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 65 people who responded to a personality test showing they were impulsive and a second independent random sample of 80 who indicated by the test that they were not impulsive. Each person was asked to report the number of criminal offenses they have committed in the last year. For the group of 65 impulsive people, they have a mean number of criminal acts of 13.5 with a standard deviation of 4.9. For the group of 80 non-impulsive people, they have mean number of criminal acts of 10.3 with a standard deviation of 4.0. Test the hypothesis that there is no difference between the two groups in the number of delinquent acts. Use an alpha of 0.01. Assume that the two population standard deviations are equal (σ1 = σ2).

What is your test statistic?