A criminologist is interested in whether there was any disparity in sentencing based on the race of the defendant. She selected a random sample of 18 burglary convictions and recorded the prison terms given to the 10 white defendants and the 8 black defendants sampled. The sentence lengths (in years) for individuals in the two groups are shown below. Using these data and a .05 alpha level, test the null hypothesis that whites and blacks convicted of burglary in this jurisdiction do not differ with respect to prison sentence length.
White defendants 
Black defendants 

3 
4 

5 
8 

4 
7 

7 
3 

4 
5 

5 
4 

6 
5 

4 
4 

3 

2 
a.What is the null hypothesis for this test?
b.What is the alternative hypothesis for this test?
c.Is this a onesided or twosided test? How do you know?
d.Will you use a ztest or a ttest in this situation? Why?
e.What is the critical value of the test statistic?
f.What is the value of the test statistic calculated from the sample results?
g.What decision about the null hypothesis does your test lead to?
h.Is the observed racial difference in sentence length statistically significant? Explain.
i.Would your decision be different if you used an alpha level of .01? Explain.
j.If you increased the size of your sample by five times so that you had 50 white defendants and 40 black defendants, but the group means and variances remained the same, would you reach the same conclusion about the statistical significance of the racial difference in sentencing? Report the numbers used to make your decision.
Using Excel we get following output:
tTest: TwoSample Assuming Equal Variances 

White defendants 
Black defendants 

Mean 
4.3 
5 

Variance 
2.233333333 
2.857142857 

Observations 
10 
8 

Pooled Variance 
2.50625 

Hypothesized Mean Difference 
0 

df 
16 

t Stat 
0.93216885 

P(T<=t) onetail 
0.182551579 

t Critical onetail 
1.745883669 

P(T<=t) twotail 
0.365103159 

t Critical twotail 
2.119905285 

Steps Involve:
Copy data > Data > Data Analysis > ttest: Two Sample Assuming Equal Variance > ok > Variable 1 range (give/ select the range of white defendant) then variable 2 range (give/ select the range of black defendant) select alpha (1^{st} 0.05) give output range >ok.
Or we can find manually also
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