Also, I want to make sure I'm not being stupid about something. I keep seeing this kind of language in my stats books and it seems wrong. For instance, they'll say, for the sampling distribution of the difference of two sample means, that the mean of is . Presumably this means, if the sample size is large enough, these are approximately equal, no?
But things get worse. Then they say, "If the sampled populations are normally distributed, then the sampling distribution of is exactly normally distributed, regardless of the sample size." Really? Even if ? Even if you just take one such sample? Or two?
Are they just being imprecise in their choice of words, even when they're emphasizing that their claim is to be taken as precise? Or am I missing something?