Styles 3. Testing the Difference between Two Sample Means (20 points) Dr. Roh wa
ID: 2946227 • Letter: S
Question
Styles 3. Testing the Difference between Two Sample Means (20 points) Dr. Roh was very 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 compared the prison terms given to the 10 whites and 9 blacks sampled. The sentence lengths (in years) are shown below for the white and black offenders. White Black 8 7 9 3 Question: Using these data and a-.05, test the null hypothesis that whites and blacks convicted of distribution of cocaine do not differ with respect to sentence length. FYI, s2.20 sž 2.84 0 PExplanation / Answer
HO: there is no significant difference in the mean sentence length between white and black. U1=u2
H1: there is a significant difference in the mean sentence length between white and black. U1=/=u2
T =
= (Xbar1-Xbar2)/sqrt(s1^2/n1 + s2^2/n2)
= (4.0909-6.2222)/sqrt(0.2083+0.3549)
-2.8400
df=
(s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1))
(0.2083+0.3549)^2/(0.2083^2/(11-1) + 0.3549^2/(9-1))
7
Alpha= 5%
t(a/2, df) =t(0.05/2,7)
p-value
2*(1-P(T<|t|)
2*(1-P(T<abs(-2.84))
T.DIST.2T(abs(-2.84),7)
0.025044609
With t=-2.84 p<5%, i reject Ho and conclude that there is a significant difference in the mean sentence length between white and black. U1=/=u2
SAMPLE 1 SAMPLE 2 N= 11 9 Mean= 4.09 6.22 S= 1.5136 1.7873 s^2/n 0.2083 0.3549