In early 2012, the proportion of mortgages that were “under water”—a negative equity position in which the homeowner owes more than the value of the home—was highest in Nevada and Arizona (s.wsj.net/public/resources/documents/info-NEGATIVE_EQUITY_0911.html). Lenders are also interested in homes at risk—those within 5% of being in a negative equity position. A sample of mortgages from these two states suggest that the problem may be less severe in Nevada. The sample found that 62 of 1369 Arizona mortgages were in a “near negative equity” state. A sample of 604 Nevada mortgages found 22 in a near negative equity state.
a) Is there evidence that the percentage of near negative equity mortgages is different in the two states?
b) Give a 90% confidence interval for the difference in proportions.