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.

white black Total

Section A 75 14 89

Section B 81 26 107

Total 156 40 196

compute all answers to three decimal places

a) What is the value of the text statistic X^2?

b) What is the P-value for the chi-square test of homogeneity?

c) Find the z-value using the two-proportion test of homogeneity?

d) what is the p-value for the two proportion Z-test?

e)What is the relationship between the z-value and x^2?

f) Compare the two p-values.

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	White	Black	Total
	section A	70.84	18.16	89
	section B	85.16	21.84	107
	total	156	40	196
chi square    χ2	=(Oi-Ei)2/Ei	White	Black	Total
	section A	0.2447	0.9543	1.1990
	section B	0.2035	0.7937	0.9973
	total	0.4482	1.7480	2.1962
test statistic X2 =		2.196

b)

p value from excel =chidist(2.196,1) =0.138

c)

x1                =	75	x2                =	81
p̂1=x1/n1 =	0.8427	p̂2=x2/n2 =	0.7570
n1                       =	89	n2                       =	107
estimated prop. diff =p̂1-p̂2    =		0.0857
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.7959
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0578
test stat z=(p̂1-p̂2)/Se =		1.482

d_)

p value =2*(1-normsdist(1.482)) =0.138

e)X² =z²

f) both p values are same