In 2005, the Internal Revenue Service (IRS) sampled 292,966 tax returns to obtain estimates of various parameters. Data were published in Statistics of Income, Individual Income Tax Returns. According to that document, the mean income tax per return for the returns sampled was $10,319.
a. Explain the meaning of sampling error in this context.
b. If, in reality, the population mean income tax per return in 2005 was $10,407, how much sampling error was made in estimating that parameter by the sample mean of $10,319?
c. If the IRS had sampled 400,000 returns instead of 292,966, would the sampling error necessarily have been smaller? Explain your answer.
d. In future surveys, how can the IRS increase the likelihood of small sampling error?