Forming an interesting in-class Statistics activity.

This Wednesday I've scheduled an in-class activity that relates some of the ideas we've discussed in my Statistics I class. So far they include surveys, descriptive statistics (mean, median, quartiles, and standard deviation), sampling, experiment design, and observational studies. Writing this on Tuesday morning, I have nothing written down but I have a couple ideas of what I want this activity to include:

• Perform an experiment and/or an observational study. I covered what these are in a lecture, but I really want them to attempt one (or both) on their own so they get a concrete idea of what they are. Doing both would be best since they would then be able to compare the methods of both.
• Take appropriate samples based on the research question. Ideally this would be done with students in the class so they can see how to take appropriate samples.
• Compute and use descriptive statistics to compare and contrast different samples. Quantitative reasoning and analysis are a core focus in statistics. 
• Talk about statistics. Whether it be in groups or in a presentation, forming ideas and communicating them to others is another core skill in statistics.

I also know what I don't want:

• A rote activity that requires no input from students. I want them to struggle with questions about sampling, which statistic to compute, what to do next. Through this struggle I want them to appreciate principles like variability, controlling for certain variables, and how to construct arguments for one action or another.

For an experiment I have a few ideas:

• Performing an intervention dealing with basic math skills. The idea would be to assess if a certain intervention (a logic puzzle, or a game) has any effect on student performance of a basic math test. We would discuss how to create a control, how to create the samples, how to administer the tests, etc. While the direct applicability of this example may be a stretch, it would be a constructed activity that students could perform.
• Have the students develop their own question and proceed from there. This has some issues, primarily because of the unending and uncertain nature of such a question. Without some guidance the possibilities are a bit too large, which generally leaves students not choosing anything at all.
• Provide a context (marketing manager, nurse's aide, etc.), and have students develop an interesting question that can be answered in-class. While being more specific we may not be able to answer such questions in-class. For example, if we wanted to do A/B testing of a website, we would have to construct this example fairly quickly, and perform the experiment on people who weren't part of the development of the website.

For an observational study:

• Given a data set have students develop an appropriate research question, and try to answer it using the data. This could be generalized further by having multiple data sets and have students pick one, or assign different groups different data sets.
• Taking the survey data collected at the beginning of the course, ask an appropriate research question that can be answered either by the previously collected data, or by another survey in class. The survey data is anonymous so it would be difficult to answer some questions.

You can probably guess which way I'm leaning, but I'll post the completed activities tomorrow. Feel free to post in the comments if you have any ideas or suggestions.