Question

Tenants at a large apartment complex recently filed a lawsuit alleging racial steering. The plaintiffs claimed that white potential renters were steered to Section​ A, while black renters were steered to Section B. The table displays the data that were presented in court to show the locations of recently rented apartments. Do you think there is evidence of racial​ steering?

white black

Section A 94 25

Section B 87 27

Compute the​ chi-square statistic.

chi squared χ2=__

​(Round to two decimal places as​ needed.)

Find the​ P-value.

The​ P-value is__

​(Round to three decimal places as​ needed.)

Based on these​ results, what is your​ conclusion?

Answer 1

The null and alternative hypothesis

H0: There is no relationship between race and section

Ha : There is a relationship between race and section

Test statistic

where Oi : observed frequency

Ei : expected frequency

The contingency table

	white	black	total
A	94	25	119
B	87	27	114
total	181	52	233

Expected frequency calculation

E(94) = 119*181/233

E(25) =119-E(94)

etc

The contingency table of expected and observed frequency

	white	black	total
A	94(92.44)	25(26.56)	119
B	87(88.56)	27(25.44)	114
total	181	52	233

The expected frequencies are in the parenthesis

Calculation of Chi square

	Oi	Ei	(Oi-Ei)^2/Ei
	94	92.44	0.0263
	25	26.56	0.0916
	87	88.56	0.0275
	27	25.44	0.0957
total			0.2411

Thus

0.24

degrees of freedom = (2-1)*(2-1) = 1

Note : degrees of freedom = ( number of rows -1) *( number of columns-1)

P value = 0.624

Since P value > 0.05

We reject H0

There is no sufficient evidence of racial steering.

Note : Excel formula for P value "=CHISQ.DIST.RT(0.24,1)"