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Management Accounting Assignment Examining The Performance Of Students

Question

Task: Assignment report on students’ performance in Management accounting subject
An Australian Business School is keen to improve students’ performance in the subject of Management accounting, and understand important differences in students’ performance across gender, campuses, trimesters and student status.
Assume you work as an Analyst for this Business school and you have been asked to study the current students’ performance. You have collected data for 362 students taking the subject in the Business School. The data is on an excel file named “Marks Accounting”. The data collected are recorded in the file as follows:
Mark - Mark of each student
Trimester 1 for trimester 1, 2 for trimester 2 and 3 for trimester 3
Status 1 for Domestic students, 2 for International students
Gender 1 for female and 2 for male
Campus 1 for Sydney campus and 2 for Wollongong campus
Assignment Tasks:
1. Visually present data for the marks from different trimesters. Calculate descriptive statistics for the marks of different trimesters. Comments on the location, shape and variability of those distributions.
2. Visually present data for the marks for domestic and internationalstudents. Calculate descriptive statistics for the marks of domestic andinternational students. Comments on the location, shape and variability ofthose distributions.
3. Visually present data for the marks of students in trimester 3 fordomestic and international students. Calculate descriptive statistics for themarks of students in trimester 3 by domestic or international status.Comments on the location, shape and variability of those distributions.
4. Many academics at business school believe that female students havehigher marks than male students in accounting area. How do you test whetherthe average mark in female students is significantly higher than the averagemark of male students? Use appropriate inferential statistical techniques.
5. Using the data collected, how do you test the claim that there is nosignificant difference of the average marks of students from the differenttrimesters? What do you find from your analysis? Use appropriate inferentialstatistical techniques.
6. The Business School is interested in understanding the performanceof domestic and international students. How do you test whether there is asignificant difference of average marks across the two groups? Useappropriate inferential statistical techniques.
7. Many academics at business school believe that Wollongongstudents perform better than Sydney students. How do you test whether theaverage marks of Wollongong students is higher than the average mark ofSydney students? Use appropriate inferential statistical techniquesMore information on this assessment will be provided during the sessiontime including the presentation of the assignment and submission toTurnitin. Please note that you should submit the assignment according tothe format given in the Moodle site.

Answer

Business Problem:
The business report on management accounting assignment tries to understand the performance of students in management accounting. For this, the report considers an Australian Business School for collecting primary data from the target population. The main concern of the report is to find whether performance of students differ significantly based on their gender, campuses, trimesters and status of students or not. In this context, it is essential to mention that the report considers 3 trimesters, which are Semester 1, 2 and 3, respectively. Moreover, gender of the students is divided into male and female while their status is also divided into domestic and international one. Furthermore, the university has campuses in Sydney and Wollongong. Therefore, the report will try to find whether the performance of students differs due to these factors or other factors influence students’ performance the most.

The main aim outlined for the study conducted in this management accounting assignment is to analyse and present real world data with proper statistical techniques. In the modern business, it is essential for an organisation to apply different statistical methods as well as concepts in business data. Furthermore, the report also focuses on hypothesis testing by applying inferential statistics with the help of MS Excel software.

What is the main statistical problem of the study examined in the management accounting assignment?
The main statistical problem of the study explored in the management accounting assignment is to summarise the variables in a descriptive way to observe the location, shape as well as variability of the dataset. In addition to this, the report also intends to provide a visual presentation of the data set for different variables with proper statistical diagram. Moreover, the report also tries to analyse the mean difference between two or more than two variables. For doing so, the report prepares statistical hypothesis for testing it with proper statistical methods. As a result, the report considers two-tailed t-test having equal variance and one-way ANOVA and measures the hypothesis at 5% significance level. For simplicity of the calculation, the report selects 362 students as sample from different trimesters from a large population size. In the report, gender, status, campus and trimesters represent categorical variables and hence they are represented with dummy variables.

The descriptive statistics represents location and shape by measuring central tendency of the data set. Furthermore, variability of the data set is measured by variance. In other words, descriptive statistics actually provide the summarise description of a specific data set. In hypothesis testing, the report considers two types of hypotheses, which are, null and alternative hypothesis. The null hypothesis presents the assumption that the report wants to prove while alternative hypothesis provides an alternative view of that assumption which completely opposite.

Analysis:
The objective of this management accounting assignment is to conduct the analysis of data set based on 7 tasks as per the requirement. The following section represents the visual presentation of the data as well as tables of corresponding findings and explains this based on statistical concepts. Here the data uses histogram, which shows data distribution based on frequency and class.

Task 1:

management accounting assignment

Figure 1: Visual presentation of marks from Semester 1
The above figure provided within this management accounting assignment shows students’ maximum marks in semester 1 lies between 50 and 60. The width of the each bar is equal which implies that the total marks for semester 1 are divided equally. From the figure, it can also be observed that fewer students get marks between 80 and 90.

Table 1: Descriptive statistics of marks from Semester 1

MARK (1)

Mean

69.81549

Standard Error

1.338143

Median

66.11

Mode

59.71

Standard Deviation

14.78028

Sample Variance

218.4565

Kurtosis

-0.81716

Skewness

0.61219

Range

47.82

Minimum

50.84

Maximum

98.66

Sum

8517.49

Count

122

The mean value shows that the marks of students in semester 1 lay around 69.82. However, the value of variance is 218.46 that imply that the marks of one student differ significantly from the mean value. The data set is skewed positively that indicates that the mean is greater than median. Moreover, from the above analysis done in this management accounting assignment, it can also be seen that median is also higher than mode (Ho and Yu 2015). Count implies that among 362 students, 122 are from semester 1.

management accounting assignment

Figure 2: Visual presentation of marks from Semester 2

The figure 2 provided in this management accounting assignment shows students’ maximum marks in semester 2 lies between 38 and 48. The width of the each bar is equal which implies that the total marks for semester 2 are divided equally. From the figure, it can also be observed that fewer students get marks between 58 and 68.

Table 2: Descriptive statistics of marks from Semester 2

MARK (2)

Mean

52.54463

Standard Error

0.871337

Median

49.19

Mode

42.44

Standard Deviation

9.6636

Sample Variance

93.38516

Kurtosis

-0.57473

Skewness

0.655492

Range

34.67

Minimum

38.63

Maximum

73.3

Sum

6462.99

Count

123

The mean value shows that the marks of students in semester 2 lay around 52.54. However, the value of variance is 93.38 that mean the marks of one student differ from the mean value. The data set analysed in this management accounting assignment is skewed positively that indicates that the mean is greater than median. Moreover, median is also higher than mode. Count implies that among 362 students, 123 are from semester 2.

management accounting assignment

Figure 3: Visual presentation of marks from Semester 3

The figure 3 shows students’ maximum marks in semester 3 lies between 36 and 46. The width of the each bar is equal which implies that the total marks for semester 3 are divided equally into four class boundaries. From the figure, it can also be observed that fewer students get marks between 56 and 66.

Table 3: Descriptive statistics of marks from Semester 3

MARK (3)

Mean

43.75085

Standard Error

0.727649

Median

44.38

Mode

42.52

Standard Deviation

7.870725

Sample Variance

61.94831

Kurtosis

0.243916

Skewness

-0.43111

Range

32.55

Minimum

26.18

Maximum

58.73

Sum

5118.85

Count

117

The mean value evaluated in the context of this management accounting assignment shows that the marks of students in semester 3 place around 43.75. However, the value of variance is 61.95, which imply that the marks of one student differ slightly from the mean value. The data set is skewed negatively as the mean is lower than median. Moreover, median is also lower than mode. Count implies that among 362 students, 117 are from this semester.

Task 2:

management accounting assignment

Figure 4: Histogram showing marks for domestic students

The figure 4 shows students’ maximum marks of domestic students on the entire semesters lies between 47 and 57. The width of the each bar is equal which implies that the total marks for those students are divided equally. From the figure, it can also be observed in this management accounting assignment that fewer students get marks within 77 to 107.

Table 4: Descriptive statistics of marks for domestic students

MARK(D)

Mean

55.05194

Standard Error

1.130053

Median

54.31

Mode

52.37

Standard Deviation

14.51579

Sample Variance

210.7081

Kurtosis

0.951958

Skewness

0.820631

Range

70.33

Minimum

27.9

Maximum

98.23

Sum

9083.57

Count

165

The mean value shows that the marks of domestic students over the 3 semesters lay around 55.05. However, the value of variance is 210.71 that imply that the mark of one student differs from the mean value by highly. The data set is skewed positively that indicates that the mean is greater than median while median is also higher than mode. Count implies that among 362 students, 165 students are from Australia.

management accounting assignment

Figure 5: Histogram showing marks for international students

The figure 5 shows students’ maximum marks of international students on the entire semesters lies between 46 and 56. The width of the each bar is equal which implies that the total marks for those students have been grouped equally. From the figure, it can also be observed in this segment of management accounting assignment that fewer students get marks between 26 and 36.

Table 5: Descriptive statistics of marks for international students

MARK (I)

Mean

55.91756

Standard Error

1.167338

Median

51.07

Mode

59.71

Standard Deviation

16.38438

Sample Variance

268.4478

Kurtosis

0.434251

Skewness

0.939936

Range

72.48

Minimum

26.18

Maximum

98.66

Sum

11015.76

Count

197

The mean value shows that the marks of international students over the 3 semesters lay around 55.92. Moreover, the value of variance is 268.45 that imply that the mark of one student differs from the mean value by large number. The data set is skewed positively that indicates that the mean is greater than median. However, median is lower than mode. Count implies that among 362 students, 197 students are from other countries.

Task 3:

management accounting assignment

Figure 6: Histogram for domestic students showing marks in semester 3

The figure 6 provided in this management accounting assignment shows students’ maximum marks of domestic students in 3rd semester lies between 37 and 47. The width of the each bar is equal which implies that the total marks for those students have been grouped equally. From the figure, it can also be observed that fewer students get marks between 57 and 67.

Table 6: Descriptive statistics for domestic students showing marks in semester 3

MARK(D)

Mean

44.85

Standard Error

0.999628

Median

44.18

Mode

43.98

Standard Deviation

8.121016

Sample Variance

65.9509

Kurtosis

-0.08068

Skewness

-0.22582

Range

30.83

Minimum

27.9

Maximum

58.73

Sum

2960.1

Count

66

The mean value shows that the marks of domestic students in semester 3 lay around 44.85. The value of variance is 65.95. It implies that the marks of one student differ from the mean value. The data set is skewed almost symmetrically. It indicates that the mean is almost equal with median. Moreover, median is also higher than mode. Count implies that among 362 students, only 66 domestic students are in the semester.

management accounting assignment

Figure 7: Histogram for international students showing marks in semester 3

The figure 7 shows students’ maximum marks of international students in 3rd semester. The number lies between 36 and 46. The width of the each bar is equal which implies that the total marks for those students have been divided in 3 equal groups. From the figure, it can also be observed that fewer students get marks between 36 and 46.

Table 7: Descriptive statistics for international students showing marks in semester 3

MARK (I)

Mean

42.32843

Standard Error

1.032088

Median

45.53

Mode

42.52

Standard Deviation

7.370579

Sample Variance

54.32544

Kurtosis

0.457551

Skewness

-0.97885

Range

25.97

Minimum

26.18

Maximum

52.15

Sum

2158.75

Count

51

The mean value identified from the analysis done in the management accounting assignment shows that the marks of international students in semester 3 lay around 42.33. The value of variance is 54.33. It implies that the marks of one student differ from the mean value. The data set is skewed negatively. It indicates that the mean is lower than median. However, median is also higher than mode. Count implies that among 362 students, only 51 international students are in the semester.

Task 4:
In this task, the report tries to understand the performance of female students and male students based on their marks in overall semesters. The main intension is to observe whether female students perform better in management accounting subject compared to male students or not. For understanding the difference, this segment covered in the management accounting assignment applies t-test with equal variance in order to test the following hypotheses:

Null hypothesis (H0): Female students perform better than male students in management accounting area

Alternative hypothesis (H1): Female students do not perform better than male students in management accounting area

Table 8: t-Test: for showing the difference between average marks of females and male students:

 

MARK (F)

MARK (F)

Mean

61.82993827

50.4144

Variance

388.5578317

65.41635

Observations

162

200

Pooled Variance

209.9324017

Hypothesized Mean Difference

0

df

360

t Stat

7.453750939

P(T<=t) one-tail

3.40895E-13

t Critical one-tail

1.649097299

P(T<=t) two-tail

6.81791E-13

t Critical two-tail

1.966575389

 

As per the table 8, it can be clearly observed in the management accounting assignment that the university has 162 female and 200 male students of management accounting in total. The female students get around 61.89 marks on average in the subject over the 3 semesters. On the other side, the male students get around 50.41 marks on average in the subject over the 3 semesters. Moreover, the variability of marks from the mean value is high for female students compared to that of males. At 5% level of significant, the P value of two-tail is 0.00. As the value is less than 0.05, the report rejects the null hypothesis by accepting the alternative one (Simonsohn, Simmons and Nelson 2015). Hence, from the finding, it is observed that female students do not perform better than male students in management accounting area by getting higher marks.

Task 5:
In this task of management accounting assignment, the report tries to understand the performance of students in 3 different trimesters. The main intension is to observe whether students perform better in only semester compared to others or not. For understanding the difference, the report applies one-way ANOVA in order to test the following hypotheses:

Null hypothesis (H0): The average marks of students in different trimesters do not have any difference

Alternative hypothesis (H1): The average marks of students in 3 trimesters have difference

The report considers one-ANOVA as the number of variables is three.

Table 9: One-way ANOVA: To analyse the difference between students’ average marks in three semesters:

SUMMARY

Groups

Count

Sum

Average

Variance

MARK (1)

122

8517.49

69.81549

218.4565

MARK (2)

123

6462.99

52.54463

93.38516

MARK (3)

117

5118.85

43.75085

61.94831

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

42226.94

2

21113.47

168.3928

2.6E-52

3.02087

Within Groups

45012.23

359

125.3823

Total

87239.17

361

       

As per the table 9, it can be stated that at 5% level of significant, the P value is 0.00. As the value is less than 0.05, the report rejects the null hypothesis by accepting the alternative one. Hence, from the finding, it is observed that the average marks of students in 3 trimesters are different.

Task 6:
In this task, the report tries to understand the performance of Australian students and international students. The main intension of the findings used to develop this management accounting assignment is to observe whether domestic students perform better in management accounting subject compared to international students in different semesters or not. For understanding the difference, the report applies t-test with equal variance in order to test the following hypotheses:

Null hypothesis (H0): The average marks of domestic students does not differ with that of international students

Alternative hypothesis (H1): The average marks of domestic students differs with that of international students

Table 10: t-Test: To analyse the difference between average marks of domestic and international students:

 

MARK(D)

MARK (I)

Mean

55.05194

55.91756

Variance

210.7081

268.4478

Observations

165

197

Pooled Variance

242.1441

Hypothesized Mean Difference

0

df

360

t Stat

-0.52712

P(T<=t) one-tail

0.299216

t Critical one-tail

1.649097

P(T<=t) two-tail

0.598432

t Critical two-tail

1.966575

 

As per the table 10, it can be observed in the management accounting assignment that at 5% level of significant, the P value is 0.60. As the value is higher than 0.05, the report accepts the null hypothesis by rejecting the alternative one. Hence, from the finding, it is observed that the average marks of domestic students are equal with that of international students.

Task 7:
In this task, the report tries to understand the performance of Wollongong students and Sydney students. The main intension of the readings examined in the management accounting assignment is to observe whether Wollongong students perform better in management accounting subject compared to Sydney students in different semesters or not. For understanding the difference, the report applies t-test with equal variance in order to test the following hypotheses:

Null hypothesis (H0): The average marks of Wollongong students is equal with that of international students

Alternative hypothesis (H1): The average marks of Wollongong students differs with that of Sydney students

Table 11: t-Test: To analyse the difference between average marks of Wollongong and Sydney students:

t-Test: Two-Sample Assuming Equal Variances

 

MARK (Sydney)

MARK (W)

Mean

48.701

64.03994

Variance

104.5884

283.0522

Observations

201

161

Pooled Variance

183.9056

Hypothesized Mean Difference

0

df

360

t Stat

-10.6944

P(T<=t) one-tail

1.15E-23

t Critical one-tail

1.649097

P(T<=t) two-tail

2.3E-23

t Critical two-tail

1.966575

 

As per the table 11 shown in the management accounting assignment, it can be stated that the university has 201 students in Sydney and 161 students in Wollongong reads management accounting. The Sydney students get around 48.70 marks on average in the subject over the 3 semesters. On the other side, the Wollongong students get around 64.04 marks on average in the subject over the 3 semesters. Moreover, the variability of marks from the mean value is high for Wollongong students compared to that of Sydney. At 5% level of significant, the P value of two-tail is 0.00. As the value is less than 0.05, the report rejects the null hypothesis by accepting the alternative one. Hence, from the finding, it is observed that the average marks of Wollongong students differ with that of Sydney students.

Conclusion:
Therefore, considering the overall analysis of the readings explored in the management accounting assignment, the report concludes that the students’ performance differ with gender, location and semesters. However, the status of the student does not play any significant role in this aspect. With the help of statistical analysis, diagrammatical representations and the analysis of inferential statistics, the report concludes that the performance of students depend gender, location of the university and semesters. Thus, the merit of students depends on these external and internal factors except status of them. Therefore, the finding obtained in the management accounting assignment will help the university to give emphasis on those issues without considering that whether the student is coming from other countries or not. Moreover, the semester wise variation of performance indicates that they perform well in some particular semester due to the easiness of syllabus. In addition to this, the university also observes that the study in Wollongong is different from Sydney.

Implications:
From the above finding and conclusion the report on management accounting assignment can draw the following implications:

  • The university needs to focus on courses in different semesters
  • The university needs to equate the educational system in Sydney with Wollongong
  • The university needs to focus on male students for understanding their difficulties in understanding management accounting
  • The university should focus on other external and internal sources that affect the students’ performance level in this aspect.

References:
Ho, A.D. and Yu, C.C., 2015. Descriptive statistics for modern test score distributions: Skewness, kurtosis, discreteness, and ceiling effects. Management accounting assignment Educational and Psychological Measurement75(3), pp.365-388.

Simonsohn, U., Simmons, J.P. and Nelson, L.D., 2015. Specification curve: Descriptive and inferential statistics on all reasonable specifications. Available at SSRN 2694998.

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