Final answer:
The most compelling statement that could weaken the argument, that parents should send their children to private schools to increase college attendance likelihood, is that many public school students choose careers in farming over attending college, thus impacting college attendance rates.
Step-by-step explanation:
The argument presented suggests that to increase the likelihood of college attendance, parents should send their children to private schools instead of public ones. However, several counterarguments could weaken this premise. The most compelling statement that would weaken the argument is option E: Since most public schools are located in rural areas of the county populated primarily by farmers, nearly 30% of students from public high schools choose to pursue farming occupations rather than apply to colleges. This statement directly addresses an alternative reason for the lower college attendance rates among public school students that has nothing to do with the quality of education but is rather based on career choice influenced by local economic opportunities.
Option A might seem to reinforce the notion that private schools perform better, but does not weaken the argument. Option B only introduces a financial consideration without addressing the effectiveness of educational outcomes. Option C provides a contrast in socio-economic factors but falls short of explaining why fewer public school students attend college. Option D points to extracurricular activities, which could indirectly support college attendance but does not directly counter the main claim.