Question

7-3) A criminologist wanted to see if there is a significant difference in the sentence length [in months] between white and minority offenders convicted of drug-related crimes. She randomly selects a sample of 35 white offenders [mean sentence length = 49; std. dev. = 14] and a sample of 25 non-white offenders [mean sentence length = 60; std. dev. = 12].

1. Formulate the null hypothesis stating no racial difference in the sentence length
2. Formulate the alternative hypothesis
3. Using the independent-sample t test, test the null hypothesis [H0]
4. List the value of the critical t you used to test H0 [df = n1 + n2 – 2; p = .05; 2-tail test]
5. Reach a statistical conclusion using p = .05, 2-tail test, and the appropriate degrees of freedom
6. Interpret your results

Answer 1

Given:

  

  

We want to test if there is a significant difference in the sentence length [in months] between white and minority offenders convicted of drug-related crimes.

a) The hypothesis testing problem is:

Null hypothesis: There is no significant racial difference in the sentence length between white and minority offenders convicted of drug-related crimes.

i.e

b) Alternative Hypothesis:There is a significant racial difference in the sentence length between white and minority offenders convicted of drug-related crimes.

i.e

c) The test statistic is:

Where

Therefore,

d) Here degrees of freedom is n1+n2-2=58 and level of significance is 0.05,for two tail test

hence the critical t value is tcrit=-2.000 ### Using t table

e) Since -3.179<-2.000, we reject the null hypothesis at 5% level of significance with 58 degrees of freedom.

f) Therefore we conclude that there is a significant racial difference in the sentence length between white and minority offenders convicted of drug-related crimes.