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```Trimester 	T1 2020
Unit Code 	HI6007
Unit Title 	Statistics for Business Decisions
Assessment Type  Assessment 2
Assessment Title  Group Assignment
Holmes Institute
```

Purpose of the assessment (with ULO Mapping)

Students are required to show the understanding of the principles and techniques of business research and statistical analysis taught in the course.

## Assignment Specifications

Purpose:

This assignment aims at Understand various qualitative and quantitative research methodologies and techniques, and other general purposes are:

1. Explain how statistical techniques can solve business problems
2. Identify and evaluate valid statistical techniques in a given scenario to solve business problems
3. Explain and justify the results of a statistical analysis in the context of critical reasoning for a business problem solving
4. Apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package
5. Justify and interpret statistical/analytical scenarios that best fits business solution

## Question 1 (4 Marks)

The higher education department of Holmes Institute recorded data on the number of students enrolled in the different study majors for the years 2018 and 2019. The data are stored in file STUDYMAJOR.xls.

1. Use an appropriate graphical technique or chart to compare the number of enrolment in 2018 and 2019 of the different study major. Display the chart. (2 marks)
2. Use an appropriate graphical technique or chart to display the percentage value of the number of enrolment of the different study major in 2018 and 2019. Display the chart.

(2 marks) Note: Questions 2 to 6 are related.

## Question 2 (8 marks)

Sociologists argued that women on average earn less than men as women often choose to work less hours. They further suggest that the choice of hours worked may be driven by various factors such as age, childcare needs, occupation choice and flexibility. To investigate the relation between hours worked and income earned by Australian men and women, a researcher plans to survey a sample of individuals across the country. Briefly explain (using no more than 250 words in total for this question)

1. What type of survey method the researcher could use and why? (2 marks)
2. What sampling method could the researcher use to select his/her sample and why?

(2 marks)

1. What are the two main variables the researcher should consider collecting data for the purpose of the above analysis and why? Identify the data type(s) for the variables. (2 marks) d) What kind of issues the researcher may face in this data collection? (2 marks)

Suppose a researcher has collected data from a sample of 65 individuals using the sampling method you have proposed in (b). For each individual, the hours worked per week and yearly income (measured in ‘000’s dollars) were recorded. The data are stored in file HOURSWORKED.xls.

## Question 3 (6 marks)

First, the researcher categorised the data into six location groups and six occupation groups, and calculated the frequencies given below.

Frequency tables

 Location Occupation Location category Frequency Occupationcategory Frequency Location group A 5 Occupation group 1 4 Location group B 7 Occupation group 2 26 Location group C 12 Occupation group 3 15 Location group D 25 Occupation group 4 12 Location group E 10 Occupation group 5 5 Location group F 6 Occupation group 6 3

Using Excel and the data in the frequency tables above, answer the following questions.

1. Which graphical technique or chart should be used if the researcher is interested in comparing the number of individuals in each location group? Explain the reason for the selection of this graphical chart. Construct and display the chart, also briefly describe what you can observe about the number of individuals belonging to each location category. (3 marks)
1. Which graphical technique or chart should be used if the researcher is interested in comparing the proportion of the number of individuals in each occupation group? Explain the reason for the selection of this graphical chart. Construct and display the chart, also briefly describe what you can observe about the proportion of the number of individuals belonging to each

occupation category. (3 marks)

## Question 4 (7 marks)

Second, the researcher wishes to use graphical descriptive methods to present summaries of the data on each of the two variables: hours worked per week and yearly income, as stored in file HOURSWORKED.xls.

1. The number of observations (n) is 65 individuals. The researcher suggests using 7 class intervals to construct a histogram for each variable. Explain how the researcher would have decided on

the number of class intervals (K) as 7. (2 marks)

1. The researcher suggests using class intervals as 10 < X ≤ 15, 15 < X ≤ 20, …, 40 < X ≤ 45 for the hours per week variable and class intervals 40 < X ≤ 45, 45 < X ≤ 50, ..., 70 < X ≤ 75 for the yearly income variable. Explain how the researcher would have decided the width of the above class

intervals (or class width). (2 marks)

1. Draw and display a histogram for each of the two variables using appropriate BIN values from part (b) and comment on the shape of the two distributions. (3 marks)

## Question 5 (5 marks)

Third, the researcher wishes to use numerical descriptive measures to summarize the data on each of the two variables: hours worked per week and yearly income.

1. Prepare and display a numerical summary report for each of the two variables including summary measures such as mean, median, range, variance, standard deviation, smallest and largest values and the three quartiles.

Notes: Use QUARTILE.EXC command to generate the three quartiles. (3 marks)

1. Compute the correlation coefficient using the relevant Excel function to measure the direction and strength of the linear relationship between the two variables. Display and interpret the correlation value. (2 marks)

## Question 6 (10 marks)

Finally, the researcher considers using regression analysis to establish a linear relationship between the two variables – hours worked per week and yearly income.

1. What is the dependent variable and independent variable for this analysis? Why? (2 marks)
2. Use an appropriate plot to investigate the relationship between the two variables. Display the plot. On the same plot, fit a linear trend line including the equation and the coefficient of determination R2. (2 marks)
3. Estimate a simple linear regression model and present the estimated linear equation. Display the regression summary table and interpret the intercept and slope coefficient estimates of

the linear model. (4 marks)

1. Display and interpret the value of the coefficient of determination, R-squared (R2).

(2 marks)

## Marking criteria

 Marking criteria Weighting 1. Student Enrolment analysis: a) Appropriate graphical technique for comparing the values b) Appropriate graphical technique for comparing the percentage values 4 marks 2 marks 2 marks 2. Analysis of Research Methodology: a) Appropriate Survey Method b) Appropriate Sampling Method c) Variable Selection d) Demerit of the methodology 8 marks 2 marks 2 marks 2 marks 2 marks 3. Analysis of Frequency Distribution: a) Graphical Technique b) Graphical Chart 6 marks 3 marks 3 marks 4. Graphical Descriptive Methods: a) Number of Class Intervals b) Width of Class Interval c) Histogram 7 marks 2 marks 2 marks 3 marks 5. Numerical Descriptive Measures a) Summary statistics b) Correlation Coefficient 5 marks 3 marks 2 marks 6. Yearly Income Analysis a) Choosing dependent and independent variables b) Graphical presentation of the relationship c) Estimated Regression Line d) Coefficient of Determination 10 marks 2 marks 2 marks 4 marks 2 marks

#### Marking Rubric

 Excellent Very Good Good Satisfactory Unsatisfactory Analysis of Student Enrolment Demonstration of outstanding knowledge on descriptive techniques Demonstration of very good knowledge on descriptive techniques Demonstration of good knowledge on descriptive techniques Demonstration of basic knowledge on descriptive techniques Demonstration of poor knowledge on descriptive techniques Analysis of Research Methodology Demonstration of outstanding knowledge on Research Methodology Demonstration of very good knowledge on Research Methodology Demonstration of good knowledge on Research Methodology Demonstration of basic knowledge on Research Methodology Demonstration of poor knowledge on Research Methodology Graphical Techniques Demonstration of outstanding knowledge on Graphical Techniques Demonstration of very good knowledge on Graphical Techniques Demonstration of good knowledge on Graphical Techniques Demonstration of basic knowledge on Graphical Techniques Demonstration of poor knowledge on Graphical Techniques Graphical Descriptive Methods Demonstration of outstanding knowledge on Graphical Descriptive Methods Demonstration of very good knowledge on Graphical Descriptive Methods Demonstration of good knowledge on Graphical Descriptive Methods Demonstration of basic knowledge on Graphical Descriptive Methods Demonstration of poor knowledge on Graphical Descriptive Methods Analysis Numerical Descriptive Measures Demonstration of outstanding knowledge on Numerical Descriptive Measures Demonstration of very good knowledge on Numerical Descriptive Measures Demonstration of good knowledge on Numerical Descriptive Measures Demonstration of basic knowledge on Numerical Descriptive Measures Demonstration of poor knowledge on Numerical Descriptive Measures Estimation and testing significance level Demonstration of outstanding knowledge on correlation and regression analysis Demonstration of very good knowledge on correlation and regression analysis Demonstration of good knowledge on correlation and regression analysis Demonstration of basic knowledge on correlation and regression analysis Demonstration of poor knowledge on correlation and regression analysis