Data handling
a. Below is the data view of the dataset
b. Shown below is the variable view of the dataset
2. Descriptive statistics
The process and results of obtaining descriptive statistics of continuous variables are as below. The mean ± standard deviation of age, exam marks, assignment marks, and IQ are 20.50 ± 1.842, 82.79 ± 12.594, 81.88 ± 10.695, 105.17 ± 16.282 respectively
Descriptive Statistics
N
Minimum
Maximum
Mean
Std. Deviation
Age
24
18
24
20.50
1.842
Exam Marks (for a maximum of 100)
24
55
99
82.79
12.594
Assignment Marks (for a maximum of 100)
24
55
95
81.88
10.695
intelligence quotient
24
72
136
105.17
16.282
Valid N (listwise)
24
The chart below shows gender is coded as 0 or 1
The following are the process and results of descriptive statistics for categorical variables. There were more females (58.3) than males. (41.7). Observe from the table that juniors (33) had the most frequency followed closely by a sophomore (29) while seniors (8) had the least frequency.
Sex (M=Male, F=Female)
Frequency
Per cent
Valid Percent
Cumulative Percent
Valid
Male
10
41.7
41.7
41.7
Female
14
58.3
58.3
100.0
Total
24
100.0
100.0
Year in College (1=Freshman; 2=Sophomore; 3=Junior; 4=Senior)
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
Freshman
5
20.8
20.8
20.8
Sophomore
7
29.2
29.2
50.0
Junior
8
33.3
33.3
83.3
Senior
2
8.3
8.3
91.7
20
1
4.2
4.2
95.8
30
1
4.2
4.2
100.0
Total
24
100.0
100.0
The pie chart below shows the distribution for years in College.
The histogram for IQ is created as below. The data follows the normal distribution.
The scatter plot of exam marks versus IQ below shows a linear association between the two.
The scatter plot of IQ versus sex is shown below. The IQ of females is distributed higher those that of males.
h. The difference in the mean IQ per gender is as below. Males have a lower mean IQ (94.5) than their female (112.79) counterparts.
Mean IQ for each gender
Mean
Sex (M=Male, F=Female)
intelligence quotient
Male
94.50
Female
112.79
Total
105.17
Data analysis
The analysis and result of the One-Sample T-test are shown below.
Null hypothesis: exam marks are not significantly larger than 75
The p-value (.006) is less than a 5% significance level therefore the null is rejected. Hence exam marks are significantly larger than 75
One-Sample Statistics
N
Mean
Std. Deviation
Std. Error Mean
Exam Marks
24
82.79
12.594
2.571
One-Sample Test
Test Value = 75
t
df
Sig. (2-tailed)
Mean Difference
95% Confidence Interval of the Difference
Lower
Upper
Exam Marks
3.031
23
.006
7.792
2.47
13.11
The following is the analysis and result of the Independent samples t-test
Null hypothesis: There are no significant differences in the exam marks between men and women. The p-value (.001) is less than a 5% significance level therefore the null is rejected. Hence there are significant differences in the exam marks between men and women.
Group Statistics
Sex (M=Male, F=Female)
N
Mean
Std. Deviation
Std. Error Mean
Exam Marks (for a maximum of 100)
Male
10
72.90
13.153
4.159
Female
14
89.86
5.641
1.508
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
Exam Marks
Equal variances assumed
14.459
.001
-4.327
22
.000
-16.957
3.919
-25.084
-8.830
Equal variances not assumed
-3.833
11.385
.003
-16.957
4.424
-26.654
-7.260
Shown below is the process and result obtained from running a paired samples t-test.
Null hypothesis: There is no significant difference between the exam marks and the assignment marks. The p-value (.659) is greater than the 5% significance level therefore the null is not rejected. Hence there is no significant difference between the exam marks and the assignment marks.
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
Exam Marks
82.79
24
12.594
2.571
Assignment Marks
81.88
24
10.695
2.183
Paired Samples Correlations
N
Correlation
Sig.
Pair 1
Exam Marks & Assignment Marks
24
.638
.001
Paired Samples Test
Paired Differences
t
df
Sig. (2-tailed)
Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the Difference
Lower
Upper
Pair 1
Exam Marks – Assignment Marks
.917
10.056
2.053
-3.330
5.163
.447
23
.659
d. The correlation analysis and result between gender, IQ, exam and assignment marks are as below. All the correlations are significant at a 5% significance level. Exam marks are positively and highly correlated to assignment marks and sex but moderately correlated to IQ. Similarly, assignment marks are positively and highly correlated to IQ but moderately correlated to sex.
Correlations
Exam Marks (for a maximum of 100)
Assignment Marks (for a maximum of 100)
intelligence quotient
Sex (M=Male, F=Female)
Exam Marks (for a maximum of 100)
Pearson Correlation
1
.638**
.461*
.678**
Sig. (2-tailed)
.001
.023
.000
N
24
24
24
24
Assignment Marks (for a maximum of 100)
Pearson Correlation
.638**
1
.768**
.450*
Sig. (2-tailed)
.001
.000
.027
N
24
24
24
24
intelligence quotient
Pearson Correlation
.461*
.768**
1
.566**
Sig. (2-tailed)
.023
.000
.004
N
24
24
24
24
Sex (M=Male, F=Female)
Pearson Correlation
.678**
.450*
.566**
1
Sig. (2-tailed)
.000
.027
.004
N
24
24
24
24
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
The dummy coding for IQ is implemented as below. IQ lower than 105 is 0 while IQ higher than 105 is 1.
Do a multiple regression analysis to explain the variance in assignment marks using the independent variables of age; sex; and IQ (dummy coded) and interpret the results.
The following is the ANOVA for the regression.
Null hypothesis: The model is not significant.
The p-value (.005) is less than a 5% significance level therefore the null is rejected. Hence the model is significant.
ANOVA
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
1212.291
3
404.097
5.698
.005b
Residual
1418.334
20
70.917
Total
2630.625
23
a. Dependent Variable: Assignment Marks (for a maximum of 100)
b. Predictors: (Constant), Year in College (1=Freshman; 2=Sophomore; 3=Junior; 4=Senior), iQ(Dummy coded), Sex (M=Male, F=Female)
The coefficients table for the analysis is shown below.
Null hypothesis: The respective model coefficients are not significant in the model. Only the constant and IQ coefficients are significant in the model. Their p-values were 0.00 and 0.017 respectively warranting the rejection of their respective null hypotheses.
Coefficients
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
78.149
3.321
23.534
.000
iQ(Dummy coded)
12.125
4.669
.579
2.597
.017
Sex (M=Male, F=Female)
-.757
4.869
-.036
-.156
.878
Year in College (1=Freshman; 2=Sophomore; 3=Junior; 4=Senior)
-.450
.281
-.279
-1.600
.125
a. Dependent Variable: Assignment Marks (for a maximum of 100)
The r-squared shows that 67.9% of the variations of assignment marks are explained in the model.
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.679a
.461
.380
8.421
a. Predictors: (Constant), Year in College (1=Freshman; 2=Sophomore; 3=Junior; 4=Senior), iQ(Dummy coded), Sex (M=Male, F=Female)