2.7. A study of recidivism classified offenders by type of punishment received: prison, jail, probation, fine, or community service. A researcher interested in the effects of these different punishments analyzes data on a sample of 967 offenders. She computes two regression models. In the first, she includes variables for age, sex, race, number of prior arrests, severity of the last conviction offense, and length of punishment. The R2 for this model is 0.27. In the second model, she adds four dummy variables for jail, probation, fine, and community service, using prison as the reference category. The R2 for this model is 0.35. Explain whether the type of punishment had an effect on recidivism (assume a 5% significance level).