Income Tax The Internal Revenue Service (IRS) publishes annual figures on indivi
ID: 3275293 • Letter: I
Question
Income Tax The Internal Revenue Service (IRS) publishes annual figures on individual income tax returns in Statistics of Income, Individual Income Tax Returns. For the year 2010, the IRS reported that the mean tax of individual income tax returns was $11,266. In actuality, the IRS reported the mean tax of a sample of 308,946 individual income tax returns from a total of more than 130 million such returns. a. Identify the population under consideration. b. Identify the variable under consideration. c. Is the mean tax reported by the IRS a sample mean or the population mean? d. Should we expect the mean tax, x, of the 308,946 returns sampled by the IRS to be exactly the same as the mean tax, mu, of all individual income tax returns for 2010? e. How can we answer questions about sampling error? For instance, is the sample mean tax, x, reported by the IRS likely to be within $100 of the population mean tax, mu? a. The population consists of all individual income tax returns for the year 2010. b. The variable is "tax" (amount of income tax).Explanation / Answer
a. Population under consideration is the individuals who are eligible to file income tax returns for the year 2010.
b. Variable is the " Income Tax for year 2010"
c. Mean tax reported by IRS is a sample mean.
d. We can expect that the mean tax of the sample could be the same of population mean but not exactly the same. That's why we use the term confidence interval term.
e. Sampling error is the difference between the sample and population values.
SO here sampling error is Population mean - sample mean
as it is asked that population mean is within $100 from sample mean. It can be only derived from the value of standard deviation of the sample mean.