9. A drug is studied for possible improvement of behavior rating of patients suffering from a specific type of mental illness. The study recruited 10 patients who were randomly assigned to a treatment group (patients receiving the drug) and a placebo group (patients receiving a placebo). Two behavioral rating scores were recorded for each subject, a "Before" score (the score at the beginning of the clinical trial) and an "After" score (the score 3 months later). You may assume normal distribution for the scores. One patient in the placebo group dropped out. (a) Find the 95% confidence interval for placebo effect. (b) Find the 95% confidence interval for the placebo-adjusted drug effect. [hint: (a) placebo effect is defined as the parameter = "mean of After" minus "mean of Before" for the placebo group; (b) the parameter of interest = ("mean of After" minus "mean of Before" for the treatment group) minus the placebo effect defined in (a)] Placebo group PL1 PL2 PL3 PL4 Before 1.9 1.5 1.7 2.4 After 1.92 1.45 1.75 2.54 Treatment TR1 group Before After TR2 TR3 TR4 TR5 1.7 2.6 1.6 1.6 2.3 2.2 2.45 1.72 1.63 2.45