An important expectation of a federal income tax reduction is that consumers wil

Question

An important expectation of a federal income tax reduction is that consumers will reap a substantial
portion of the tax savings. Suppose estimates of the portion of total tax saved, based on a random
sampling of 35 economists, have a mean of 26% and a standard deviation of 12%.
a. What is the approximate probability that a sample mean, based on a random sample of n = 35
economists, will lie within 1% of the mean of the population of the estimates of all economists?
b. Is it necessarily true that the mean of the population of estimates of all economists is equal to
the percentage of tax savings that will actually be achieved? Why?

Explanation / Answer

The standard error is 12/sqrt35=2.028 So to be within 1% of the mean, we would have to have z scores of +/- 1/2.028=0.493. Consulting a normal curve table, we find that the percentage of z scores that are equal to or less than 0.493 are 37.6%. Since these are estimates, and economic ones at that, the actuals could differ significantly from these numbers.

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