Question

There are three loan officers at farmers National Bank. All decisions on mortgage loans are made by one of these officers. The president of the bank would like to be sure that the rejection rate is about the same for the three officers. A sample of 200 recent applications yielded the following results. Is the rejection rate related to the officer that processes the loan? Use the 0.05 significance level.

	Loan Officer
	Felix	Otis	Foxburrow
Approved	50	70	55
Rejected	10	10	5
Total	60	80	60

a. State the null and alternate hypothesis.

H0:____________________

H1:____________________

b. State the decision rule.

c. Compute the value of the test statistic.

d. What is you decision regarding the null hypothesis? Interpret the result.

Answer 1

a)

HO: rejection rate is not related to the officer that processes the loan

H1: rejection rate is related to the officer that processes the loan

b)

for 2 df and 0.05 level of signifcance critical region       χ2=

5.991

decision rule. :reject Ho if test statistic X² >5.991

c)

applying chi square test:

Expected	Ei=row total*column total/grand total	Felix	Otis	Foxburrow	Total
	Approved	52.500	70.000	52.500	175
	Rejected	7.500	10.000	7.500	25
	total	60	80	60	200
chi square    χ2	=(Oi-Ei)2/Ei	Felix	Otis	Foxburrow	Total
	Approved	0.1190	0.0000	0.1190	0.238
	Rejected	0.8333	0.0000	0.8333	1.667
	total	0.952	0.000	0.952	1.905

value of the test statistic X² =1.905

d)as test statistic is not in rejection region ; we can not reject null hypothesis

we do not have evidence at 0.05 level to conclude that rejection rate is related to the officer that processes the loan