Question: A rent-to-own (RTO) agreement appeals to low-income and financially distressed consumers. It allows immediate access to merchandise, and by making all payments, the consumer acquires the merchandise. At the same time, goods can be returned at any point without penalty. Suppose a recent study documents that 65% of RTO contracts are returned, 30% are purchased, and the remaining 5% default. In order to test the validity of this claim, an RTO researcher looks at the transaction data of 420 RTO contracts, of which 283 are returned, 109 are purchased, and the rest defaulted.

a. Set up the competing hypothesis to test whether the return, purchase, and default probabilities of RTO contracts differ from 0.65, 0.30, and 0.05, respectively.

b. Compute the value of the test statistic.

c. Conduct the test at the 5% level of significance and interpret the test results.