Vintner Mortgage Company in Chicago, Illinois, markets residential and commercial loans to customers in the region. Although the company had generally tried to avoid the “sub-prime” loan market, recently the company’s board of directors asked whether the company had experienced a difference in the proportion of loan defaults between residential and commercial customers. To prepare an answer to this question, company officials selected a random sample of 200 residential loans and 105 commercial loans that had been issued prior to 2005. The loans were analyzed to determine their status. A loan that is still being paid was labeled “Active” and a default loan was labeled “Default.” The resulting data are in a file called Vintner.
a. Based on the sample data and a significance level equal to 0.05, does there appear to be a difference in the proportion of loan defaults between residential and commercial customers?
b. Prepare a short response to the Vintner board of directors. Include in your report a graph of the data that supports your statistical analysis.
c. Consider the outcome of the hypothesis test in part a. In the last five audits, 10 residential and 10 commercial customers were selected. In three of the audits, there were more residential than commercial loan defaults. Determine the probability of such an occurrence.