Quantitative Methods for Business

Business Statistics

Assignment – Semester, 2 2015

Total Marks: 60, Worth: 20% of final assessment

This assignment requires a considerable amount of computer work and written comment. You may need to seek guidance from your tutor along the way. Do not leave things until too late. Each question carefully describes what you are required to do, so please follow the instructions carefully. Your answer to each question should begin with the number of the question.

In this assignment you will examine statistical data consisting of student records who studied Under Graduate Subject (BUS100) and Post Graduate Business Subject BUS600 in a University. The data collected from students records in March, July and Nov semesters during 2012 and 2013. Data was collected and contained in a file called ‘BUS Result Data.xls’ and the columns of the file contain the following information:

Column Name Description

A Student ID Number Number to identify each student

B Student Gender 1= Male

2= Female

C Student Age Age (Years)

D Motivation A score between 0 and 100

E Attendance Rate Student attendance percentage (%) per semester.

F Student final mark Student mark out of maximum mark of 100

G Student Grade HD: High Distinction

D: Distinction

C: Credit

P: Pass

MF: Marginal Fail

F: Fail

H Program U= Undergraduate

P= Postgraduate

I Subject Code BUS100= Undergraduate Business Subject

BUS600= Postgraduate Business Subject

J Year -2012

-2013

K Semester - March

- July

- November

Before you begin any analysis you must take a random sample of 200 records from the 257 provided in the file BUS Result Data.xls.xls. Use the Random Sample Generator, available on Moodle in the Lab Bundle, to do this. Your answers to the assignment tasks below are to be based on your sample of 200 records. Make sure you keep a safe copy of your sample, since you cannot use the Random Sample Generator to reproduce the first sample.

To prepare your data file ready for analysis, you must take the following steps:

1. Use the file Random Sample Generator, in the Lab Resources Bundle on Moodle, to generate a random sample of 200 records from the file.

2. Copy your sample to another spread sheet for working on your assignment and save it with another file name. Remember to save another copy of your sample under a different name as a backup.

Assignment Tasks

For each task below, you must answer all the questions in sequential order and submit all of the required printouts, graphs, tables and summaries required.

NB: Each graph and table should have a heading and each axis should have a label!!

1. Introduction, Variable List and Data: Give a brief introduction to your report. Using the variables listed in the table above state for each variable whether it is qualitative or quantitative, if it is qualitative state whether it is nominal or ordinal, and if it is quantitative state whether it is discrete or continuous. Provide a printout of the data in your sample, sorted in ascending order based on Student ID number.

[4 Marks]

2. Produce 2 Pareto Graphs showing the grade distribution of the BUS100 and BUS600 subjects. Provide your comments on the graph shape, grade distribution and best measure for centre.

[6 Marks]

3. Create histograms and side by side boxplots showing the distribution of student’s marks for the BUS100 and BUS600. Comment upon the shape of the distribution in each graph: is it symmetric? If it is not, is it positively or negatively skewed?

[6 Marks]

4. Produce the following Pivot Tables:

a) Create a pivot table to show the average student marks per semester for BUS100 & BUS600 in 2012 and 2013. Provide your comments on similarities or differences and any conclusions you can draw in each case.

b) Construct a pivot table that shows the number of student succeeded or failed per semester, per year for BUS100 and BUS600. Place subjects and semesters in the rows, years and final result (passed, failed) in the columns and a count of students in the body of the table.

c) Convert the above table in b into another table by converting the student numbers into relative frequencies (% of success and failure rates) in each case. Provide your comments and conclusions on the results.

[12 Marks]

5. T-Test and CI: The students believe that students mean mark and success rate in summer semester (Nov) in both BUS100 & BUS600 are significantly higher than in March and July semesters.

a) Obtain appropriate descriptive statistics and so calculate a 95% confidence interval for the mean student marks in March and July semesters 2012 and 2013. Please explain the meaning of this confident interval in context of this problem.

b) Assuming that that the summer mean mark for both BUS100 & BUS600 is 70 marks. Test the hypothesis that the students’ mean mark in March and July semesters is significantly lower than in Nov. semester. Mention any assumptions, include relevant hypotheses and report the results and conclusion in the conventional manner.

[12 marks]

6. Create a table of correlation coefficients for the following variables: age, motivation, attendance rate, and marks. Discuss your results and state which pairs of variables have the highest and the lowest correlation coefficients.

[4 marks]

7. Use Excel to carry out a regression analysis on the two variables: attendance Rate (independent variable) and Student mark (dependent variable).

a) Copy the output into your assignment and use it to determine the answers to the following questions.

b) Write down the regression equation.

c) State the R-squared value and the standard error and explain what they mean with respect to the data.]

d) Write down the value of the gradient of the regression line and explain what it means for this data.

e) Are the values for the constant and the gradient (slope) significant (i.e. significantly different from zero) in this case? Justify your answer.

f) Do you think this regression model is a good model? Justify your answer using the regression output.

[12 marks]

8. Using the information obtained for your analyses write a short conclusion about what you found from the study above.

[4 marks]

Business Statistics

Assignment – Semester, 2 2015

Total Marks: 60, Worth: 20% of final assessment

This assignment requires a considerable amount of computer work and written comment. You may need to seek guidance from your tutor along the way. Do not leave things until too late. Each question carefully describes what you are required to do, so please follow the instructions carefully. Your answer to each question should begin with the number of the question.

In this assignment you will examine statistical data consisting of student records who studied Under Graduate Subject (BUS100) and Post Graduate Business Subject BUS600 in a University. The data collected from students records in March, July and Nov semesters during 2012 and 2013. Data was collected and contained in a file called ‘BUS Result Data.xls’ and the columns of the file contain the following information:

Column Name Description

A Student ID Number Number to identify each student

B Student Gender 1= Male

2= Female

C Student Age Age (Years)

D Motivation A score between 0 and 100

E Attendance Rate Student attendance percentage (%) per semester.

F Student final mark Student mark out of maximum mark of 100

G Student Grade HD: High Distinction

D: Distinction

C: Credit

P: Pass

MF: Marginal Fail

F: Fail

H Program U= Undergraduate

P= Postgraduate

I Subject Code BUS100= Undergraduate Business Subject

BUS600= Postgraduate Business Subject

J Year -2012

-2013

K Semester - March

- July

- November

Before you begin any analysis you must take a random sample of 200 records from the 257 provided in the file BUS Result Data.xls.xls. Use the Random Sample Generator, available on Moodle in the Lab Bundle, to do this. Your answers to the assignment tasks below are to be based on your sample of 200 records. Make sure you keep a safe copy of your sample, since you cannot use the Random Sample Generator to reproduce the first sample.

To prepare your data file ready for analysis, you must take the following steps:

1. Use the file Random Sample Generator, in the Lab Resources Bundle on Moodle, to generate a random sample of 200 records from the file.

2. Copy your sample to another spread sheet for working on your assignment and save it with another file name. Remember to save another copy of your sample under a different name as a backup.

Assignment Tasks

For each task below, you must answer all the questions in sequential order and submit all of the required printouts, graphs, tables and summaries required.

NB: Each graph and table should have a heading and each axis should have a label!!

1. Introduction, Variable List and Data: Give a brief introduction to your report. Using the variables listed in the table above state for each variable whether it is qualitative or quantitative, if it is qualitative state whether it is nominal or ordinal, and if it is quantitative state whether it is discrete or continuous. Provide a printout of the data in your sample, sorted in ascending order based on Student ID number.

[4 Marks]

2. Produce 2 Pareto Graphs showing the grade distribution of the BUS100 and BUS600 subjects. Provide your comments on the graph shape, grade distribution and best measure for centre.

[6 Marks]

3. Create histograms and side by side boxplots showing the distribution of student’s marks for the BUS100 and BUS600. Comment upon the shape of the distribution in each graph: is it symmetric? If it is not, is it positively or negatively skewed?

[6 Marks]

4. Produce the following Pivot Tables:

a) Create a pivot table to show the average student marks per semester for BUS100 & BUS600 in 2012 and 2013. Provide your comments on similarities or differences and any conclusions you can draw in each case.

b) Construct a pivot table that shows the number of student succeeded or failed per semester, per year for BUS100 and BUS600. Place subjects and semesters in the rows, years and final result (passed, failed) in the columns and a count of students in the body of the table.

c) Convert the above table in b into another table by converting the student numbers into relative frequencies (% of success and failure rates) in each case. Provide your comments and conclusions on the results.

[12 Marks]

5. T-Test and CI: The students believe that students mean mark and success rate in summer semester (Nov) in both BUS100 & BUS600 are significantly higher than in March and July semesters.

a) Obtain appropriate descriptive statistics and so calculate a 95% confidence interval for the mean student marks in March and July semesters 2012 and 2013. Please explain the meaning of this confident interval in context of this problem.

b) Assuming that that the summer mean mark for both BUS100 & BUS600 is 70 marks. Test the hypothesis that the students’ mean mark in March and July semesters is significantly lower than in Nov. semester. Mention any assumptions, include relevant hypotheses and report the results and conclusion in the conventional manner.

[12 marks]

6. Create a table of correlation coefficients for the following variables: age, motivation, attendance rate, and marks. Discuss your results and state which pairs of variables have the highest and the lowest correlation coefficients.

[4 marks]

7. Use Excel to carry out a regression analysis on the two variables: attendance Rate (independent variable) and Student mark (dependent variable).

a) Copy the output into your assignment and use it to determine the answers to the following questions.

b) Write down the regression equation.

c) State the R-squared value and the standard error and explain what they mean with respect to the data.]

d) Write down the value of the gradient of the regression line and explain what it means for this data.

e) Are the values for the constant and the gradient (slope) significant (i.e. significantly different from zero) in this case? Justify your answer.

f) Do you think this regression model is a good model? Justify your answer using the regression output.

[12 marks]

8. Using the information obtained for your analyses write a short conclusion about what you found from the study above.

[4 marks]

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