renjana wrote:
Can you explain option B in detail . it seems a little confusing
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A study showed that only ten percent of American dog owners enroll their dogs in formal obedience training classes. More than twenty percent of these dog owners, the study also showed, participate in dog shows. Thus, it is obvious that people who train their dogs are more likely to participate in dog shows than are people who do not train their dogs.
The conclusion above is correct provided which of the following statements is also true?
(A) It is impossible for a dog to compete in a dog show if the dog has not completed at least one formal obedience training class.
(B) The proportion of dog owners who enroll their dogs in formal obedience training classes is representative of the proportion who train their dogs outside such classes.
(C) Dog owners who participate in dog shows only train their dogs by enrolling them in formal obedience training lessons.
(D) Participation in dog shows is a reliable indicator of how much attention a dog owner pays to his dog.
(E) Only purebred dogs can participate in dog shows, so many owners who enroll their dogs in formal obedience training classes are excluded from this activity.
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I understand it this way.
Conclusion: Thus, it is obvious that people who train their dogs are more likely to participate in dog shows than are people who do not train their dogs.
Question: The conclusion above is correct provided which of the following statements is also true?
Answer: (B) The proportion of dog owners who enroll their dogs in formal obedience training classes is representative of the proportion who train their dogs outside such classes.
Imagine that there are 100 participants in the dog show in America in 2018.
45 of them took obediance class. It is representative of the the proportion who train their dogs outside such classes. So number of participants that are trained outside these classes (by owners themselves or by coaches or whatever) is of that order (45) - something similar (20, 30, 40, 45, 50)
So the sum will be more than 50 of 100 and this means that number of such participants is more than a half. It is what wee need.
Now imagine that proportion of dog owners who enroll their dogs in formal obedience training classes is
NOT representative of the proportion who train their dogs outside such classes.
There are 100 participants in the dog show in America in 2018. 45 of them took obediance class. Because it is not representative the number of participants who is trained outside these classes can be 0,1,2
And the sum is less than 50 - less than half - conclusion breaks apart.
So we choose B.
Why this is bad option from the other side and it is not a great question?
Because:
Imagine again that there are 100 participants in the dog show in America in 2018.
10 of them took obediance class. It is representative of the the proportion who train their dogs outside such classes. So number of participants that are trained outside these classes (by owners themselves or by coaches or whatever) is of that order (10) - something similar (5, 9, 15, 19)
The sum will be less than 50 - less than a half.
Because we know nothing about the number/proportion of dog owners who do not train their dogs.