A criminologist was interested in whether there was any disparity in sentencing

Question

A criminologist was interested in whether there was any disparity in sentencing based on the race of the defendant. She selected a random sample of 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.

(a) using these data and a = 0.05, Test the null hypothesis that whites and blacks convicted of distribution of cocaine do not differ with respect to sentence length.

3. A criminologist was interested in whether there was any disparity in sentencing based on the race of the defendant. She selected a random sample of 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 4 a. Using these data and .05, test the null hypothesis that whites and blacks convicted of distribution of cocaine do not differ with respect to sentence length. b Using these same data and = 01, what is the result? Explain why the result is the same or different.

Explanation / Answer

PART A.
Given that,
mean(x)=4
standard deviation , s.d1=1.5635
number(n1)=10
y(mean)=6.2222
standard deviation, s.d2 =1.7873
number(n2)=9
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.306
since our test is two-tailed
reject Ho, if to < -2.306 OR if to > 2.306
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =4-6.2222/sqrt((2.44453/10)+(3.19444/9))
to =-2.87
| to | =2.87
critical value
the value of |t | with min (n1-1, n2-1) i.e 8 d.f is 2.306
we got |to| = 2.8703 & | t | = 2.306
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -2.8703 ) = 0.021
hence value of p0.05 > 0.021,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -2.87
critical value: -2.306 , 2.306
decision: reject Ho
p-value: 0.021
that whites
and blacks convicted of distribution of cocaine differ
with respect to sentence length

PART B, WHEN ALPHA = 0.01
critical value
the value of |t | with min (n1-1, n2-1) i.e 8 d.f is 3.355
we got |to| = 2.8703 & | t | = 3.355
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -2.8703 ) = 0.021
hence value of p0.01 < 0.021,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -2.87
critical value: -3.355 , 3.355
decision: do not reject Ho
p-value: 0.021
that whites
and blacks convicted of distribution of cocaine do not differ
with respect to sentence length. the result we achived is diffrent since we compare the test statistic with diffrent signficance value

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