Analysing Household Data

Statistics for Business and Finance (BUS5SBF)
Have you been part of a national census? Privacy issues aside, a census provides lots of data that can inform a government policies and actions - but to be useful, the data needs to be analysed and interpreted.

In this assignment, we will use statistical methods to analyse and interpret real world demographic data.

The goal of this assignment is to
- Test your understanding of statistical methods and approaches
- Improve your ability to use Excel for manipulation of data
- Understand the real-world applications and implications of statistics

To complete this assignment you must
- Complete a set of statistical analysis tasks on a unique data set (both tasks and data set will be provided to you)
- Submit in a report in word detailing your response to each task (the final answer and reasoning / calculations that led to it)
- Submit an excel document that contains your data set and the calculations you used to complete the tasks

Important:
- This is an individual Assignment worth 30%. Each student will use a unique data set to complete the assignment.
- You should use Excel for all your computational work.

- Please provide detailed calculations for all the tasks. Not explaining how you arrived at your conclusions may result in only partial marks being awarded for those tasks.
- Present your computer results in appropriate tabular form. Also include graphs where required to support your answers.

Instructions: Analysing Australian Household Data

In this assignment you will be analysing and interpreting real data of two thousands (2000) Australian households. This data has been taken from 2005 HILDA (Household, Income and Labour Dynamics in Australia) Survey. We will treat these 2000 Households as population and would perform a statistical analysis by drawing a sample (which, indeed,would be a subsample!) of 200 households.

Step 1: Prepare Data Set
- You need to download and modify the generic data set to identify the sample you will be working on. More information on the data set is available below.
- Important: You do not need to analyse the entire data set - only draw a random sample of 200 households. This must be done first and the rest of your statistical analysis will be based on this data set.
- You will need to know how to manipulate data in Excel. You can use any other compatible spreadsheet tool (for example Numbers for Mac OS, OpenOffice, LibreOffice etc) but be aware that some of the functions differ slightly.
- There are plenty of resources online and in this LMS that will show you how to perform these tasks in Excel. Use these resources (and Google) to improve your skills as you progress. If you have a particularly difficult challenge, share it in the forum and your tutors or peers will help.

Step 2: Analyse Data & Submit Report
- You will be presented with a set of tasks to run on your unique data set (of 200 samples) - the full list of tasks are listed below.
- As much as possible, complete these tasks within the excel document. You will need to submit your excel document at the end of the assignment.
- You will also submit a brief report in word addressing all the tasks below. When responding to the tasks, please explain the reasoning behind your answer, and refer to your Excel sheet.

Data Set: Household data

The Data Set for this Assignment is available on LMS (Data Set for Assignment01.xls). This includes information of 2000 households across the following variables.
- Income: Annual Income in AUD,
- ATaxInc: After tax annual income in AUD
- Grocery: Annual expenditures on groceries in AUD
- Alcohol: Annual expenditures on alcohol in AUD
- Meals: Annual expenditures on meals eaten out in AUD
- Fuel: Annual expenditures on fuel in AUD
- Cloth: Annual expenditures on clothing in AUD
- Phone: Annual expenditures on phone in AUD
- Utilities: Annual expenditures on utilities (Water, Gas, Electricity) in AUD
- Texp: Annual total expenditures in AUD
- Children: Number of children in a household
- Adults: Number of adults in a household
- OwnHouse: This is a categorical variable and takes value 1 if a household owns a house and 0, otherwise.
- GHH: Gender of the Head of Household (M: Male, F: Female)
- Highest Degree: Highest Level of Education, where the Highest Level of Education is;
P: Primary
S: Secondary
I: Intermediate
B: Bachelor
M: Master

Tasks for Analysis of Data Set
Complete the following tasks based on the unique data set you generated. These questions should be answered in a Word document, with brief reasoning to justify your answers. Your answers and reasoning should correlate with the tables and graphs from the excel sheet.

Task 1
A. Draw a random sample of two hundred (200) households as per the sample selection procedure. What sampling method have you used to select your sample data? In your opinion, is this the best method of sampling, why or why not?
B. Compute the descriptive statistics and draw a Box-Whisker plot of Expenditures on the following variables (all series in one graph!);
(i) Alcohol (ii) Meals (iii) Fuel (iv) Phone
C. Also, use an appropriate measure of variation to compare the variability in expenditures on these four variables. Explain, why is this an appropriate measure.
D. Present a summary of your findings about the shape and spread of the distribution of these variables using information from the boxplots and the descriptive statistics.

Task 2
A. Construct a frequency distribution of the expenditures on Utilities, using the following classification (9 classes);
1 2 ... 8 9
Classes 0 - 400 400 - 800 ... 2800 - 3200 More than 3200
B. What is the percentage of households that spend on Utilities
1.
a.
i. at the most $ 1200 per annum
ii. between $1200 and $2400 per annum, and
iii. more than $2400 per annum.

C. Draw the histogram of the expenditures on Utilities by households in your sample. Do you think the utility expenditures are normally distributed? Provide the "statistical reason" for your answer?

Task 3
A. What is the top 10% value and the bottom 10 % value of household's annual after tax income (AtaxInc)? What does these two values imply?
B. What does the mean (average) of variable OwnHouse imply?
C. What is the probability that a randomly selected household will have a family size (FS= Adults + Children) equal to 5?
D. Draw a scatter plot of natural log of total expenditures against natural log of after tax income, that is, ln(texp) against ln(ataxinc) and compute the coefficient of correlation. Express your finding about the relationship between the two variables.

Task 4
A. Construct a contingency table between the gender and the level of education. Using information in this table, can we say that male and female heads of the households differ in their higher level of qualification?
B. What is the probability that the head of household is a female and her higher level of education is Intermediate?
C. What is the probability that the head of household is a male and has the Bachelor degree?
D. What is the proportion of having the Secondary as the highest degree from among females?
E. Do you think that the events "gender of household head is male" and "having the Master Degree" are independent?

Attachment:- Data Set.xlsx