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.

White   Black Total
Section A   88   10 98
Section B   92   31 123

Total 180 41 221

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 squared χ2= ?

​(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.

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

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	white	Black	Total
	Section A	79.8190	18.1810	98.00
	Section B	100.1810	22.8190	123.00
	total	180.00	41.00	221.00
chi square    χ2	=(Oi-Ei)2/Ei	white	Black	Total
	Section A	0.839	3.681	4.5198
	Section B	0.668	2.933	3.6011
	total	1.5066	6.6143	8.121
test statistic X2 =		8.121

from excel: p value =chidist(8.121,1) =0.004

b)

z =sqrt(X² )=sqrt(8.121)=2.85

p value =0.004