Question

4. 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: TechniqueA: 23.1,21.4,31.6, 34.5, 21.9,36.0,30.2, 33.1,39.5 TechniqueB:32.7,36.8, 39.1, 37.3,40.3,46.8,41.4, 53.0,55.6,54.1, 28.3 We wish to test vs. using a 0.05 (a) Graph the data as you see fit. Why did you choose the graph(s) you did and what does it (do they) tell you? Also calculate summary statistics relevant to the research question (b) Use the bootstrap to perform the test, using B 10000 resamplings and set.seed(1 Display the histogram of your generated values. Compute your tob and a p-value. Make a reject or not reject decision. Finally, state your conclusion in the context of the problem (c) Use R to perform a two-group t test for means (i) assuming equal variance and then ii) not assuming equal variance (Welch's T) and report the p values from each. Describe how the three p values are related. Explain how the histogram in part (b) and the summary statistics in part (a) hinted at this relationship

Answer 1

Solution: Construct the Wilcoxon Rank Sum test by using R-lang State the hypothesis: Null hypothesis: Alternative hypothesis: Level of significance α = 0.05 R-language Procedure Step 1: Enter the x values. Step 2: Enter the Y values. Step 3: Enter analysis name as "Wilcox test(x, y)" R-language output > x<-c 23.1, 21.4, 20.6, 15.5, 21.9, 36.0, 30.2, 33.1, 33.4) >y<-c( 32.7, 36.8, 39.1, 37,3, 40,3, 순6.8, 75.5, 53.0, 55.6, 54.1, 55.7) wilcox.test (x,y) Wilcoxon rank sum test data: x and y W3, p-value8.335e-05 alternative hypothesis: true locati n shift is n t equal to 0 From the output, the p-value is 0.0000 Conclusion: Since p-value (0.000) lesser than level of significance α-0.05 . we reject the null hypothesis. Therefore, the mean of two independent variables is not to zero