Dr. Kirkland R. Gable studied 20 male juvenile delinquents who had each spent 6 months or more in a Massachusetts juvenile detention center. He wondered whether simply asking the juvenile delinquents to talk would help them stay out of jail in the future. The subjects were paid to talk into a tape recorder about anything they wanted for one hour, 3-5 days a week for 6 months; there was no therapist present. A control group was formed by matching each subject in the experimental group with a juvenile delinquent who was the same age, had the same ethnic background, grew up in the same town, had committed the same types of offenses, and had spent the same amount of time incarcerated. The control group received no treatment. The experimental and control groups were followed for three years. The data are available at the website... for the number of months of incarceration in the 3-year period following the 6-month long experiment; The histogram shows the differences for the entire data set: experimental minus control. A negative difference means a subject in the experimental group spent less time in jail than did his control (which is the outcome the researcher is hoping for). Although these subjects were not a random sample, we can test to see whether the difference is too large to attribute to chance if we assume the matched subjects in the control group were chosen at random.
a. Summarize the months of incarceration for both groups in one or two sentences. Include appropriate numerical summaries.
b. Perform a sign test to determine whether the typical amount of jail time after the experiment was less for the treatment group than for the control group. Use a significance level of 0.05.

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10 6 4 2 -20-15-10 -5 0 5 10 Difference, Experimental minus Control (months)