When I am attempting to test understanding of carrying out a simulation test about a single proportion, I like to use the following problem, or some variation of it. I’m fond of animals and studies that show that animals are clever, so this study and ones like it, appeals to me.
A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in 7 of 8 scenarios that she was presented. In order to judge whether Sarah understands how to solve problems we will define π to be the probability Sarah will pick the photo of the correct solution.
I don’t let them get away with just claiming that the p-value is some particular number – they have to explain how they know it is that number.