Question

Chris’s mother, the accountant, is on yet another rant, this time about the, in her words, “blatant stupidity” of economists who, when comparing mean yearly incomes of samples of different sub-populations to the population as whole routinely use the normal distribution. As Chris’s mother correctly points out, the population distribution of yearly incomes is anything but normal (indeed, she correctly notes, “it is highly positively skewed”), so, she exclaims, “How can they get away with using the normal distribution”? Is Chris’s mother correct: are economists doing it all wrong or not? Explain.

Answer 1

Chris's mother would be correct in saying that annual mean salary would not be normally distributed. if population is not normal, then we cannot assume the sample mean to follow a normal distribution. However for large sample a normal test can be applied by the economists since for large sample and for any any statistic t we have

z=[t-E(t)]/S.E(t) approximately follows Normal distribution with mean 0 and variance 1.

hence economists won't be doing all wrong if sample size is moderately large.

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