Two new mathematics learning techniques are being tested Twe

Two new mathematics learning techniques are being tested. Twenty students were randomly selected from a population. nA = 9 of them were randomly assigned to use technique A, and nB = 11 of them were randomly assigned to use technique B. Each student spent 30 minutes learning the technique to which they were assigned, and then were asked to complete a task. The time to complete the task was recorded, in seconds. A shorter time indicates better mastery of the task. The data are below: Technique A: 23.1, 21.4, 20.6, 15.5, 21.9, 36.0, 30.2, 33.1, 33.4 Technique B: 32.7, 36.8, 39.1, 37.3, 40.3, 46.8, 75.5, 53.0, 55.6, 54.1, 55.7 We wish to test: H0 : µA µB = 0 vs. HA : µA µB 6= 0, using = 0.05. (a) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you? (b) Use the bootstrap to perform the test, using B = 10000 resamplings. Compute a p-value, and make a reject or not reject decision. Finally, state your conclusion in the context of the problem. (c) Use the Wilcoxon Rank Sum test to perform the test. You may use R. Compute a p-value, and make a reject or not reject decision. Finally, state your conclusion in the context of the problem.

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