Question

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. ​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.		New Renters
		White	Black	Total
	Section A	75	15	90
	Section B	75	28	103
	Total	150	43	193

​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

chi squaredχ2​?

chi squaredχ2=?

​(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.z procedures.

Find the​ z-value for this approach.

z=?

​(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

Applying chi square test:

Expected	Ei=row total*column total/grand total	white	Black	Total
	Section A	69.9482	20.0518	90.00
	Section B	80.0518	22.9482	103.00
	total	150.00	43.00	193.00
chi square    χ2	=(Oi-Ei)2/Ei	white	Black	Total
	Section A	0.365	1.273	1.6376
	Section B	0.319	1.112	1.4309
	total	0.6837	2.3848	3.069
test statistic X2 =		3.069

degree of freedom(df) =(rows-1)*(columns-1)=

1

from excel: p value =chidist(3.069,1) =0.080

z =1.75

p value =0.080