A subtle form of racial discrimination in housing is \"racial steering.\" Racial

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 were presented in court to show the locations of recently rented apartments.

Is there evidence of racial steering? Answer the questions below concerning the appropriate hypothesis test.

Question 1. What is the appropriate null hypothesis?

1

Section A and black renters are not independentSection and race of renter are not independent     Race of renter and Section are independent.Section B and white renters are independent

Question 2. What is the value of the test statistic for this hypothesis test?

Question 3. What is the P-value for this test?

Note: To find the P-value using Excel:

In Excel 2010, in the menu bar click on "Formulas > Insert Function"; in the Insert Function dialoge window, in the Category area choose "Statistical", in the "select a function" area, choose CHISQ.DIST.RT

In Excel 2007, in the menu bar click on "Formulas > Insert Function"; in the Insert Function dialoge window, in the Category area choose "Statistical", in the "select a function" area, choose CHIDIST.

In Excel 2003, in the menu bar click "Insert > Function"; in the Insert Function dialoge window, in the Category area choose "Statistical", in the "select a function" area, choose CHIDIST.

3 (Use 6 decimal places)

Question 4. Let p1 and p2 be the proportions of black renters in Section A and Section B, respectively. What is the value of the test statistic for the 2-sided hypothesis test using the two-proportion z procedure?

4

Question 5. What is the P-value for this test?

5 (Use 6 decimal places)

Question 6. What is the relationship between these two hypothesis tests?

The negative of the square of the test statistic in question 2 is equal to the test statistic in question 4 and the P-values are equal.The square of the test statistic in question 4 is equal to the test statistic in question 2 and the P-values are equal.    The square of the P-value in question 3 is equal to the P-value in question 5 and the square of the test statistic in question 4 is equal to the test statistic in question 2.

New Renters White Black Section A 87 8 Section B 83 34

Explanation / Answer

1)

null - Race of renter and Section are independent.

2)

hence TS = 14.0577

3) p-value = 0.000177

4)

Test and CI for Two Proportions

Sample   X    N Sample p
1        8   95 0.084211
2       34 117 0.290598

Difference = p (1) - p (2)
Estimate for difference: -0.206388
95% CI for difference: (-0.305821, -0.106955)
Test for difference = 0 (vs 0): Z = -3.75 P-Value = 0.000

Fisher’s exact test: P-Value = 0.000

TS = -3.75

5)p-value = 0.000

6)

The square of the test statistic in question 4 is equal to the test statistic in question 2 and the P-values are equal.  

c1 c2 total r1 87 8 95 r2 83 34 117 total 170 42 212 Oi 87 8 83 34 Ei 76.17925 18.82075 93.82075 23.17925 TS (O--Ei)^2/Ei 1.537016 6.221256 1.248005 5.051447 14.05772 critical value 3.84 p-value 0.000177284

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