The dark side of grad school... I can't even listen to NPR without getting into hyper analytical mode.
Take Garrison Keillor's description of Lake Wobegon, where all the women are strong, all the men are good-looking, and all the children are above average. Teehee, you say, how can ALL the children be above average (snicker snicker). I am apparently incapable of enjoying simple humor, and instead miss the point entirely.
Instead, I assume that this can be explained by the Central Limits Theorem, and decide that the null hypothesis should reflect that all the children score above average on some scale. To do so, we assume that the scale is normally distributed, with the average score being 50.
H(sub o): mu > 50
H (sub a): mu < or = 50
What I'm sure we'd find in a sample of the population is a confidence interval where the mean may be above 50, meaning that we fail to reject the null hypothesis at, say, 90% confidence. I do not know if we could ever conclude that the mean of the population is above or below average with any degree of statistical significance, not being in possession of a data set. It is troubling that the contention is about all children, and not the mean of the children, but I can't really apply statistics to that, just common sense, which is not part of the curriculum.