Lisa’s father, the accountant, is on yet another rant, this time about the, in h

Question

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

Explanation / Answer

lisa's father 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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