In clinical experiments involving distinct groups of independent samples, it is important that the groups be similar in the important ways that affect the experiment. In an experiment designed to assess the effectiveness of paroxetine for treating bipolar depression. subjects were measured using the Hamilton depression scale with the surmnary results given below [based on data om a \"Double-Blind. Placebo- Controllecl Comparison of Imipramine and Paroxetine in the Treatment of Bipolar Depression." by Nemeroffet 31.,Americon Journal ofPsychian'y, Vol. 158: No. 6]. [lower scores indicate lower depression] Calculate the 90% confidence inten'al for the population difference in mean Hamilton depression scale scores for the treatment and placebo groups \"by-hand\" by coding the steps in R. Then use an R function to check your results. Report and interpret the interval in the context of the problem. Assume equal population variances 1a-'hen doing your calculations. (2 points)