The U.S Internal Revenue Service (IRS), published the Annual Income Tax figures

Question

The U.S Internal Revenue Service (IRS), published the Annual Income Tax figures on individual Income Tax returns in Statistics of Income, Individual Income Tax Returns for the year 2005,the IRS reported the average tax of individuals Income tax as $10,500.00. In actual fact the IRS reported the average tax returns of a sample of 180,000 individuals’ Income tax return from a total of more than 135 Million such returns.

(i).What is the population under consideration.

(ii).What is the variable of interest.

(iii).Is the average tax reported by IRS a population mean or a sample mean?

(iv).Do you agree that we should expect the average tax Xbar of the 180,00 individuals sampled by the IRS to be exactly the same as the mean tax µ of all individual income tax returns for the year 2005.If Yes, fine but if no explain why you do not agree.

(v).How can we answer questions about sampling errors?. For instance, is the sample mean tax Xbar reported by the IRS likely to be within $200 of the population mean tax µ.

Explanation / Answer

1) POPULATION UNDER CONSIDERTAION IS THE TAX PAYING POPUATION - INDIVIDUAL TAX INCOME

2) VARIABLE OF INTEREST IS THE DIFFERENT AMOUNT OF THE TAX AMOUNT FROM DIFFERENT PEOPLE

3)THE MEAN GIVEN IS THE POPULATION MEAN AS ITS THE AVERAGE RETURN OF INCOME TAX FOR THE YEAR 2005 FOR ENTIRE POPULATION

4) NO WE CANT EXPECT THE MEAN TO BE SAME BECAUSE IN THE SAMPLE THE ENTIRE POPULATION WILL BE LESS THAN THE ACTUAL POPULATION.ALSO THE MEAN OF THIS SAMPLE EITHER CAN INCREASE OR DECREASE THEN ACTUAL

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