A program to reduce recidivism has been in effect for two years in a large northeastern state. A sociologist investigates the effectiveness of the program by taking a random sample of 200 prison records of repeat offenders. The records were selected from the files in the courthouse of the largest city in the state. The average length of time out of prison between the first and second offenses is 2.8 years with a standard deviation of 1.3 years.
a. Use this information to estimate the mean prison- free time between first and ­second offenses using a 95% confidence interval.
b. Identify the group for which the confidence interval would be an appropriate estimate of the population mean.
c. Would it be valid to use this confidence interval to estimate the mean prison-free time between first and second offenses for all two- time offenders in the whole state? In a large southern state?