Step 1: Understanding the Argument.
The argument suggests that a decline in the football team's performance will lead to a decrease in alumni contributions. This implies that alumni contributions are related to the team's performance, specifically its record. The assumption is that alumni are more likely to contribute if the team is successful.
Step 2: Analysis of Options.
- (A) The college's reputation for academic excellence depends on the performance of its football team: Incorrect. The argument does not say that academic excellence itself depends on the football team's performance, only that alumni contributions are linked to the team's success.
- (B) Contributions from alumni are needed for the college to produce a winning football team: Incorrect. The argument focuses on alumni contributions decreasing due to poor performance, but it does not suggest that these contributions are necessary for the team's success.
- (C) Struthers alumni contributions depend to an extent on a winning record by the college's football team: Correct. This option directly addresses the assumption that alumni contributions are tied to the football team's performance, which is central to the argument.
- (D) The college's football team will continue its losing streak next year: Incorrect. The argument does not assume this, only that the team's performance this year has led to a decline in alumni contributions. It does not predict next year's performance.
- (E) As a group, the college's alumni will have at least as much discretionary money to give away next year as this year: Incorrect. The argument does not assume that the amount of money alumni have available will remain the same; it focuses on the link between contributions and team performance.
Step 3: Conclusion.
The correct answer is (C) Struthers alumni contributions depend to an extent on a winning record by the college's football team.
Final Answer: \[ \boxed{(C) \, \text{Struthers alumni contributions depend to an extent on a winning record by the college's football team.}} \]