2. [16 marks] Work out your answer to the following questions 'by hand'. You may still use R to obtain probabilities and quantiles from the appropriate distributions. A study investigated if psychotherapy combined with limited administration of 3,4 Methylenedioxymetham phetamine (MDMA) can reduce symptoms of post-traumatic stress disorder. Severity of symptoms was measured Via the CAPSIV score with higher scores indicating more severe symptoms. Fortyeight patients recruited to the study with twenty-four patients being ran- domly allocated each of the two dosage levels (Low 40 mg, High 125 mg). The primary outcome was the reduction in CAPS-IV score one month after the end of treatment. The forty-eight patients at the commencement of the study had an average CAPS-IV score of 81.35 with a sample standard deviation of 17.54. At the end of treatment, the High dose group experienced an average drop in CAPS-IV score of 24.2 with a sample standard deviation of 23.1. The Low dose group experienced an average drop in CAPS-IV score of 12.7 with a sample standard deviation of 19.4. (a) Determine a 95% condence interval of the population mean CAPS-IV score of pa- tients at commencement of the study. [2 marks] (b) Does the data provide evidence that the high dose MDMA treatment is associated with a decrease in mean CAPS-IV score? State the null and alternative hypotheses, and determine the appropriate test statistic and pvalue. What do you conclude? [2 marks] (C) (d) Researchers would like to determine if patients experience a greater decrease in CAPS- IV score with the high dose MDMA treatment than low dose MDMA treatment. State the null and alternative hypotheses, and determine the appropriate test statistic and pvalue. What do you conclude? [4 marks] A secondary outcome was whether the patient experienced a drop of 20% or more in CAPS-IV score. In the high dose treatment group 11 patients experienced such a drop in CAPS-IV score. Construct a 95% condence interval for the population proportion of patients that would experience a 20% or more drop in CAPS-IV score with the high dose treatment. [2 marks] In addition to the 11 patients in the high dose treatment group who experienced a 20% or more drop in CAPS-IV score, 6 patients in the low dose treatment group also experienced a 20% or more drop in CAPS-IV score. The researchers would like to test if the population proportion of patients that would experience a 20% or more drop in CAPS-IV score is greater with a high dose treatment than the low dose treatment. State the null and alternative hypotheses, and determine the appropriate test statistic and pvalue. What do you conclude? [4 marks] Do you have any concerns that the assumptions for the analysis in part (e) are satis- ed? Justify your answer. [2 marks]