entire population contains more than 20% with a safety belt we can safely say that there are drivers who wore a seat belt and were not seriously injured. Lets do the math. Assume 101 drivers. At least 21 must have worn a safety belt. If there are 100 serious accidents then 80 did not have one on and 20 did. All those without seatbelts were hurt while there was at least 1 safe with it. Thus its better. Lets say there are 10 accidents. 8 without, 2 with. That means 8/80 non seat belt wearers were injured while 2/21 seatbelt wearers were injured. Thats a 10% chance of being hurt without a seatbelt and a 9.5% chance of being seriously hurt with one. Thus wearing the seatbelt must reduce the risk of injury.

Thank you for explaining it! Very clear!

[diebeatsthegmat]

i think its knewton question

imo D

More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.

if it is true than the conclusion can be drawn that wearing seat belt can reduce the risk of severely injured

i doubt that this is a knewton question. this is an OG 11 question, also a question from OG11 with red cover
and its OA is A