1. It is often said that the criminal sentences given to minority offenders are more severe than those given to whites. You examine how this works in a federal district court. You take a sample of 100 bank robbery cases where the convicted offender was white and a second independent sample of 100 cases where the convicted offender was either African-American or Hispanic. Here's the data that you get:

White Minority

n₁ = 100 n₂ = 100

s₁ = 17s₂ = 28

Test the null hypothesis that there is no difference between the two groups versus the alternative hypothesis that white suspects are sentenced on average to fewer months.Use an alpha of .05 and label each step of your hypothesis test. You cannot assume that the two population standard deviations are equal (_{1 2}), make sure to state each step of the hypothesis test and properly interpret your results, and use 20 as your degrees of freedom. What conclusion would you draw from these data?

2. The District of Columbia Police has recently tried to increase the number of arrests made by police officers. You want to know if arrests have actually increased. You look at a sample of 6 police officers, and measure the number of arrests each month for the month before and after the policy change. Test the null hypothesis that the before and after number of arrests are equal, against the alternative that the number of arrests are higher after the policy change. Use an alpha of .01. What are your conclusions?

Person	Before x1	After x2
A	1	3
B	3	2
C	0	2
D	2	3
E	0	2
F	1	4