Even before the “Ownership Society” programs of Presidents Clinton and Bush, the federal government was heavily involved in the housing market, primarily in the form of tax deductions for mortgage interest payments. In a study just prior to the foreclosure crisis starting in 2008, the Urban Institute stated about 80% of the estimated $200 billion of federal housing subsidies consisted of tax breaks (mainly deductions for mortgage interest payments). Samples indicated that federal housing benefits average $8,268 for those with incomes between $200,000 and $500,000 and only $365 for those with incomes of $40,000 to $50,000. The respective standard deviations were $2,100 and $150. They were obtained from sample sizes of 150.
To determine the appropriate hypothesis test concerning the average federal housing benefits of the two income groups, it is necessary to determine if the population variances are equal. Conduct a test of hypothesis to this effect using a significance level of 0.02.