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?[2]
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?[1]

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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