The Federal Reserve reported in its comprehensive Survey of Consumer Finances, released every three years, that the average income of families in the United States declined from 2001 to 2004. This was the first decline since 1989–1992. A sample of incomes was taken in 2001 and repeated in 2004. After adjusting for inflation, the data that arise from these samples are given in a file entitled Incomes.

a. Determine the percentage decline indicated by the two samples.

b. Using these samples, produce a 90% confidence interval for the difference in the average family income between 2001 and 2004.

c. Is it plausible that there has been no decline in the average income of U.S. families? Support your assertion.

d. How large an error could you have made by using the difference in the sample means to estimate the difference in the population means?