Question

Problem 2. The Citizen Bank employs two appraisers. When approving borrowers for mortgages, it is imperative that the appraisers value the same types of properties consistently. To make sure that this is the case, the bank examines six properties (in $1,000) that the appraisers had valued recently.

Proprty	Appraiser 1	Appraiser 2
1	235	239
2	195	190
3	264	271
4	315	310
5	435	437
6	515	525

A. Let µD = µ1 − µ2, where µ1 is the mean value of properties from Appraiser 1, and µ2 is the mean value of properties from Appraiser 2. Specify the competing hypotheses that determine whether there is any difference between the values estimated by Appraiser 1 and Appraiser 2.

B. Assuming the value difference is normally distributed, calculate the value of the test statistic. (Please round your answer to 4 decimal places.)

C. Find the p-value in this test. (Please round your answer to 4 decimal places. You can either approximate the p-value using t-table or and the exact p-value using Excel or any software.)

D. At the 5% significance level, is there sufficient evidence to conclude that the appraisers are inconsistent in their estimates? Please explain.

E. Construct a 95% confidence interval of the mean difference between values estimated by Appraiser 1 and Appraiser 2, i.e., 95% confidence interval of µD. (Please round your answer to 4 decimal places.)

Answer 1

A)

null Hypothesis:μd		=	0
alternate Hypothesis: μd		≠	0

B)

value of the test statistic =-0.8591

C)

p value =0.4296 (from excel tdist(0.8591,5,2) function)

d)

since p value >0.05 , we do not have sufficient evidence to conclude that the appraisers are inconsistent in their estimates

e)

for 95% CI; and 5 degree of freedom, value of t=			2.571
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		6.483
lower confidence limit                     =		-8.6500
upper confidence limit                    =		4.3167