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 87 14 101
Section B 100 37 137

Total 187 51 238

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	79.3571	21.6429	101.00
	Section B	107.6429	29.3571	137.00
	total	187.00	51.00	238.00
chi square    χ2	=(Oi-Ei)2/Ei	white	Black	Total
	Section A	0.736	2.699	3.4350
	Section B	0.543	1.990	2.5324
	total	1.2787	4.6887	5.967
test statistic X2 =		5.967

from excel: p value =chidist(5.967,1) =0.015

b)

z =sqrt(X²) =2.44

p value =0.015