Two new mathematics learning techniques are being tested. Twenty students are ra
ID: 3150784 • Letter: T
Question
Two new mathematics learning techniques are being tested. Twenty students are randomly selected from a population. nA = 9 of them are randomly assigned to use technique A and the other nB = 11 are assigned to use technique B. Each student spends 30 minutes learning his or her assigned technique and then are asked to complete a task. The time to complete the task is recorded in seconds. A shorter time indicates better mastery of the task. The data are: 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.
Explanation / Answer
a) Ans: We can not plot the data. Because, it contain different sample sizes.
b) Ans: Test Hypothesis: H0 : µA µB = 0 vs. HA : µA µB 6= 0, using = 0.05.
The calculated p-value using bootstrap is 0.003 and it is less than 0.05. Therefore, we reject the null hypothesis and accept the alternative hypothesis. Hence, we can conclude that the mean time to complete the task using technique B is longer than technique A mean that technique A is better than technique B.
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