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 increased between in 2010 and 2013. A sample of incomes was taken in 2010 and again in 2013. After being adjusted for inflation, the data that arise from these samples are given in a file titled Federal Reserve.

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

b. Using these samples, produce a 90% confidence interval for the difference in the average family incomes between 2010 and 2013.

c. Is it plausible that there has been no increase 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?