A rent-to-own (RTO) agreement appeals to low-income and financially distressed c

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. Use Table 3. a. Choose the appropriate alternative hypothesis to test whether the return, purchase, and default probabilities of RTO contracts differ from 0.65, 0.30, and 0.05, respectively. At least one of the pi (i = 1, 2, 3) differs from its hypothesized value. All pi (i = 1, 2, 3) values differ from its hypothesized value. b. Compute the value of the test statistic. (Round the intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic c-1. Calculate the critical value at the 5% level of significance. (Round your answer to 3 decimal places.) Critical value c-2. Interpret the test results. H0. Therefore, we claim that the proportions of return, purchase, and default are different from 0.65, 0.30, and 0.05, respectively. rev: 11_05_2015_QC_CS-31836

Explanation / Answer

null hypothesis:Ho:  return, purchase, and default probabilities of RTO contracts follow 0.65, 0.30, and 0.05 proportion respectively

alternative hypothesis:H1: At least one of the pi (i = 1, 2, 3) differs from its hypothesized value

applying chi square goodness of fit test on above:

Test statistic =4.993

degree of freedom =number fo categories-1=2

critical value at the 5% level of significance =5.991

as test statistic is less then critical value we do not have evidence that  the proportions of return, purchase, and default are different from 0.65, 0.30, and 0.05

observed Expected Chi square flavour Probability O E=total*p =(O-E)^2/E return 0.650 283.000 273.00 0.37 purchase 0.300 109.000 126.00 2.29 default 0.050 28.000 21.00 2.33 1 420 420 4.9933

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