Commercial Colleges (2)

[RaffaeleM39]

For-profit colleges serve far fewer students than either public or private non-profit colleges. At the same time, relative to non-profit colleges, for-profit colleges draw a disproportionate share of federal and state financial aid, such as tuition grants and guaranteed loans, for their students. It must be, then, that for-profit colleges enroll a greater proportion of financially disadvantaged students than do non-profit colleges.

In assessing the argument above, it would be most useful to compare:

(A) the proportion of financially disadvantaged students served by public and private non-profit colleges
(B) the extent to which for-profit and non-profit colleges engage in fraudulent practices in helping their students obtain unneeded federal and state financial aid
(C) the number of students receiving federal and state financial aid at for-profit colleges and non-profit colleges
(D) the quality of education received by financially disadvantaged students at for-profit colleges and non-profit colleges
(E) the rates of default on loan repayments among graduates of for-profit and non-profit colleges

Hi,

"For-profit colleges serve far fewer students than either public or private non-profit colleges." and, at the same time, "relative to non-profit colleges, for-profit colleges draw a disproportionate share of federal and state financial aid".

Let's make an example.

For-profit college: 100 students
Public college: 1k students

For-profit college aid: 1k$
Public college aid: 100$

It follows that:

For-profit college aid per student: 1k$/100 = 10 $/student
Public college aid per student: 100$ /1k = 0.1 $/student

That is, the aid per student in for-profit college is higher than the aid per student in non-profit college.

This may be because the for-profit college is frauding the State (answer B), or because the for-profit college costs more, it has higher tuition than non-profit college, so the aid must be higher.
This is a reasonable assumption: for-profit colleges need to make a profit, while non-profit college has zero profit.
One way to make a profit is to have higher revenues, which for a college means higher tuitions.
It is unlikely that the for-profit college is hiring professor of lower quality, paying them less.

So, the aid is higher because, most likely, the tuition is higher.
If we evaluate answer E ("the rates of default on loan repayments among graduates of for-profit and non-profit colleges") this would strengthen or weaken this assumption. A loan of a high amount is more difficult to pay back than a loan of a lower amount.

If the rate of defaults on the loans is greater for for-profit graduates than for non-profit graduates, the author conclusion would be weakened: the for-profit college does not have a higher proportion of poor student, it just has higher tuition fees.

If, on the other hand, the rate of defaults on the loan is the same, the author conclusion would be strengthened: it is likely that the loans are for the same amount and the same interest rate, so the prospective graduate students in for-profit are either richer (so they ask for a loan which is, in proportion to the tuition fee, less), or the tuition fees are more or less the same, thus making it more likely (but not necessary true) that the college has more poor students.

What is wrong with my reasoning?

[Sage Pearce-Higgins]

I think you're overcomplicating things here.

Let's make an example.
For-profit college: 100 students
Public college: 1k students
For-profit college aid: 1k$
Public college aid: 100$
It follows that:
For-profit college aid per student: 1k$/100 = 10 $/student
Public college aid per student: 100$ /1k = 0.1 $/student
That is, the aid per student in for-profit college is higher than the aid per student in non-profit college.

I agree with you that the average aid per student must be higher for students at for-profit students, but that doesn't matter. We're not interested in the average, but in the number of 'financially disadvantaged students'.

One way to make a profit is to have higher revenues, which for a college means higher tuitions.
It is unlikely that the for-profit college is hiring professor of lower quality, paying them less.
So, the aid is higher because, most likely, the tuition is higher.

This is a possible explanation, but it's not the only one. Perhaps the tuition is the same, but the costs are lower. Be really careful about introducing your own assumptions.

A loan of a high amount is more difficult to pay back than a loan of a lower amount.

Not necessarily. If the students have a better education, then they might get more highly paid jobs and repay the loans more easily.

If, on the other hand, the rate of defaults on the loan is the same, the author conclusion would be strengthened: it is likely that the loans are for the same amount and the same interest rate, so the prospective graduate students in for-profit are either richer (so they ask for a loan which is, in proportion to the tuition fee, less), or the tuition fees are more or less the same, thus making it more likely (but not necessary true) that the college has more poor students.

How did you jump from 'financially disadvantaged students' to richer graduate students? These two categories are not the same.

In class I describe this kind of reasoning as the "many steps trap". You've made lots of small assumptions and reached a position pretty far removed from what the question is really asking about. Compare your reasoning to the reasoning given in the answer explanation for answer B and you'll see that answer B is much more directly related to the argument.