This exercise presents a real example of Simpson's paradox (Wagner, 1982). The total income and total taxes paid in each of five income categories are given for 2 years, 1974 and 1978, in the following table:

a. The "tax rate" for any income category is calculated as tax divided by income. Calculate the tax rates for each income bracket in each year.

b. Calculate the overall tax rate for each of the 2 years.

c. Did the tax rates within each income bracket increase or decrease from 1974 to 1978?

d. Did the overall tax rate increase or decrease from 1974 to 1978?

e. Compare your results in parts (c) and (d). Explain them in terms of Simpson's paradox.