Question

New Renters A complex is divided into two parts: Section A and Section B. The plaintiffs in a lawsuit claimed that white potential renters were steered to section A, while black renters were steered to section B. The table displays the locations of recently rented apartments. Do you think there is evidence of a racial bias? Assume the conditions for inference are satisfied. Complete parts a through c. White Black - Section A Section B Total 100 127 227 NOTE: With respect, this data can be considered sensitive to some individuals, but the intent of this question is to better understand some aspects of a relevant social issue in society through the use of science; in this case, statistical analysis. Please keep in this mind as you complete the question. Total 184 a) Perform a chi-square test of homogeneity to determine if there is evidence that blacks are less likely to rent in section A than in section B. What is the value of the test statistic x?? x2 = (Round to three decimal places as needed.) What is the P-value of the chi-square test of homogeneity? P-value = (Round to three decimal places as needed.) b) You can also check the data for evidence of racial bias using two-proportion z procedures. Find the z-value for this approach za (Round to two decimal places as needed.) What is the P-value of the two-proportion z-test? P-value = (Round to three decimal places as needed.)

Answer 1

a)Applying chi square test:

Expected	Ei=row total*column total/grand total	white	Black	Total
	section A	81.0573	18.9427	100
	section B	102.9427	24.0573	127
	total	184	43	227
chi square    χ2	=(Oi-Ei)2/Ei	white	Black	Total
	section A	0.5947	2.5446	3.1393
	section B	0.4682	2.0036	2.4719
	total	1.0629	4.5482	5.6111

test statistic X2 =		5.611
p value =		0.018

b)

Section A Pz=xz/n, = P:=xg/n = 0.8800 100 estimated difference in proportion =P:-P2 estimator of pooled proportion p =(x2+xz)/(n2+nz) Section B 96 0.7559 127 0.1241 0.8106 std error Se= VlP1*(1-.)*(1/n4+1/nz) 0.0524 test stat z = (P.-P2)/se 2.369

fom above test statistic z =2.37

p value =0.018