Are my responsibilities as a lecturer the same as a teacher at school?
Teaching and studying at a university is different, and I sympathise with your frustrations. However, learning how to effectively study in a university needs to be learned as well. We cannot expect students just out of school to know how to study. So if the stats lecture takes place early in the program, as is the case with the stats lecture I teach, then you cannot expect them to behave like proper students yet. Part of the learning goals of that lecture must be to teach them how to study. Just assuming that they know how to study and how a lecture at a university works, is just going to lead to endless frustration on your part and on the students part. This means you will have to spent a substantial part of your teaching time on the learning how to study part, rather than statistics. We  do not have to pamper students, but we cannot expect miracles from them either.