Question

Dr. Roh was interested in whether there was any disparity in sentencing based on the race of the defendant. He selected at random 19 drug convictions for cocaine distribution and completed the prison terms given to the 10 whites and 10 blacks sampled. The sentence lengths (in years) are shown below for the white and black offenders

White	Black
3	4
5	8
2	7
7	7
4	5
5	9
5	7
4	4
3	5
2	8

FYI,

White	Black
s2/1= 2.20	s2/2=2.84

1. Please write down the null and Dr. Roh’s research hypotheses. (5 points)
2. What is the critical t – value from t-table based on df and an alpha level of .05? (5 points)
3. What is the obtained t – value based on your calculation? (10 points)
4. State your final conclusion regarding the results from this test. (10 points)

Answer 1

(a)

H0: Null Hypothesis: \mu 1=\mu 2 (There is no disparity based on the race of the defendant)

HA: Research Hypothesis: \mu 1\neq \mu 2 (There is disparity based on the race of the defendant)

(b)

\alpha = 0.05

ndf = n1 + n2- 2 = 10 + 10 - 2 = 18

From Table, critical values of t = \pm 2.1009

(c)

From the given data, the following statistics are calculated:

n1 = 10

\bar{x}1 = 4

s1 = 1.5635

n2 = 10

\bar{x}2 = 6.4

s2 = 1.7764

Test Statistic is:

t = (4-6.4)/0.7483 = - 3.2072

So,

t - value = - 3.2072

(d)

Since calculated value of t = - 3.2072 is less than critical value of t = - 2.1009, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that there is disparity based on the race of the defendant