Over the years, I picked up many Statistics Concepts in by a variety of situations and means. I studied some Statistics maybe for a couple semesters almost 10 years back. But I also picked up concepts while doing Machine Learning work. I only understood things in a narrow scope - I always tried to get away knowing only what I need to know for a project etc.
Consequently, I do not have a big picture understanding of Statistics. For eg. I know vaguely what a t-test is and what a chi-square test is. But I can't relate both these concepts solidly in my head. And without relating each of these concepts I feel they are useless and not as powerful.
I have come to understand that the only way I understand anything is by working on hard problems chosen by experts. It should be hard so that I take some time to work it, also it should be chosen carefully by experts so that each problem contains a 'moral' which takes me one step closer to enlightenment.
So, help me assemble a set of problems to work through to seek out zen through statistics. Scope is all of statistics (regression, ANOVA, t-tests etc, Structural Equations of Latent Variables etc).