I use this project to help introduce students to the four randomization-based sampling methods: Simple Random Sample, Stratified, Cluster, and Systematic. Each group gets 120 "people" that they must use on a poster to illustrate their assigned sampling method. After they use randomization to select a sample of size n > =30, they compare their sample to the 120 person population to see how well their sample represents the population distribution.
This bundle contains the four big group projects I use throughout my statistics course: Exploring Data, Sampling Methods, Probability in Games, and Inference. I use these to try and let me students really become statisticians. The biggest payoff I've seen over the years is an increase in correct statistical vocabulary use. I also have lots of posters to hang on my walls of student work.
I use this project as a culmination of my statistics course. It includes sampling methods and inference (confidence interval and hypothesis test). The project progresses at short intervals with different steps having different due dates along the way. I utilize a live/shared google doc and google sheet with each group to comment on their work electronically and update their process. You could just as easily have periodic progress checks in your class with physical components. This is a Word doc