. An economist is curious to know if level of education has an impact on the per
ID: 3328014 • Letter: #
Question
. An economist is curious to know if level of education has an impact on the per capita income of an individual. He finds out that individual’s age also impacts their per capita income. He administers survey to 100 participants. The economist wants to answer the following research question: Is there a difference in per capita income (measured in $) depending on level of education after accounting for differences in the age of the participant? The SPSS outputs are provided below. Respond to the following questions based on the SPSS outputs.
State the null and alternate hypothesis. 1 point
What is/are the independent variable(s) and how many levels do they have? 1 point
What is the dependent variable? 1 point
What is the covariate? 1 point
Comment on the homogeneity of variance assumption. 1 point
Does age have a significant influence on per capita income? 1 point
Does education level have a significant influence on per capita income? 1 point
Are there any statistically significant differences in per capita income based on level of education? 1 point
Write up the summary results in a scholarly manner. 2 points
Between-Subjects Factors
Education Level
N
1
25
2
25
3
25
4
25
Levene's Test of Equality of Variances
F
df1
df2
Sig.
.022
3
96
.995
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
Design: Intercept+Age+Education Level
Tests of Between-Subjects Factors
Source
Type III Sum
of Squares
DF
Mean
Square
F
Sig.
Corrected Model
1667.436a
7
238.205
5.218
.000
Intercept
17079.57
1
17079.57
374.163
.000
Education Level
193.595
3
64.532
1.414
0.244
Age
231.69
1
231.69
5.076
0.027
Education Level*Age
11.363
3
3.788
0.083
0.969
Error
4199.564
92
45.647
Total
126276.000
100
Corrected Model
5867.000
99
R Squared = .284 (Adjusted R Squared = .230)
Descriptive Statistics
Education Level
Mean
Std. Deviation
N
1
30.68
6.713
25
2
69.8
6.708
25
3
31.56
6.272
25
4
36.76
7.513
25
Total
34.7
7.698
100
Tests of Between-Subjects Factors
Source
Type III Sum
of Squares
DF
Mean
Square
F
Sig.
Corrected Model
1656.073a
4
414.018
9.34
.000
Intercept
17505.92
1
17505.92
394.94
.000
Age
249.233
1
249.233
5.623
.002
Education Level
1323.306
3
441.102
9.951
.000
Error
4210.927
95
44.326
Total
126276
100
Corrected Model
5867
99
R Squared = .282 (Adjusted R Squared = .252)
Education Level
Education Level
Mean
Std. Error
95% Confidence
Interval
Lower
Bound
Upper
Bound
1
30.883a
1.334
28.234
33.532
2
39.882a
1.332
37.238
42.527
3
31.695a
1.333
29.05
34.341
4
36.339a
1.343
33.672
39.006
Covariates appearing in the model are evaluated at the following values: Actual Age = 36.28
Estimated Marginal Means of Per Capita Income
Education Level
Education Level
Mean
Std. Error
95% Confidence
Interval
Lower
Bound
Upper
Bound
1
30.883a
1.334
28.234
33.532
2
39.882a
1.332
37.238
42.527
3
31.695a
1.333
29.05
34.341
4
36.339a
1.343
33.672
39.006
Covariates appearing in the model are evaluated at the following values: Actual Age = 36.28
Education Level
N
1
25
2
25
3
25
4
25
Explanation / Answer
1. H0: There is no difference in per capita income (measured in $) depending on level of education after accounting for differences in the age of the participant
H1: There is difference in per capita income (measured in $) depending on level of education after accounting for differences in the age of the participant
2. Dependent variance is Per capita income
3. Covariance for education level and age = 3.788
4. According Levene's test, P=0.995 which is greater than 0.05, so we accept H0
That is there is no significance difference between their varainces
5. P-value of age = .027 which is less than alpha 0.05, so we do not accept H0
Thus we conclude that age have a significant influence on per capita income
6. P-value of Education level = .244 which is > alpha 0.05, so we accept H0
Thus we conclude that education level have not a significant influence on per capita income
7. There is no statistically significant differences in per capita income based on level of education
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