Question

13-22: A loan officer wished to determine if the marital status of loan applicants was independent of the approval loans. The following table represents the result of her survey:

                                      Approved                       Rejected

               Single            213                                  189

               Married 374                                  231

               Divorced 358                                  252

1. Conduct the appropriate hypothesis test that will provide an answer to the loan officer. Use a significance level of 0.01.
2. Calculate the p-value for the hypothesis test in part a.

Answer 1

Claim : To test whether that the marital status of loan applicants was independent of the approval loans or not

Hypothesis : Ho: marital status of loan applicants and the approval loans are independent

H1: marital status of loan applicants and the approval loans are dependent

Test statistics :

Where

	Approved	Rejected	Total
single	213	189	402
married	374	231	605
divorced	358	252	610
Total	945	672	1617

we get the expected frequencies as

Simmilarly , E12 = 167.06, E21= 353.57, E22=251.43 , E31=356.49 and E32=253.51

we can calculate test statistics as

Oi	Ei	(Oi-Ei)	(Oi-Ei)^2	(Oi-Ei)^2/E
213	234.94	-21.94	481.3636	2.04887886
189	167.06	21.94	481.3636	2.88138154
374	353.57	20.43	417.3849	1.18048732
231	251.43	-20.43	417.3849	1.66004415
358	356.49	1.51	2.2801	0.00639597
252	253.51	-1.51	2.2801	0.00899412
			Total	7.79

we get test statistics =      

Pvalue : By using excel we get exact pvalue

Excel command is =CHIDIST(X,Degrees of freedom)

=CHIDIST(7.79,2)

=0.0203

...............( Given)

Decision Rule : We Fail to reject Ho

Conclusion : There is sufficient evidence to conclude that marital status of loan applicants and the approval loans are independent