A criminologist is interested in possible disparities between sentences given to

Question

A criminologist is interested in possible disparities between sentences given to males and females convicted in murder-for-hire cases. Selecting 14 cases involving men convicted of trying to solicit someone to kill their wives and 16 cases involving women convicted of trying to solicit someone to kill their husbands, the criminologist finds the following.

Mean length of sentence for males= 7.34 years with a standard deviation of 2.51 years

Mean length of sentence for females= 9.19 years with a standard deviation of 3.78 years

Assume that you're working with a .05 level of significance

a. formulate an appropriate null hypothesis

b. calculate t statistic

c. identify the critical value

d. state your conclusion

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0   [ANSWER]

***************************

b)

At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    7.34          
X2 =    9.19          
              
Calculating the standard deviations of each group,              
              
s1 =    2.51          
s2 =    3.78          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    14          
n2 = sample size of group 2 =    16          
Thus, df = n1 + n2 - 2 =    28          
Also, sD =    1.158892636          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -1.596351501   [ANSWER]

******************************

c)      
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is, by table/technology,              
              
tcrit =    +/-   2.048407142   [ANSWER]

****************************

d)  
              
As |t| < 2.048,    WE FAIL TO REJECT THE NULL HYPOTHESIS.          

Hence, there is no significant difference between the average sentences given to males and females convicted in murder-for-hire cases at 0.05 level. [CONCLUSION]

*****************************************************

Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.