Question

Online classes are becoming more and more prevalent at the college level. A statistics instructor randomly sampled ten students from his traditional face-to-face class and ten students from his online class to compare their comprehension of the material that was taught in the class. He administered the same evaluation to each student and wants to use the Wilcoxon Rank Sum test to compare their scores. The results are shown below:

Traditional Class

82 91 75 68 93 85 74 70 56 82

Online Class

67 66 72 73 77 76 48 81 86 92

What alternative hypothesis should the instructor test to show that the students in the traditional class outperformed the students in the online class? 4) A) The distribution of the scores for the traditional class is shifted to the right of the distribution of the scores for the online class. B) The distribution of scores for the traditional class is shifted to the right or to the left of the distribution of scores for the online class. C) The distribution of scores for the traditional class is shifted to the left of the distribution of scores for the online class. D) The distribution of scores for the traditional class is identical to the distribution of scores for the online class

Answer 1

Solution:

The given data is presented below;

Sample	Traditional		Sample	Online
1	82		2	67
1	91		2	66
1	75		2	72
1	68		2	73
1	93		2	77
1	85		2	76
1	74		2	48
1	70		2	81
1	56		2	86
1	82		2	92

First, we combine the samples together and organize it in ascending order, by retaining the sample numbers which is shown in the table below:

Sample	Scores
2	48
1	56
2	66
2	67
1	68
1	70
2	72
2	73
1	74
1	75
2	76
2	77
2	81
1	82
1	82
1	85
2	86
1	91
2	92
1	93

Now, that the values that are in ascending order are assigned ranks to them, taking care of assigning the average rank to values with rank ties

Sample	Scores	Rank	Adjusted for tie
2	48	1	1
1	56	2	2
2	66	3	3
2	67	4	4
1	68	5	5
1	70	6	6
2	72	7	7
2	73	8	8
1	74	9	9
1	75	10	10
2	76	11	11
2	77	12	12
2	81	13	13
1	82	14	14.5
1	82	15	14.5
1	85	16	16
2	86	17	17
1	91	18	18
2	92	19	19
1	93	20	20

The sum of ranks for sample 1:

R1=2+5+6+9+10+14.5+14.5+16+18+20=115

The sum of ranks for the second sample

R2=1+3+4+7+8+11+12+13+17+19=95

Hence, the test statistic is R=R1=115.

Rejection region:

The rejection region for this test is Rc=60, and the Null hypothesis will be rejected of R<60.

Decision: Since R=115>60, we fail to reject the null hypothesis and conclude that there is not enough evidence to claim that the population median of differences is greater than 0, at the 0.05 significance level.

What alternative hypothesis should the instructor test to show that the students in the traditional class outperformed the students in the online class?

4) A) The distribution of the scores for the traditional class is shifted to the right of the distribution of the scores for the online class.