As I was discussing yesterday night with my daughter about a practice stats exam she had just taken in medical school, I came upon the following question:
What is the probability that women have the same risk of cancer as men in the entire population given that the selected sample concluded against equality?
Which just means nothing, since conditioning on the observed event, say |X|>1.96, cancels any probabilistic structure in the problem. Worse, I have no idea what is the expected answer to this question!
