Administrators at the Graduate School were interested in finding out the effects
ID: 3133721 • Letter: A
Question
Administrators at the Graduate School were interested in finding out the effects of two variables: college attended (Private [PR] versus public [PU]) and computer literacy (familiar with computers [FA] versus not familiar with computers [NF]) on the GRE scores of applicants to their various graduate programs. They collected data on 24 applicants and saved these in a SPSS dataset (listed below, show how it was inputed)
College 1=PR 2=PU Computer 1=FA 2=NF GRE
1 1 2200
1 1 2400
1 1 2200
1 1 2400
1 1 2300
1 1 2200
1 2 2200
1 2 1600
1 2 1900
1 2 1900
1 2 1400
1 2 2400
2 1 2200
2 1 2400
2 1 2300
2 1 2300
2 1 2300
2 1 2200
2 2 1700
2 2 1500
2 2 1400
2 2 1800
2 2 1700
2 2 1500
They had the following alternative hypotheses:
Hypothesis 1: applicants who attended private colleges will on average have significantly higher GRE scores than those who attended public universities
Hypothesis 2: applicants who are not familiar with comuters will on average have significantly lower GRE scores than those who are familiar with computers, and
Hypothesis 3: the effect of computer literacy on GRE scores will vary significantly depending on whether one attended a public or a private university.
(1) What type of analysis should you use for this problem?
(2). In SPSS, perform the appropriate analysis on the difference among the effects on GRE scores? write each step down
(3). Report the results for hypothesis 2: Hypothesis 2: F(______,_____)=________,p_________
(4). Write your conclusion about the hypothesis 2 results in everyday language. Be sure to include a statement about whether or not hypothesis 2 was supported.
(5). Report the results for hypothesis 3: F(______,_____)=________,p________
(6). Write your conclusion about the results for hypothesis 3 in everyday language. Be sure to include a statement about whether or not hypothesis 3 was supported.
(7). What are the GRE score mean and standard deviation of those who attended private colleges and are not familiar with computers? Mean=_______, SD=_______
Explanation / Answer
Two sample t test and ANOVA
Administrators at the Graduate School were interested in finding out the effects of two variables: college attended (Private [PR] versus public [PU]) and computer literacy (familiar with computers [FA] versus not familiar with computers [NF]) on the GRE scores of applicants to their various graduate programs. They collected data on 24 applicants and saved these in a SPSS dataset (listed below, show how it was inputed)
College
Computer
GRE
1
1
2200
1
1
2400
1
1
2200
1
1
2400
1
1
2300
1
1
2200
1
2
2200
1
2
1600
1
2
1900
1
2
1900
1
2
1400
1
2
2400
2
1
2200
2
1
2400
2
1
2300
2
1
2300
2
1
2300
2
1
2200
2
2
1700
2
2
1500
2
2
1400
2
2
1800
2
2
1700
2
2
1500
(1) What type of analysis should you use for this problem?
Here, we have to use the two sample t test and two way analysis of variance (ANOVA).
(2). In SPSS, perform the appropriate analysis on the difference among the effects on GRE scores? Write each step down
The t test for checking the significant difference in GRE scores for the private and public colleges is given as below:
Group Statistics
College
N
Mean
Std. Deviation
Std. Error Mean
GRE
Private
12
2091.6667
326.01822
94.11335
Public
12
1941.6667
375.27767
108.33333
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
GRE
Equal variances assumed
1.715
.204
1.045
22
.307
150.00000
143.50413
-147.60934
447.60934
Equal variances not assumed
1.045
21.578
.307
150.00000
143.50413
-147.94690
447.94690
Here, we get the p-value as 0.307 which is greater than the given level of significance 0.05, so we do not reject the null hypothesis that there is no any significant difference in the average GRE scores for the private college and public college.
Now, we have to check the significant difference between the average GRE scores for the familiar with computers and not familiar with computers by using the t test. The t test is given as below:
Group Statistics
Computer
N
Mean
Std. Deviation
Std. Error Mean
GRE
Familiar with computers
12
2283.3333
83.48471
24.09996
Not Familiar with computers
12
1750.0000
311.88576
90.03366
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
GRE
Equal variances assumed
10.092
.004
5.722
22
.000
533.33333
93.20337
340.04137
726.62530
Equal variances not assumed
5.722
12.568
.000
533.33333
93.20337
331.27433
735.39234
Here, we get the p-value as 0.00 which is less than the given level of significance 0.05, so we reject the null hypothesis that there is no any significant difference in the average GRE scores for the familiar with computers and not familiar with computers.
Now we have to check whether there is a significant interaction between the type of college and familiarity of computer for GRE scores by using the two way ANOVA which is given as below:
Between-Subjects Factors
Value Label
N
College
1.00
Private
12
2.00
Public
12
Computer
1.00
Familiar with computers
12
2.00
Not Familiar with computers
12
Tests of Between-Subjects Effects
Dependent Variable:GRE
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Intercept
Hypothesis
9.761E7
1
9.761E7
57.191
.084
Error
1706666.667
1
1.707E6
College
Hypothesis
135000.000
1
135000.000
1.000
.500
Error
135000.000
1
135000.000b
Computer
Hypothesis
1706666.667
1
1706666.667
12.642
.175
Error
135000.000
1
135000.000b
College * Computer
Hypothesis
135000.000
1
135000.000
3.080
.095
Error
876666.667
20
43833.333c
a. MS(Computer)
b. MS(College * Computer)
c. MS(Error)
For the interaction, we get the p-value as 0.095 which is greater than the alpha value 0.05, so we do not reject the null hypothesis that there is no any significant interaction between the type of college and familiarity of computer for GRE scores.
(3). Report the results for hypothesis 2: Hypothesis 2: F(10.092, 22) ,p = 0.004
(4). Write your conclusion about the hypothesis 2 results in everyday language. Be sure to include a statement about whether or not hypothesis 2 was supported.
We concluded that there is no any significant difference in the average GRE scores for the familiar with computers and not familiar with computers.
(5). Report the results for hypothesis 3: F(3.080,1), p = 0.095
(6). Write your conclusion about the results for hypothesis 3 in everyday language. Be sure to include a statement about whether or not hypothesis 3 was supported.
We concluded that there is no any significant interaction between the type of college and familiarity of computer for GRE scores.
(7). What are the GRE score mean and standard deviation of those who attended private colleges and are not familiar with computers? Mean= 2091.6667, SD= 94.11335
Group Statistics
College
N
Mean
Std. Deviation
Std. Error Mean
GRE
Private
12
2091.6667
326.01822
94.11335
Public
12
1941.6667
375.27767
108.33333
College
Computer
GRE
1
1
2200
1
1
2400
1
1
2200
1
1
2400
1
1
2300
1
1
2200
1
2
2200
1
2
1600
1
2
1900
1
2
1900
1
2
1400
1
2
2400
2
1
2200
2
1
2400
2
1
2300
2
1
2300
2
1
2300
2
1
2200
2
2
1700
2
2
1500
2
2
1400
2
2
1800
2
2
1700
2
2
1500
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