2. (12 points) Research examined the clinical efficacy of a new antidepressant in 15 study participants with depression. Participants were randomly assigned to one of three groups: a placebo, low dose of the drug, or moderate dose of drug. After 2 months of treatment, the subjects completed the Beck Depression Inventory (httpsz/lwwwapa.org/pi/about/publications/caregivers/practice- settings/assessment/tools/beckdepression) in which a higher score represents higher depression. Using the data from the study below, use the appropriate test to help the researchers understand the efficacy of their drug. You may use SPSS or hand calculations. Placebo Low Dose Moderate Dose 38 22 14 47 19 26 39 8 11 25 23 18 42 31 5 39 21 13 46 18 25 37 9 11 25 22 19 40 30 6 41 23 15 48 17 24 4O 10 14 26 22 17 41 30 6 a) What test will you use and why? (b) What is the null hypotheses? (c) Compute the Test Statistic. State the degrees of freedoms associated with your test statistic. (d) Compare your computed test statistic to the critical test statistic for alpha=.05. State your conclusion based on this comparison. Explain how you chose the critical test statistic for comparison. (e) Is there a significant difference between groups? Clearly state each null hypothesis and show your results supporting significant pairwise differences between the 3 groups