THE PROBLEM: The U.S. Department of Education (USDE) issues periodic reports on
ID: 3340224 • Letter: T
Question
THE PROBLEM: The U.S. Department of Education (USDE) issues periodic reports on variables related to higher education. One concern for the country is the amount of student debt incurred by those attending universities and colleges. Does the type of institution affect debt status? The USDE investigates both the amount of debt owed and the percent of borrowed amount still owed after 12 years. Large amounts of debt make these types of purchases average percent of borrowed amount still owed after 12 years? To investigate the USDE sampled average amounts of debt owed among the 5 basic types of institutions: 1) public 2-years institutions, 2) public 4-ye institutions, 3 institutions. The data collected is shown below. it more difficult for college graduates to buy major purchases such as vehicles and homes. Delaying affects the overall US economy. Does the type of institution attended affect the institutions, 3) private non-profitinstitutions, 4) private for-profit institutions and S) other classes of YOUR TASK: Perform the necessary statistical analysis to determine whether the mean percent of borrowed amount still owed after 12 years differs among the 5 classes of higher education institutions. Public 2YR Public 4YR PrivateNP PrivateP Others 62.1 66.2 67.3 83.4 77.5 70.9 84.4 61.8 57.4 54.3 50.5 57.5 64.8 64.9 67.4 67.1 57.6 55.6 69.1 52.9 52.0 59.8 59.0 62.4 50.7 57.2 52.1 54.2 50.4 73.3 42.5 49.3 58.066.866.6 63.0 73.0 62.3 77.9 58.7 60.9 63.6 78.8 70.9 81.0 74.8 73.0 67.0 69.1 65.1 60.6 77.0 69.8 70.4 60.1 66.1 65.6 76.8 68.9 77.2 78.2 76.9 75.1 64.2Explanation / Answer
Solution:
Here, we have to check the hypothesis or claim whether the mean percent of the borrowed amount still owed after 12 years differs among the 5 classes of higher education institutions or not. For checking this claim, we have o use single factor ANOVA or one way analysis of variance. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: Mean percent of the borrowed amount still owed after 12 years do not differs among the 5 classes of higher education institutions.
Alternative hypothesis: Ha: Mean percent of the borrowed amount still owed after 12 years differs among the 5 classes of higher education institutions.
H0: µ1 = µ2 = µ3 = µ4 = µ5
Versus
Ha: H0 is not true.
We assume 5% level of significance ( = 0.05) for this test.
Required ANOVA test is given as below:
(Calculations are carried out by using excel data analysis.)
ANOVA: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Public 2YR
13
954.1
73.39230769
50.4458
Public 4YR
13
780.9
60.06923077
37.4573
Public NP
13
720.9
55.45384615
57.1910
Public P
13
877.7
67.51538462
48.4331
Others
13
910.1
70.00769231
31.1841
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
2819.2148
4
704.8037
15.6824
0.0000
2.5252
Within Groups
2696.5354
60
44.9423
Total
5515.7502
64
Level of significance
0.05
From the above ANOVA table, test statistic F is given as 15.6824.
P-value = 0.00 < = 0.05
So, we reject the null hypothesis that Mean percent of the borrowed amount still owed after 12 years do not differs among the 5 classes of higher education institutions.
There is sufficient evidence to conclude that Mean percent of the borrowed amount still owed after 12 years differs among the 5 classes of higher education institutions.
ANOVA: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Public 2YR
13
954.1
73.39230769
50.4458
Public 4YR
13
780.9
60.06923077
37.4573
Public NP
13
720.9
55.45384615
57.1910
Public P
13
877.7
67.51538462
48.4331
Others
13
910.1
70.00769231
31.1841
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