ECON940 Statistics for Decision Making: Analyzing Student Performance

This report analyzes student performance in 'Statistics for Business' (ECON940) based on gender and international student status, aiming to improve overall results. The study uses descriptive and inferential statistics on a sample of 60 students, evenly distributed across gender and international status. Descriptive statistics summarize the sample data, while inferential statistics draw conclusions about the population. Results indicate that gender significantly impacts performance, but international student status does not show the same effect. The analysis includes histograms, descriptive statistics for different classes and student groups, and hypothesis testing (t-tests and ANOVA) to determine statistically significant differences in marks. Recommendations are offered to enhance student performance in the subject. Desklib provides past papers and solved assignments for students.

STATISTICS FOR DECISION MAKING
ECON940
STUDENT ID:
[Pick the date]

Executive Summary
The objective of the given study is to analyse the performance of students in ‘Statistics for
Business’ based on their gender, international student status and hence recommend measures
to improve the performance. The sample data consists of 60 students which have been evenly
distributed across gender and international student status. The general methodology adopted
for the study is a mix of suitable descriptive statistical and inferential statistical techniques.
The descriptive statistics technique tends to focus on summarising the sample data. However,
the focus of the inferential statistics is to derive meaningful and valid conclusions about the
population based on the sample data. The results indicate that gender is a key differentiator of
performance in the subject but the same cannot be concluded about international student
status. Also, suitable recommendations have been offered based on the conclusions drawn so
that overall performance can witness an improvement in the given subject.
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TABLE OF CONTENTS
Business Problem.......................................................................................................................3
Statistical Problem.....................................................................................................................3
Analysis......................................................................................................................................3
Conclusion................................................................................................................................12
Implications..............................................................................................................................12
References................................................................................................................................14
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Business Problem
An Australian business school intends to understand the difference in performance of
students studying “Statistics for Business”. The key parameters identified for the study is the
underlying gender of the students along with the international student status. Besides, the
business school also intends to find ways based on the given study in order to improve the
performance of students in the subject.
Statistical Problem
A sample data comprising of the marks of 60 current students has been provided. Both
descriptive statistics and inferential statistics techniques have been applied to the given data.
The objective of the descriptive statistics techniques is to summarise the key trends in marks
across the gender and international student status. However, the descriptive statistics
techniques do not offer any conclusion about the population. As a result, inferential statistics
techniques such as hypothesis testing have been used in order to derive meaningful
conclusion about the population based on the given sample data.
Analysis
The objective of the given section is to analyse the data provided using suitable statistical
tools in order to answer the various questions raised.
1) Histograms have been used to provide s grouped summary of the marks obtained by
students in different classes. This is indicated below.
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0 to 46 46 to 52 52 to 59 59 to 66 More than 66
0
1
2
3
4
5
6
7
8
HISTOGRAM: MARKS OF CLASS 2
Marks Range of Class 2 Students
Frequency
0 to 33 33 to 39 39 to 46 46 to 52 More than 52
0
2
4
6
8
10
12
HISTOGRAM: MARKS OF CLASS 3
Marks Range of Class 3 Students
Frequency
The requisite descriptive statistics for the marks of students in the three classes are as
highlighted below.
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Comment
Class 1 marks – The average or mean marks for this class stands at 70.87. The median marks
are 66.85 which imply that 50% of the students have marks lower than or equal to 66.85.
Further, no two students have the same marks due to which the mode is not defined. Also, the
shape of the marks distribution is asymmetric with a positive skew or tail on the right side as
is apparent from the histogram. The dispersion in the marks is low to medium considering the
various parameters such as standard deviation and range (Flick, 2015).
Class 2 marks – The average or mean marks for this class stands at 53.66. The median marks
are 66.85 which imply that 50% of the students have marks lower than or equal to 51.52.
Further, no two students have the same marks due to which the mode is not defined. Also, the
shape of the marks distribution is asymmetric with a positive skew or tail on the right side as
is apparent from the histogram. The dispersion in the marks is low to medium considering the
various parameters such as standard deviation and range (Hair et. al., 2015).
Class 3 marks – The average or mean marks for this class stands at 43.80. The median marks
are 66.85 which imply that 50% of the students have marks lower than or equal to 44.18.
Further, no two students have the same marks due to which the mode is not defined. Also, the
shape of the marks distribution is asymmetric with a negative skew or tail on the left side as
is apparent from the histogram. The dispersion in the marks is quite low considering the
various parameters such as standard deviation and range (Hastie, Tibshirani and Friedman,
2011).
2) The graphical representation of the marks for domestic and international students has been
enabled through the following histograms.
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The requisite descriptive statistics for the marks of domestic and international students are as
highlighted below.
Comment:
Marks of domestic students – The descriptive statistics highlight that the average marks
scored by a domestic student is 55.58 which is marginally higher than the median marks of
54.37. Further, since no two students have scored the same marks, hence mode does not exist.
The shape of the marks distribution would not be symmetric owing to existence of positive
skew to the extent of 0.78. This leads to a rightward tail as is apparent from the histogram.
The dispersion for the marks is medium considering the range and other aspects such as
standard deviation keeping the mean in mind (Hillier, 2006).
Marks of international students - The descriptive statistics highlight that the average marks
scored by an international student is 56.65 which is significantly higher than the median
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marks of 51.52. Further, since no two students have scored the same marks, hence mode does
not exist. The shape of the marks distribution would not be symmetric owing to existence of
positive skew to the extent of 0.87. This leads to a rightward tail as is apparent from the
histogram. The dispersion for the marks is on the higher side considering the range and other
aspects such as standard deviation and variance (Hastie, Tibshirani and Friedman, 2011).
3) The objective here is to graphically represent the marks of only class 1 students that need
to be distributed into two categories namely foreign and domestic students. The requisite
graphs are highlighted as follows.
The requisite descriptive statistics for the marks of domestic and international students in
class 1 are as highlighted below
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Comment:
Domestic Students Class 1 Marks – The average marks scored by domestic students in class 1
amount to 68.76. The median marks for these students are slightly lower at 66.20. The non-
coincidence of the above two values implies that the marks distribution is not symmetric.
This is further supported by the fact that positive skew is present in the data which has
resulted in a rightward tail. Also, the dispersion in the marks is medium to high considering
the range of marks from 52 to 98. Besides, the variance and standard deviation values also
support this conclusion (Eriksson and Kovalainen, 2015).
International Students Class 1 Marks - The average marks scored by international students in
class 1 amount to 72.28. The median marks for these students are slightly lower at 71.15. The
non-coincidence of the above two values implies that the marks distribution is not symmetric.
This is further supported by the fact that positive skew is present in the data which has
resulted in a rightward tail. Also, the dispersion in the marks is medium to high considering
the range of marks from 51 to 98. Besides, the variance and standard deviation values also
support this conclusion (Flick, 2015).
4) The objective is to analyse using appropriate statistical tool if there exists any difference in
the marks of male and female students. Since, the conclusion has to be drawn for the
population based on the sample data, hence hypothesis testing needs to be performed using
the provided sample data (Hillier, 2006).
The requisite hypotheses are as highlighted below.
Null Hypothesis (H0): μM = μF i.e. the average marks of male and female candidates does not
show any statistically significant difference
Alternative Hypothesis (HA): μM ≠ μF i.e. the average marks of male and female candidates
does show statistically significant difference
The relevant test statistic for the given hypothesis test would be t since the population
standard deviation is not known for either of the genders. Also, considering the alternative
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hypothesis, it is apparent that the given test would be two tailed. Besides, the two samples are
independent; hence a two sample independent t test would be deployed (Lieberman et. al.,
2013). The output of the test obtained from Excel is highlighted below.
From the above test output, it is apparent that the relevant two tail p value is 0.004. Assuming
a level of significance as 5%, it is apparent that the p value is lesser than the level of
significance. As a result, the available evidence is sufficient to cause rejection of null
hypothesis and acceptance of alternate hypothesis. Thus, it may be concluded that based on
the sample data, the difference between the marks of male and female is statistically
significant. Hence, average marks across the two genders are different (Hair et. al., 2015).
5) The objective of the given statistical test is to analyse if significant difference exists
between the marks of students belonging to different classes. It is noteworthy that for the
data collected, there are three classes which ought to be simultaneously compared. A t test
cannot be used here since it is appropriate only when two samples need to be compared.
Hence, the appropriate test for the given objective would be ANOVA or Analysis of
Variance. Also, considering the given data, a single factor ANOVA ought to be conducted
(Fehr and Grossman, 2013).
The relevant hypotheses are as stated below.
Null Hypothesis (H0): μclass1 = μclass2 = μclass3 i.e. the average marks across the three classes
does not show any significant difference.
Alternative Hypothesis (HA): Atleast one of the classes has average marks which is not equal
to the other class
The single factor ANOVA analysis has been performed through Excel and the relevant output
has been pasted below.
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From the above ANOVA output, it is apparent that the p value has come out to be 0.00.
Assuming a level of significance as 5%, it is apparent that the p value is lesser than the level
of significance. As a result, the available evidence is sufficient to cause rejection of null
hypothesis and acceptance of alternate hypothesis. Thus, it may be concluded that based on
the sample data, that the average marks across the three classes is not the same and there is
atleast one class which tends to have average marks significant different from the other
(Eriksson and Kovalainen, 2015).
6) The objective of this statistical test is to determine whether the performance of the
domestic students and international students differs or not. Hypothesis test would be
conducted in order to ascertain if there is any statistically significant difference in the
marks of these two groups of students.
The relevant hypotheses are as stated below.
Null Hypothesis (H0): μDomestic = μInternational i.e. the average marks of domestic students and
international students does not exhibit any significance difference.
Alternative Hypothesis (HA): μDomestic ≠ μInternational i.e. the average marks of domestic students
and international students does exhibit statistically significance difference.
The relevant test statistic for the given hypothesis test would be t since the population
standard deviation is not known for either the domestic or international student marks. Also,
considering the alternative hypothesis, it is apparent that the given test would be two tailed.
Besides, the two samples are independent; hence a two sample independent t test would be
deployed. The output of the test obtained from Excel is highlighted below (Harmon, 2011).
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From the above test output, it is apparent that the relevant two tail p value is 0.799. Assuming
a level of significance as 5%, it is apparent that the p value is greater than the level of
significance. As a result, the available evidence is insufficient to cause rejection of null
hypothesis and acceptance of alternate hypothesis. Thus, it may be concluded that based on
the sample data, the difference between the marks of domestic and international students is
not statistically significant. Hence, average marks of both the groups (i.e. domestic and
international students) do not differ (Koch, 2013).
7) The objective of this statistical test is to determine whether the performance of the
domestic students and international students belonging to class 1 differs or not. Hypothesis
test would be conducted in order to ascertain if there is any statistically significant
difference in the marks of these two groups of students studying in class 1.
The relevant hypotheses are as stated below.
Null Hypothesis (H0): μDomestic(1) = μInternational(1) i.e. the average marks of domestic students and
international students in class 1 does not exhibit any significance difference.
Alternative Hypothesis (HA): μDomestic(1) ≠ μInternational(1) i.e. the average marks of domestic
students and international students in class 1does exhibit statistically significance difference.
The relevant test statistic for the given hypothesis test would be t since the population
standard deviation is not known for either the domestic or international student class 1
marks . Also, considering the alternative hypothesis, it is apparent that the given test would
be two tailed. Besides, the two samples are independent; hence a two sample independent t
test would be deployed. The output of the test obtained from Excel is highlighted below
(Liebermen et. al., 2013).
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