Impact of Part-Time Work on Student Performance

This study examines the impact of part-time work on student performance. Data analysis is conducted to evaluate the relationship between part-time work and academic success. The findings suggest that there is no significant correlation between the number of hours spent working and final marks.

Introduction
The performance of students in higher education institutions is affected by various
factors. A Subject Coordinator at MMP is concerned about the performance of his student
over the past seven years. He obtains the data which contains various information about
students enrolled in particular subjects. The aim for this paper is to the data and help the
Subject Coordinator understand whether engagement in part time work really affects the
performance of his students.
The first task was to use implement two different sampling methods to obtain
samples within the same data set. The first sample of 25 students, Sample 1, was selected
randomly from the original data with 200 students. The Data Analysis Toolpak in Microsoft
Excel was used to identify the using the randomized technique. The second sample of 25
students, Sample 2, was systematically selected using Microsoft Excel Data analysis Toolpak,
where we selected the periodic technique so that every 8th Student Id was picked for the
sample. Then, we analyzed the data using descriptive statistics, confidence intervals,
hypothesis testing, and regression analysis to evaluate the relationships among the various
variables in the data set.
Data Analysis
In the sample of 200 students, 68 percent of students were enrolled in the accounting
major while 32 percent were enrolled in the business major.

Accounting
68%
Business
32%
Proportion of Students in the two Majors
Figure 1: Chart Showing the Proportion of Students Enrolled in the two Majors.
Of the students enrolled in the accounting major, 40 percent are female and 60 percent
are male. On the other hand, 45 percent of the students enrolled in the business major are
female and 55 percent are male. Therefore, from the sample we can say that there are more
male students enrolled in the accounting major compared to the business major.
A c c o un ti n g B u s i ne s s
P rop ort ion of St u d en t s in t h e Tw o M a j ors ba sed on
Gen d er
Figure 2: Chart Comparing Proportion of Students in the Two Majors Based on their Gender

Most of the student, which is 33.5% of sample, had a final grade of PA, with more
male students than female student scoring PA in their final grade. 78 percent of students who
attained grade CR were male while only 22 percent were female. Only 8.5% of the students
scored the highest grade, HD, with 53% of them being male and 47% being female. There
was a very slight difference in between the genders for the 15.5 percent of students who
scored D in their finals. There was an equal number of males who scored N and CR in the
finals. However, more female students scored N than CR in their finals.
HD D CR PA N
8
15
8
32
21
9
16
28
35
28
Distribution of Grades according to Gender
Female Male
Figure 3: Distribution of Grades according to Gender
In the business major, most student scored either N or PA in their finals. This number
makes up 75 percent of the students in the sample who have enrolled for the business major.
However, more accounting major students got a final grade of PA. There were more students
who attained the highest grade, HD in the accounting major than in the business major. This
was also similar for the grades D and CR. Almost the same number of students scored N in
both majors.

HD
D
CR
PA
N
15
22
31
43
25
2
9
5
24
24
Distribution of Grades according to Major
Business Accounting
Figure 4: Distribution of Grades according to Major
The sample average mark in the finals for the accounting major is 57.59 while the
sample average mark in the business major was 46.27. Overall, a female student seem to
perform better than a male student. This is because the pivot chart below show that the
average final score for female students was 54.57 which is greater than the average final
score of male students at 53.53.
The standard deviation is used to measure the variation of set of data relative to its
mean. In the sample, the standard deviation of the final score for female students and male
students is 21.50 and 21.58 respectively. Hence, the marks obtained by female students are
less variable than those of male students.

F M
53.00
53.20
53.40
53.60
53.80
54.00
54.20
54.40
54.60
Figure 5: Pivot Chart for Average Final Score according to Gender
The mean score in the finals for accounting major students was 57.59 while that of the
business major students was 46.27. Therefore, the sample data indicates that on average,
students who major in Accounting do better than students who are enrolled in Business
major.
Accounting
Business
0.00 10.00 20.00 30.00 40.00 50.00 60.00
Average Final Score according to Major
Figure 6: Pivot Chart for Average Final Score according to Major
In the sample, the average number of hours worked per week by students was 5.13
hours, while the average number of hours devoted to studying the subject was found to be
1.90 hours. From the table below we find that female students devoted an average of 2.01

hours per week to study the subject compared to an average of 5.40 hours per week spent
working. Similarly, male students spent an average of 4.92 hours per week working and an
average of 1.83 hours per week was devoted to studying. The results from the sample clearly
express that the students, regardless of gender, spent more hours per week working than
studying the subject.
Average hours devoted to
study
Average hours worked per
week
Female 2.01 5.40
Male 1.83 4.92
Table 1: Average Hours Spent Studying and working according to Gender
Inferential Statistics
Confidence Interval for Average Final Mark
We used the sample mean as our point estimate, which is the average final mark from
the students in our sample to estimate the mean mark for all students. The sample mean, for
final mark is, X = 53.98, the sample size, n = 200, with a sample standard deviation, s =
21.47
Since the sample is large (n > 30) we use the Z-test. The Z critical value at 95% confidence
level is 1.96. Therefore, the 95% confidence interval (CI) was obtained as:
X ± 1.96 ( s
√n )= 53.98 ± 1.96 ( 21.47
√ 200 ) = 53.98 ± 2.98
Hence, the lower limit for the population mean is 51.00 and the upper limit is 56.96.
This means that if other samples were collected, the mean of each of the sample would fall in
the interval [51.00, 56.96], 95% of the time.

Confidence Interval for Average Final Mark Obtained by Gender
In our previous calculations, we found that the average final mark for female students
was 54.56, with a standard deviation of 21.50. The sample size, n = 84. At 95% confidence
level, the Z critical value is 1.96. Hence, we found the 95% CI for mean mark of female
students to be: X ± 1.96 ( s
√n )= 54.56 ± 1.96 ( 21.50
√84 ) =54.56 ± 4.60. The lower limit is 49.96
and the upper limit is 58.86.
Similarly, we found that the average final mark for male students was 53.53, with a
standard deviation of 21.58. The sample size, n = 116. At 95% confidence level, the Z critical
value is 1.96. Hence, we found the 95% CI for mean mark of male students to be:
X ± 1.96 ( s
√n )= 53.53 ± 1.96 ( 21.58
√ 116 ) =53.53 ±3.93. The lower limit is 49.60 and the upper
limit is 57.46.
We can say that there is a 95 percent chance that the confidence interval [49.96,
58.86] contains the true average mark for all female students, and the confidence interval
[49.60, 57.46] contains the population mean of the final mark for all male students.
Hypothesis Testing
Hours Devoted to Studying
The past experience of the subject coordinator makes him believe that for a student to
pass the subject, they should devote on average, at least 1.9 hours per week to study the
material of the subject. We used hypothesis testing to verify the claim by the subject
coordinator. First, we set the null and alternate hypotheses as:
H0 : μ=1.9
Ha : μ<1.9
We used the Z-test, and calculated the test statistic as: x−μ
σ / √n = 1.9025−1.90
1.66/ √200 = 0.0213

The Z critical value at 5% significance level for one-tailed test is 1.645. The statistical
decision is to fail to reject the null hypothesis because the test statistic, 0.0213 < the critical
value, 1.645. Therefore we can conclude that there is no sufficient statistical evidence at 95
percent confidence level, to support the claim that if a student devotes on average at least 1.9
hours per week on the subject, the student is likely to pass the subject.
Hours Spent on Part-time Work
Earlier we found that the students in our sample spent an average of 5.13 hours per
week on part-time work. The sample standard deviation is 3.31, and the sample size is 200.
As established, the Z critical value at 95% confidence level is 1.96. Therefore, the 95%
interval estimation for the average number of hours worked by all students was calculated as:
X ± 1.96 ( s
√n )= 5.13 ± 1.96 ( 3.31
√ 200 ) =5.13 ± 0.4587 = [4.67, 5.59]
Supposing the true average is 5.125 hours, the sample results are statistically accurate
because this average fall between the calculated interval estimation of between 4.67 hours
and 5.59 hours. The results indicate that our methodology was quite accurate ant the results
are acceptable at 5 percent significance level.
The Subject coordinator claims that from past experience, he believes that is a student
works less than 5 hours per week, the student is likely to pass the subject. To test this claim
we set the null and alternative hypothesis as:
Analysis of relationships
The correlation coefficient, r, is used to determine whether a relationship exists
between two variables. The correlation coefficient between the number of hours spent
studying per week and the marks obtained for the subject, was found to be; r = 0.7845.
Hence, there is a strong, positive relationship between the two variables. Using simple

regression analysis, we obtained the linear equation; y=10.16 x +34.63 where y is the final
mark and x is the hours devoted to study. The model shows that is a students increased their
hours devoted to study by 1 hour, then their final mark would increase by 10.16. The
coefficient of determination, R-squared is 0.6154. This means that hours devoted to study
explain about 61.54% of the variation in the final mark scored by the student. The model is
statistically significant because the p-value = 0.00 < 0.05 as indicated in the table below.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.7845
R Square 0.6154
Adjusted R Square 0.6135
Standard Error 13.3648
Observations 200
ANOVA
df SS MS F Significance F
Regression 1 56595.0217 56595.0217 316.8511 0.0000
Residual 198 35366.1840 178.6171
Total 199 91961.2057
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 34.6306 1.4398 24.0518 0.0000 31.7912 37.4700
Hours devoted to Study 10.1637 0.5710 17.8003 0.0000 9.0377 11.2897
Table 2: Regression output for Final Mark and Hours Devoted to Study
The correlation coefficient between the variables hours worked per week and Final
marks was found to be r = -0.0844. Therefore, there is no significant relationship between the
number of hours spent working per week and the final marks obtained for the subject. From
the regression output, the simple linear equation obtained was, y=−0.55 x +56.77; where x is
the hours worked per week and y is the final marks. The R-squared for this model is 0.0071,
which means only 0.71% of the variation in final marks can be explained by the hours
worked per week. More so, the p-value = =.2350 > 0.05. Therefore, the relationship between
hours worked per week and final marks obtained for the subject is not statistically significant,
neither is the model.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.0844
R Square 0.0071
Adjusted R Square 0.0021
Standard Error 21.4743
Observations 200
ANOVA
df SS MS F Significance F
Regression 1 654.3338 654.3338 1.4189 0.2350
Residual 198 91306.8718 461.1458
Total 199 91961.2057
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 56.7748 2.8040 20.2482 0.0000 51.2454 62.3043
Hours worked per week -0.5479 0.4599 -1.1912 0.2350 -1.4549 0.3591
Table 3: Regression output for Final Mark and Hours Worked per Week
There is no significant relationship between the number of hours spent working per
week and the number of hours spent studying. The correlation coefficient, r = - 0.0501, which
indicate a very weak or negligible relationship in terms of magnitude, and a negative
relationship in terms of direction. The resulting model is not statistically significant and
cannot be accepted because the p-value = 0.4814 > 0.05. Therefore, Hours worked per week
and Hours devoted to study ado not have an appropriate model.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.0501
R Square 0.0025
Adjusted R Square -0.0025
Standard Error 1.6613
Observations 200
ANOVA
df SS MS F Significance F
Regression 1 1.3732 1.3732 0.4975 0.4814
Residual 198 546.4955 2.7601
Total 199 547.8688
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 2.0311 0.2169 9.3632 0.0000 1.6033 2.4589
Hours worked per week -0.0251 0.0356 -0.7054 0.4814 -0.0953 0.0451
Table 4: Regression Output for relationship between Hours Devoted to Study and Hours Worked per
week

Discussion and Conclusion
From the data analysis and interpretation of results above, we can conclude that the
data provided can be adequately used to provide a good perspective of the performance of all
students. However, more insights can be obtained if other variables are included because
there are many other factors that affect the final marks obtained by students in their subject of
study.