Question

A subtle form of racial discrimination in housing is "racial steering." Racial steering occurs when real estate agents show prospective buyers homes only in neighborhoods already dominated by that family's race. This violates the Fair Housing Act of 1968. According to an article in Chance magazine (Vol. 14, no. 2 [2001]), tenants at a large apartment complex recently filed a lawsuit alleging racial steering. The complex is divided into two parts, Section A and Section B. The plaintiffs claimed that white potential renters were steered to Section A, while African Americans were steered to Section B. The table below shows the data that was presented in court to show the locations of recently rented apartments.
New Renters
White Black
Section A 87 8
Section B 83 34
Is there evidence of racial steering?

Compute a p-value and confidence interval.

Answer 1

	Observed Frequencies
	WHITE	BLACK					Total
A	87	8					95
B	83	34					117
Total	170	42					212
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	WHITE	BLACK					Total
A	170*95/212=76.179	42*95/212=18.821					95
B	170*117/212=93.821	42*117/212=23.179					117
Total	170	42					212
	(fo-fe)^2/fe
A	1.537	6.221
B	1.248	5.051

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   14.058
  
Level of Significance =   0.05
Number of Rows =   2
Number of Columns =   2
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1
  
p-Value =   0.0002
Decision:    p-value < α , Reject Ho
Critical Value =   3.841
Decision: test stat,X² > critical value , So, Reject the null hypothesis  

There is racial steering

Please revert back in case of any doubt.

Please upvote. Thanks in advance.