求教一道KAPLAN的CR

zl35

Choi: All other factors being equal, children whose parents earned doctorates are more likely to earn a doctorate than children whose parents who did not earn doctorates.

Harts: But consider this: Over 70 percent of all doctorate holders do not have a parent who also holds a doctorate.

Which of the following is the most accurate evaluation of Hart's reply?

a. It establishes that Choi's claim is an exaggeration.
b. If true, it effecively demonstrates that Choi's claim cannot be accurate.
c. It is consisitent with Choi's claim.
d. It provides alternative reasons for accepting Choi's claim.
e. It mistakes what is necessary for an event with what is sufficient to determine that the event will occur.

sdcar2010

Good analysis.

zl35

有点太过复杂了，不过thanks anyway。这题我觉得出得有点牵强，forget it

yiayia

Er....C is the right answer. this is a maths problem.
First, let us suppose children whose parents earned doctorates are as likely to earn a doctorate as are children whose parents who did not earn doctorates. Then the proportion of  children whose parents earned doctorates and earning a doctorate should equal to the proportion of children whose parents earning doctorates. For example, there are 100 children. 10 children have parents earning doctorates, the balance of children does not have that kind of parents. Then the probability of all the children earning a doctorate is 0.1. For the former 10 children, it will be 1 child who earn a doctorates. For the latter 90 children, on the other hand, the number should be 9. Thus，we can see the same conclusion which I draw above.

However, what if  the proportion of  children whose parents earned doctorates and earning a doctorate now is about 30%? It shows that children whose parents earned doctorates are more likely to earn a doctorate than children whose parents who did not earn doctorates. Here is the sequence. Because of the same other factors, it does not matter that there are twins or more children in a family. In addition, the argument has a unstated assumption that  the proportion of  children whose parents earned doctorates is very  low, far smaller than 30%. The experience tell us it is right. Are your friends who have parents owning a doctorate in a  proportion more about 30%?

babybearmm

Considering it a math problem, you will suddenly find this question very easy.

Draw a 2X2 matrix

Y=1	p01	p11
Y=0	p00	p10
joint probability	X=0	X=1

X axis is for parents: X=0 means "parents without Doctoral degree" and X=1 means "parents with Doctoral degree"
Y axis is for children: Y=0 means "children without Doctoral degree" and Y=1 means "children with Doctoral degree"

What is Choi talking about? "likelihood" - The odds ratio!
If we translate Choi's statement into mathematical expression, it is simply "odds ratio > 1"
odds ratio = (p00*p11)/(p01*p10) > 1      (Choi)

Again, let's translate Harts' statement into mathematical expression, it is simply
p01/p11 > 7/3                  (Harts)

From the above two mathematical expressions, we can clearly see that these two have nothing to do with each other. In other words, they could co-exist. Hence choice C is correct. (No mistakes, no inconsistencies, no weakening ....)

Choi: All other factors being equal, children whose parents earned doctorates are more likely to earn a doctorate than children whose parents who did not earn doctorates.

Harts: But consider this: Over 70 percent of all doctorate holders do not have a parent who also holds a doctorate.

Which of the following is the most accurate evaluation of Hart's reply?

a. It establishes that Choi's claim is an exaggeration.
b. If true, it effecively demonstrates that Choi's claim cannot be accurate.
c. It is consisitent with Choi's claim.
d. It provides alternative reasons for accepting Choi's claim.
e. It mistakes what is necessary for an event with what is sufficient to determine that the event will occur.

-- by 会员 zl35 (2012/3/26 23:43:58)

zl35

我也选了E，答案选C，崩溃

sdcar2010

Eeeeeeeeeeeeeeeeeee

zl35

求救~