I do believe that exams provide an effective mechanism to assess students' knowledge of statistical concepts, ability to apply statistical methods, and skill at interpreting and communicate statistical findings. An important aspect of this for me is that exams given in a controlled environment are one way to assess the knowledge and ability of an individual student, as opposed to a homework or project assignment where students are encouraged to work collaboratively. While I am a proponent of collaborative learning and also supportive of making the development of teamwork skills a secondary goal of my courses, I do believe that it is important to assess students' individual abilities as well.
These are in-class, timed exams. I allot students as much time as the scheduling of the course permits. In other words, when I teach in 110-minute time slots, students can use the entire 110 minutes. When I teach in a 50-minute time slot, then students only have 50 minutes to complete the exam, and I try to rewrite the exam accordingly. On final exams students are welcome to use the entire 170 minutes scheduled for the exam. I expect all students who have studied well to finish the exam. My goal is for no students to work at a steady pace on the exam and run out of time. Typically more than half of my students are still in the room at the end of the class period, but I believe that the big majority are either checking their work or going back to work on questions that they found difficult.
To try to minimize student cheating, I prepare multiple versions of exams, with slight differences among them. I also copy these version on different colors of paper in an effort to discourage cheating just from students' knowledge that multiple versions exist.