A recruiter for a computer company would like to determine whether there are dif
ID: 3150264 • Letter: A
Question
A recruiter for a computer company would like to determine whether there are differences in sales ability between business, arts, and science graduates. She takes a random sample of 12 business graduates who have been working for the company for the past 2 years. She then takes a sample of 12 from graduates with an arts degree and graduates from a science degree. The commission earned (in $1,000s) by each student in the sample was recorded as is recorded as follows:………… Business Degree: 42.8, 25.9, 33.1, 43.5, 51.7, 30.2, 46.3, 42.8, 43.7, 47.7, 44.1, 41.5.………... Arts Degree: 34.1, 28, 34.9, 36.2, 40.9, 25.3, 50.3, 43, 40.1, 47.5, 42.9, 43.3………….. Science Degree: 34.4, 31, 26, 32.9, 44.7, 29.8, 41.3, 33.4, 24.5, 25.8, 30.5, 21.9. Answer the following questions......... Part a. What is the response variable in this experiment?............ Part b. What are the treatments in this experiment?.............Part c. Can you conclude that there are differences in mean earned commissions among the three types of degrees? Perform the appropriate test at alpha = .10. Be sure to show all the required parts of a hypothesis test. Part d. Provide a post hoc analysis if you find a difference exists using the method
Explanation / Answer
a. What is the response variable in this experiment?
Solution: The response variable for this experiment is given as the commission earned by student.
b. What are the treatments in this experiment?
Solution: There are three treatments in this experiment such as business degree, arts degree and science degree.
c. Can you conclude that there are differences in mean earned commissions among the three types of degrees? Perform the appropriate test at alpha = .10. Be sure to show all the required parts of a hypothesis test.
Solution:
Here, we have to use the one way analysis of variance or ANOVA for checking the significant differences in the mean earned commissions among the three types of degrees. We are given a level of significance as 0.10.
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There is no significant difference in the earned commission by students in the three types of degrees such as business degree, arts degree and science degree.
Alternative hypothesis: Ha: There is a significant difference in the earned commission by students in the three types of degrees such as business degree, arts degree and science degree.
We are given a following data for the earned commissions among the three types of degrees.
Business Degree
Arts Degree
Science Degree
42.8
34.1
34.4
25.9
28
31
33.1
34.9
26
43.5
36.2
32.9
51.7
40.9
44.7
30.2
25.3
29.8
46.3
50.3
41.3
42.8
43
33.4
43.7
40.1
24.5
47.7
47.5
25.8
44.1
42.9
30.5
41.5
43.3
21.9
The ANOVA table for this test is given as below:
ANOVA: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Business Degree
12
493.3
41.10833333
56.7517
Arts Degree
12
466.5
38.875
55.6020
Science Degree
12
376.2
31.35
44.7300
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
627.3539
2
313.6769
5.9906
0.0060
2.4710
Within Groups
1727.9217
33
52.3613
Total
2355.2756
35
Level of significance
0.1
Here, we get the p-value as 0.006 which is less than the given level of significance 0.10 so we reject the null hypothesis that there is no significant difference in the earned commission by students in the three types of degrees such as business degree, arts degree and science degree.
d. Provide a post hoc analysis if you find a difference exists using the method
Solution:
For the above analysis, we get the p-value as 0.006 which is less than the given level of significance 0.10 so we reject the null hypothesis that there is no significant difference in the earned commission by students in the three types of degrees such as business degree, arts degree and science degree.
The post hoc tests for the above analysis are given as below:
Post Hoc Tests
Multiple Comparisons
Dependent Variable:Commision
(I) Degree
(J) Degree
Mean Difference (I-J)
Std. Error
Sig.
90% Confidence Interval
Lower Bound
Upper Bound
Tukey HSD
Business Degree
Arts Degree
2.23333
2.95413
.732
-4.0469
8.5135
Science Degree
9.75833*
2.95413
.006
3.4781
16.0385
Arts Degree
Business Degree
-2.23333
2.95413
.732
-8.5135
4.0469
Science Degree
7.52500*
2.95413
.041
1.2448
13.8052
Science Degree
Business Degree
-9.75833*
2.95413
.006
-16.0385
-3.4781
Arts Degree
-7.52500*
2.95413
.041
-13.8052
-1.2448
Scheffe
Business Degree
Arts Degree
2.23333
2.95413
.753
-4.3339
8.8005
Science Degree
9.75833*
2.95413
.009
3.1911
16.3255
Arts Degree
Business Degree
-2.23333
2.95413
.753
-8.8005
4.3339
Science Degree
7.52500*
2.95413
.052
.9578
14.0922
Science Degree
Business Degree
-9.75833*
2.95413
.009
-16.3255
-3.1911
Arts Degree
-7.52500*
2.95413
.052
-14.0922
-.9578
LSD
Business Degree
Arts Degree
2.23333
2.95413
.455
-2.7661
7.2328
Science Degree
9.75833*
2.95413
.002
4.7589
14.7578
Arts Degree
Business Degree
-2.23333
2.95413
.455
-7.2328
2.7661
Science Degree
7.52500*
2.95413
.016
2.5255
12.5245
Science Degree
Business Degree
-9.75833*
2.95413
.002
-14.7578
-4.7589
Arts Degree
-7.52500*
2.95413
.016
-12.5245
-2.5255
Bonferroni
Business Degree
Arts Degree
2.23333
2.95413
1.000
-4.3275
8.7942
Science Degree
9.75833*
2.95413
.007
3.1975
16.3192
Arts Degree
Business Degree
-2.23333
2.95413
1.000
-8.7942
4.3275
Science Degree
7.52500*
2.95413
.047
.9641
14.0859
Science Degree
Business Degree
-9.75833*
2.95413
.007
-16.3192
-3.1975
Arts Degree
-7.52500*
2.95413
.047
-14.0859
-.9641
*. The mean difference is significant at the 0.10 level.
Homogeneous Subsets
Commision
Degree
N
Subset for alpha = 0.10
1
2
Tukey HSDa
Science Degree
12
31.3500
Arts Degree
12
38.8750
Business Degree
12
41.1083
Sig.
1.000
.732
Scheffea
Science Degree
12
31.3500
Arts Degree
12
38.8750
Business Degree
12
41.1083
Sig.
1.000
.753
Means for groups in homogeneous subsets are displayed.
a. Uses Harmonic Mean Sample Size = 12.000.
Business Degree
Arts Degree
Science Degree
42.8
34.1
34.4
25.9
28
31
33.1
34.9
26
43.5
36.2
32.9
51.7
40.9
44.7
30.2
25.3
29.8
46.3
50.3
41.3
42.8
43
33.4
43.7
40.1
24.5
47.7
47.5
25.8
44.1
42.9
30.5
41.5
43.3
21.9