There is a big distinction between understanding a solution and being able to produce it yourself. When you read a solution presented in a solution manual, you will undoutably understand it; however, this does not mean that you will be able to produce a similar solution yourself at another time. If you don't believe me, just ask Richard Feynman. Solution manuals often give the illusion of proficiency; more often than not, this illusion is cruelly shattered by exams.
This trap is very easy to fall into and is indeed one that many a good student (myself included) have fallen prey to. In a course like Stat 134 where the problems you face are especially tricky, a large part of the learning process is struggling through problems and confronting the bleak sense of helplessness you might feel when faced with a problem unlike anything you've seen before. It is hard to find many things more rewarding in life than that "Eureka" moment, that arises after hours of hard, fruitless labour, when what seemed so opaque merely seconds prior becomes so suddenly and entirely clear. Don't deprive yourself of the beauty of such moments.
Do yourself a favour and don't use solution manuals, even if to just "check your work". If you need help with the homework assignments, please reach out to the GSIs or make use of any one of the SLC's many services.