The director of the MBA program wishes to investigate if the average GPA of MBA
ID: 3322992 • Letter: T
Question
The director of the MBA program wishes to investigate if the average GPA of MBA students varies with the size of university (small, medium and large) and type of MBA (regular, professional and executive) program. In order to investigate this issue, the director randomly picked 4 universities for each of the 9 university type-MBA program combinations and collected the average GPA of the MBA students. The data is in MBA.sav. Does the mean GPA differ for the three sizes of the university? Does the mean GPA differ for the three types of MBA programs? Does the MBA type affect the mean GPA of the university size? State the appropriate hypothesis, run the appropriate statistical test and provide interpretation. Which combination of university size and MBA program type results in the lowest average GPA?
Univ Size MBA Type GPA
1 1 2.56
1 1 2.69
1 1 2.71
1 1 2.47
1 2 2.78
1 2 2.67
1 2 2.60
1 2 2.76
1 3 2.84
1 3 2.95
1 3 2.82
1 3 2.91
2 1 2.64
2 1 3.18
2 1 2.82
2 1 2.91
2 2 3.09
2 2 3.15
2 2 3.00
2 2 3.24
2 3 4.05
2 3 3.98
2 3 4.09
2 3 3.82
3 1 3.20
3 1 3.40
3 1 3.04
3 1 2.89
3 2 3.64
3 2 3.45
3 2 3.55
3 2 3.38
3 3 3.40
3 3 3.45
3 3 3.18
3 3 3.60
Explanation / Answer
Solution:
Here, we have to use two way analysis of variance or ANOVA test for testing the significant difference in population means. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: Average GPA of MBA students do not varies with the size of university and type of MBA.
Alternative hypothesis: Ha: Average GPA of MBA students varies with the size of university and type of MBA.
For this hypothesis test, we will assume 5% level of significance. = 0.05
Descriptive statistics and ANOVA table for this test by using excel are summarised below:
Descriptive Statistics
Dependent Variable: GPA
University Size
MBA type
Mean
Std. Deviation
N
Small
Regular
2.6075
.11325
4
Professional
2.7025
.08342
4
Executive
2.8800
.06055
4
Total
2.7300
.14251
12
Medium
Regular
2.8875
.22500
4
Professional
3.1200
.10100
4
Executive
3.9850
.11902
4
Total
3.3308
.51352
12
Large
Regular
3.1325
.21869
4
Professional
3.5050
.11387
4
Executive
3.4075
.17385
4
Total
3.3483
.22795
12
Total
Regular
2.8758
.28379
12
Professional
3.1092
.35408
12
Executive
3.4242
.48504
12
Total
3.1364
.43655
36
Source
DF
SS
MS
F
P
University type
2
2.9746
1.4873
70.649
0.00
MBA type
2
1.8174
0.9087
43.165
0.00
Interaction
4
1.3099
0.3275
15.556
0.00
Error
27
0.5684
0.0211
1
Total
35
6.6702
For this ANOVA table, we get p-value for university type as 0.00 which is less than = 0.05, so university type is statistically significant. P-value for MBA type is 0.00 and P-value for interaction of the university type and MBA type is also 0.00; this means MBA type and interaction are statistically significant. All variables and interaction is statistically significant.
So, we reject the null hypothesis that Average GPA of MBA students do not varies with the size of university and type of MBA.
There is sufficient evidence to conclude that Average GPA of MBA students varies with the size of university and type of MBA.
Descriptive Statistics
Dependent Variable: GPA
University Size
MBA type
Mean
Std. Deviation
N
Small
Regular
2.6075
.11325
4
Professional
2.7025
.08342
4
Executive
2.8800
.06055
4
Total
2.7300
.14251
12
Medium
Regular
2.8875
.22500
4
Professional
3.1200
.10100
4
Executive
3.9850
.11902
4
Total
3.3308
.51352
12
Large
Regular
3.1325
.21869
4
Professional
3.5050
.11387
4
Executive
3.4075
.17385
4
Total
3.3483
.22795
12
Total
Regular
2.8758
.28379
12
Professional
3.1092
.35408
12
Executive
3.4242
.48504
12
Total
3.1364
.43655
36