Quantitative Analysis

Running Head: QSO/501 1
Quantitative Analysis
By (Name of Student)
(Institutional Affiliation)
(Date of Submission)

QSO/510
2
Question 1
A subtle form of racial discrimination in housing is "racial steering." Racial steering
occurs when real estate agents show prospective buyers only homes in neighborhoods
already dominated by that family's race. Tenants at a large apartment complex recently
filed a lawsuit alleging racial steering. The plaintiffs claimed that potential renters were
steered to Section A, while African-American renters were steered to Section B. The
accompanying 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?
Data to use on this question
- White
African-
American Total
Section 91 9 100
Section 91 28 119
Total 192 37 219
Solution
To solve this problem, we need to first state the null and alternative hypotheses under
consideration before we compute the χ2 statistic.
Ho: There is no association between race and the section of the apartment complex.
HA: There is an association between race and the section of the apartment complex.
The formula for computing χ2 statistic is given by;
χ2∗=∑ (Oi−Ei) 2/Ei, where Oi and Ei is the ith observation and the ith expected count.

QSO/510
3
From the data given, we then calculate the expected count using the formula;
E= (row total × column total)/sample size.
We compute the χ2 statistic as follows;
Observed (O) Expected
(
Observed-Expected)^2/Exp
ected
Section A, white 91 78.38776 0.557762051
Section A,African
American 9 13.61224 3.211941445
Section B, white 91 88.61224 0.49340495
Section B,African
American 28 15.38776 2.84133089
TOTAL 219 196 7.104439336
χ2 = 7.104439336,
χ2 = 7.104 (rounded to 3 decimal .places)
Find the P-value.
Solution
Degrees of freedom = (2-1)*(2-1) = 1, χ2 = 7.1044
P-value from chi-square calculator is 0.007689
Decision

QSO/510
4
State your conclusion at the significance level α = 0.05.
Solution
If the p- value less than or equal to the alpha α or level of significance, then we reject the null
hypothesis in favor of the alternative hypothesis, otherwise we fail to reject the null hypothesis.
In this case, the p-value, 0.007689, is less than alpha (α = 0.05). That is 0.007689<0.05.
Therefore, we reject the null hypothesis.
Reject H0. There is sufficient evidence to conclude that there is an association between race and
the section of the apartment complex in which people live.
Question 2
Newspaper headlines at the time and traditional wisdom in the succeeding decades have
held that women and children escaped a sunken ship in greater proportion than men.
Here's a table with the relevant data. Do you think that survival was independent of
whether the person was male or female? Defend your conclusion.
Female Male Total
Alive 393 315 708
Dead 116 1348 1464
Total 509 1663 2172
Solution
A. H0: Survival was independent of gender on the ship. 0
HA: There is an association between survival and gender on the ship.
B. Are the conditions for inference satisfied?