Philanthropic organizations care about the return on their investment. 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 a study, 125 children were randomly assigned to a year of regular education or to an intensive preschool program that cost an additional $11,700 per pupil in 2005. By age 27, those in the preschool program averaged 2.3 fewer crimes (with standard error 0.89) than those who were not in the preschool program. Complete parts (a) through (c) below. (a) Explain why it is important that the children in this study were randomly assigned to the preschool program. Choose the correct answer below. OA. Randomly assigned children will result in a 100% confidence interval. OB. Randomly assigned children will result in bias data. OC. The random assignment of the children is important because this will allow the margin of error to be zero. D. The random assignment of the children is important in order to claim that the results from the study are not bias. (b) Does the 95 % confidence interval for the reduction in crime in the preschool group include zero? A. Yes, the 95% confidence interval for the population proportion is to ]. [ (Round to two decimal places as needed.) B. No, the 95% confidence interval for the population proportion is [0.55 to 4.05]. (Round to two decimal places as needed.) Is this important? OA. No, this is not important because confidence intervals always contain zero. OB. Yes, if zero is included in the confidence interval, then it is possible that there is a difference between the preschool programs. OC. No, this is not important because confidence intervals never contain zero. D. Yes, if zero is included in the confidence interval, then it is possible that there is no difference between the preschool programs. (c) If the total cost per crime averages $22,000 (in costs for police, courts, and prisons), give a confidence interval for the savings produced by this preschool program using your interval in (b). The 95% confidence interval for the mean cost is [$ to $. (Round to the nearest cent as needed.)