Q5 13 Points The Hamilton Anxiety Rating Scale is a measure of severity of anxiety in humans. The scale ranges from 0 to 56 with higher scores indicating greater anxiety. Twenty-four university students were recruited, then randomly assigned to two equal-sized groups. The first group attended an aerobic exercise class three times a week. The second group attended a yoga class three times a week. After 12 weeks, each student's anxiety score was recorded. The first few lines of data are shown below. > head (anxiety) treatment score 1 aerobics 25 2 aerobics 15 3 aerobics 27 4 aerobics 22 5 aerobics 18 6 aerobics 23 Stacked histograms of the data are shown below. O IN WO IN W 0- 1- 2- 3- 1- 0- 2- aerobics yoga 10 20 score 30 Output from a summary() command and results of a Wilcoxon rank-sum test are shown below. > summary(anxiety$treatment) aerobics 12 yoga 12 > summary(anxiety$treatment) aerobics 12 yoga 12 > wilcox.test(score-treatment, data=anxiety, alternative="greater", exact=FALSE, correct=FALSE) + Wilcoxon rank sum test data: score by treatment W = 105.5, p-value = 0.02624 alternative hypothesis: true location shift is greater than 0 Q5.1 Statistical conclusion 8 Points Write a statistical conclusion to answer the research question, "does yoga reduce anxiety more than aerobics?" Enter your answer here Q5.2 Causal inference 3 Points Based on the results of the analysis above, can one say that differences in the treatments caused differences in anxiety? Answer yes or no, and explain briefly. Enter your answer here Q5.3 Two-sided test 2 Points What would the p-value be from a two-sided Wilcoxon rank-sum test using the data described above? Enter your answer here