Philanthropic organizations, such as the Gates Foundation, care about the return of their investment, too. For example, if a foundation spends $7,000 for preschool education of children who are at risk, does society get a reasonable return on this investment? A key component of the social benefit is the reduction in spending for crimes later in life. In the High/Scope Perry Preschool Project, 128 children were randomly assigned to a year of regular education or to an intensive preschool program that cost an additional $10,600 per pupil in 2005. By age 27, those in the preschool program averaged 2.3 fewer crimes (with standard error 0.85) than those who were not in the preschool program.

a) Explain why it is Important that the children in this school were randomly assigned to the preschool program.
b) Does the 95% confidence interval for the reduction in crime in the preschool group include zero? Is this Important?
c) If the total cost per crime averages $25,000 (in costs for police, courts, and prisons), give a confidence interval for the savings produced by this preschool program using your interval in (b)