Inferential Statistics: A Different Approach

For the longest time I've given thought to providing instruction on inferential statistics in a unique fashion.  If you're an AP Stat teacher, it means a departure from the One-Proportion Z-test, Two-Proportion Z-test, One Sample t-test, Two-Sample t-test, Matched Pair t-test, Chi-Squared Test(s), t-tests for slopes of regression lines.

So here's how I'd start...all data collection.  Spend a couple of days collecting data for each situation.  One of the essential questions I'd like my students to explore throughout the year is "Which model is the most appropriate for data you have collected?"  Here's where we go into depth about why certain models are more appropriate than others...

Data to Collect

1. Number of victories in 100(or so) games of Rock-Paper-Scissors
2. Toss a thumbtack and record proportion of "up" 
3. Drop a piece of buttered toast 50(or so) times and measure how many times it lands "buttered-side down"
4. Give a dummy homework assignment and measure the proportion in each class that complete the assignment
5. Compare batting averages of two baseball players
6. Time how long it will take kids to walk to the pool and back
7. Prices of items at clothing stores (found through browsing catalogs online)
8. Number of each type of animal cracker per box
9. How long it will take you to sort beans on to bulls-eyes with a dominant/non-dominant hand
10. Give the ol' Memory Experiment(groups rate sentence on how hard they are to pronounce/how easily they can form a vivid mental image) and compare number correct for each group
11. Count the number of each color of M&M you receive in a sample of M&M's
12. Change drop-height/rotor length of paper helicopters and record the time it takes to fall

After you spend about a week or so doing data collection, ask students to reflect on how data was collected. Notice also that some activities are done the same way (measuring proportions/means).  I'm fairly certain this has to be done to guide reflections, make kids confused, and ultimately learn something about making generalizations (mathematical modeling at its finest).

Ideas for Reflection:

1. What was measured in each data collection?  How does it compare with other types of data?
2. Which activities were useful for making comparisons?
3. If we're not making a comparison, what can we do with the data we collect?
4. Does it matter than some samples are smaller than others?  
5. Create a display for each activity with the raw data.  Which models tend to be the most appropriate?

I can see this being two weeks of AP Stat where kids think about collecting data and fitting similar models to similar methods of data collection.  Once they start fitting models to each situation for comparison, then you bring about some hypothesis testing procedures.

If you're a Stat teacher or not, provide your suggestions and ideas for data to collect.  It'd be great to get a new type of data to collect from somebody outside of the Stat realm.