In a recent study 32 convicts were given a course in great works of literature. To be accepted for the program the convicts had to be literate and to convince a judge of their intention to reform. After thirty months of parole only 6 of these 32 had committed another crime. This group's performance was compared against a similar group of 40 parolees who were not given the literature course; 18 of these 40 had committed a new crime after thirty months.

(a) Can we use a large sample confidence interval with this data or do we need a plus four confidence interval? Explain.

(b) Give a 99.9% large sample confidence interval if it can be trusted; otherwise, give the plus four confidence interval.