The best-known credit rating for consumers in the United States is the FICO score (named for the company Fair Isaac). The score ranges from 300 to 850, with higher scores indicating that the consumer is a better credit risk. For the following table, consumers with scores below 620 are labeled Risky. Those having scores between 620 and 660 are labeled Uncertain. Those between 660 and 720 have an Acceptable credit rating, and consumers with scores over 720 have Perfect credit. A department store kept track of loans (in the form of a store credit card) given to customers with various ratings. This table shows the proportion of customers within each risk category that did not repay the loan (defaulted).

(a) Is the credit score (as defined by these four categories) associated with default? How can you tell?
(b) What would it mean for the use of the FICO score as a tool for stores to rate consumers if there were no association between the category and default?
(c) If virtually all customers at this store have accept-able or perfect credit scores, will the association be strong or weak? Suppose that the store has 10,000 loans, with 50 made to risky customers, 100 to uncertain customers, 9,000 to acceptable customers, and the rest to perfect customers.
(d) If a higher proportion of the loans had been made to customers who were risky or uncertain, would the association have remained the same, increased, or decreased?

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Score Range Defaulted Repaid Risky Uncertain Acceptable Perfect 30% 2200 2% 2% 70% 78% 98% 98%