Statistics for Business and Finance - Analysing Household Data

Have you been part of a national census? Privacy issues aside, a census provides lots of data that can inform 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 (see here for some guides on using Excel)
- 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 a report in word detailing your response to each task (the final answer and reasoning including calculations that led to it)
- Submit an excel document that contains your data set and the calculations you used to complete the tasks

- Use the marking rubric as a guide when working on your assignment.
Instructions: Analysing Household Data
In this assignment you will be analysing and interpreting household data.

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 250 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 250 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 Assignment 01.xls). This includes information of 2000 households across the following variables.
- Income: Annual Income in AUD,
- ATaxlnc: 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;

Task 1

A. Draw a random sample of two hundred (250) 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 particularly when one is interested in characteristics like the gender of the household head, education levels etc., 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. Use information from the descriptive statistics and the boxplots in part (B) above to present a summary of your findings by contrasting different features of these distributions.

Task 2
A. Construct a frequency distribution of the expenditures on Utilities, using the following classification (11 classes).
1 2 ... 10 11

Classes 0 - 300 300 - 600 ... 2700 - 3000 More than 3000
B. Using frequency distribution of the utilities above, what is the percentage of households who spend on Utilities
a. at the most $900 per annum
b. between $1500 and $2700 per annum, and
c. more than $3000 per annum.

Task 3
A. Find the top 5% value and the bottom 5% value of household's annual after-tax income (Ataxlnc). What do these two values imply?
B. The series OwnHouse represents whether a household owns a house or not. Let X be a random variable such that X = Number of households who own a house.
(i) Is this a quantitative or a qualitative variable?
(ii) What would be the probability distribution of this random variable if we choose randomly (a) Only 1 household? (b) 250 households? Provide any relevant condition(s) to justify your answer.
C. Draw a scatter plot of natural log of total expenditures against natural log of after-tax income, that is, In(texp) against In(ataxinc) and compute the coefficient of correlation. Express your finding of the relationship between the two variables.

Task 4
A. Construct a contingency table between the gender and the level of education.
B. What is the probability that the head of household is a male and her higher level of education is Intermediate?
C. What is the probability that the head of household is a female and has the Bachelor degree?
D. What is the proportion of having the Secondary as the highest degree from among males?
E. Do you think that the events "gender of household head is female" and "having the Master Degree" are independent?