A criminologist is interested in sentences given to males and females convicted

Question

A criminologist is interested in 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.

It is assumed that a 1-year difference in the length of sentence is considered substantial. The criminologist is trying to show that sentences for females are substantially longer than those for males. Answer questions (a) -- (f) based on the above information.

(d) The degrees of freedom of the test are

(f) What is the conclusion?

Explanation / Answer

a)

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

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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]

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

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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]

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