1. Some criminologists argue there is a relationship between “impulsivity” and criminal offending. The idea is that impulsive people act on immediate gratification and that since crime involves quick pleasure and only the long-term possibility of any cost (getting caught and punished), it should be highly attractive to them. To test this notion you take a random sample of 120 people, you give them a personality test that includes a measure of impulsivity. Based on this test, you divide your sample into two groups: (1) the non-impulsive group (n=80) and, (2) the impulsive group (n=40). You then ask each person to report the number of criminal offenses they have committed in the last year. Finally, you calculate the mean number of self-reported offenses for each group, and here is the data you get:
n1 = 40 n2 = 80
X1= 13.5 X2 = 10.3
s1 = 4.9 s2 = 4.0
a). Test the null hypothesis that there is no difference between the two groups versus the alternative hypothesis that those who are impulsive commit more criminal offenses. Use an alpha of .01 and label each step of your hypothesis test. Assume that the two population standard deviations are equal (σ1 = σ2), and make sure to properly interpret your results.
I've got no idea how to do this, anybody that can help?