2} In a paper published in 1905 in The Journal of Physiology (vol. 32, pp. 501510}, the famous Scottish pharmacologist and physiologist Arthur Cushny (1856-1926) and an instructor at the University of Michigan, Alvin Peebles {18841917}, compared various tropane alkaloids as hypnotics. Ten patients with chronic sleep loss were each tested on four treatments, namely a control and three drugs: duboisine and a left or right isomer of hyoscine (also known as Devilis Breath). The table below gives the average hours of sleep for each patient with no drug, and their amount of sleep averaged over the three drugs. Patients Condition 1 2 3 4 5 ti 7 8 9 10 Drug 1.97 3.20 5.00 4.90 5.30 7.50 7.47 4.10 4.20 5.87 Control 0.60 1.10 2.50 2.80 2.90 3.00 3.20 4.?0 5.50 6.20 Nonparametric tests were conducted in order to determine whether the patients are sleeping longer on average under the "drug" condition than under the "no drug" condition. (a) Does the sign test reject the null hypothesis at the 1% level? TRUE O FALSE O (b) What is the expected value of Wilcoxon's signed rank statistic under Ho? (c) What is the p-value of the signed rank test in this case? (d) Which of the sign test and the signed rank test is more likely to detect a difference between the two groups, given that a real difference exists? Justify your