Wilcoxon Rank-Sum Test A researcher is comparing the annual income of students w
ID: 2622412 • Letter: W
Question
Wilcoxon Rank-Sum Test
A researcher is comparing the annual income of students who graduated from Belair College with students who graduated from Chapman University. A random sample was chosen from each college were selected. At a .10 level of significance is there a difference in the incomes of the students from the two colleges? Show all five steps of the hypothesis test. Show your ranking of the data.
Belair Chapman
Income
(in thousands)
Rank
Income
(in thousands)
Rank
31.6
58.5
33.4
31.1
14.7
36.4
30.5
24.3
36.1
46.2
33.6
30.5
31.3
39.5
35.6
51.5
57.0
41.2
37.8
22.2
20.5
36.4
28.1
72.8
34.9
41.6
33.7
28.8
40.3
32.4
36.3
56.4
44.5
33.4
37.4
Income
(in thousands)
Rank
Income
(in thousands)
Rank
31.6
58.5
33.4
31.1
14.7
36.4
30.5
24.3
36.1
46.2
33.6
30.5
31.3
39.5
35.6
51.5
57.0
41.2
37.8
22.2
20.5
36.4
28.1
72.8
34.9
41.6
33.7
28.8
40.3
32.4
36.3
56.4
44.5
33.4
37.4
Explanation / Answer
We calculate the necessary data for the given values
Step 1) Stating the Research Question
The population of interest is the income of the students of the 2 colleges. The parameter of interest is the difference in the two means. Since the parameter is the difference of the two population means a t test of a mean should be performed.
Step 2) Define Hypothesis:
Null Hyp: There is no difference in the incomes of the students from the two colleges
Alt Hyp: There is a significant difference in the incomes of the students from the two colleges
Step 3) Calculate the Test statistic
t = [ (x1 - x2) ] / SE
Where SE is standard error and is given by
SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(9.252/15) + (12.332/20)] = 3.65
Thus t = [ 33.27 - 40.07 ] / 3.65 = -1.863
Step 4) Compute probability of test statistic
Degrees of Freedom = n1 + n2- 2 = 15 + 20 - 2 = 33
P value for t=-1.863 and DoF = 33 is 0.071
5) Conclusions
Since the significance level is 0.10 the p value obtained is less than it.
0.071 < 0.10
Hence we reject the Null Hyp and conclude that There is a significant difference in the incomes of the students from the two colleges
The Ranked data is gicen below
Belair Chapman Mean 33.27333 40.07 Stdev 9.252217 12.32896 n 15 20Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.