Filling in these numbers helps students understand the idea of 'Expected Frequencies' through building on their intuitive understanding if the idea!
Now we went on to consider how the numbers in the table might look if we imagined quite a strong dependence between the two variables. Try these....
What is nice about approaching things this way is that the essential concept behind the statistical test has been explored before any mention of the technique and analysis itself. The whole idea depends on the difference between what we would expect to happen if there was no dependence and what actually did happen. With this established we can go on to analyse those differences.
Of course, to do that, we need data about what did happen and this is where today's connected world has a real edge! We put a quick survey together using a google doc and decided we would collect some age data as well.... (Please feel free to add your own responses below) We then employed the power of the social network to get some responses. Students posted it on their facebook pages and we used what ever means we could to get some responses. We hadd 100s in no time and were able to use some real live data to perform and independence test on!