Two new mathematics learning techniques are being tested. Twenty students were r
ID: 3151940 • Letter: T
Question
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.
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
Explanation / Answer
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.
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
R script
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, 46.8, 75.5, 53.0, 55.6, 54.1, 55.7)
wilcox.test(x,y)
R output
Wilcoxon rank sum test
data: x and y
W = 3, p-value = 8.335e-05
alternative hypothesis: true location shift is not equal to 0
Calculated P=0.00008335 which is < 0.05 level.
The null hypothesis is rejected.
There is significant difference between the two new mathematics learning techniques.
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