There are three loan officers atFarmer National Bank. All decisions on mortgage
ID: 2914625 • Letter: T
Question
There are three loan officers atFarmer National Bank. All decisions on mortgage loans are made byone of these officers. The president of the bank would like to besure that the rejection rate is about the same for the threeofficers. A sample of 200 recent applications yielded the followingresults. Is the rejection rate related to the officer thatprocesses the loan? Use the 0.05 significance level.
Felix
Otis
Approved
50
70
55
Rejected
10
10
5
Total
60
80
60
H0:
H1:
b. State thedecision rule.
c. Compute the value of the teststatistic.
d. What isyour decision regarding the null hypothesis? Interpret theresult.
Loan Officer
Felix
Otis
FoxburrowApproved
50
70
55
Rejected
10
10
5
Total
60
80
60
Explanation / Answer
Null Hypothesis: rejection rate is not relatedto the officer that processes the loan Alternative Hypothesis: rejection rate relatedto the officer that processes the loan Consider the following table Felix Otis Foxburrow TOTAL Approved 50 70 55 175 Rejected 10 10 5 25 Total 60 80 60 200 Felix Otis Foxburrow Approved 52.5 70 52.5 Rejected 7.5 10 7.5 Oi Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 50 52.5 6.25 0.119048 10 7.5 6.25 0.833333 70 70 0 0 10 10 0 0 55 52.5 6.25 0.119048 5 7.5 6.25 0.833333 1.904762 Felix Otis Foxburrow TOTAL Approved 50 70 55 175 Rejected 10 10 5 25 Total 60 80 60 200 Felix Otis Foxburrow Approved 52.5 70 52.5 Rejected 7.5 10 7.5 Oi Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 50 52.5 6.25 0.119048 10 7.5 6.25 0.833333 70 70 0 0 10 10 0 0 55 52.5 6.25 0.119048 5 7.5 6.25 0.833333 1.904762The critical value of chi-square at (2-1)X(3-1)=2dfand at 0.05, the level of signifiance is 5.99 Since the calcualted value of chi-square isless than the critical value of chi-squaer so we accept the nullhypothesis and conclude that rejection rate is not related to theofficer that processes the loan Felix Otis Foxburrow TOTAL Approved 50 70 55 175 Rejected 10 10 5 25 Total 60 80 60 200 Felix Otis Foxburrow Approved 52.5 70 52.5 Rejected 7.5 10 7.5 Oi Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 50 52.5 6.25 0.119048 10 7.5 6.25 0.833333 70 70 0 0 10 10 0 0 55 52.5 6.25 0.119048 5 7.5 6.25 0.833333 1.904762