Assignment -
The assignment has a total of seven (7) tasks for students to complete. The assignment consists of two parts. Part I is to collect a set of sample data which will be used to answer six questions in Part II.
Introduction - The Assignment Data (PopulationPropertyData.xls) file, which you can access from the Assessment Information page on the unit website contains, in the range A1:I401, real estate sales data for a population of 400 properties around Melbourne in a particular week. You are required to select a random sample of 50 properties from this population. The variables in the data set are as follows:
V1 = Region where property is located (1 = North, 2 = West, 3 = East, 4 = Central)
V2 = Property type (0 = Unit, 1 = House)
V3 = Sale result (1 = Sold at auction, 2 = Passed-in, 3 = Private sale, 4 = Sold before auction). Note that a blank cell for this variable indicates that the property did not sell.
V4 = Building type (1 = Brick, 2 = Brick veneer, 3 = Weatherboard, 4 = Vacant land)
V5 = Number of rooms
V6 = Land size (Square metres)
V7 = Sold Price ($000s)
V8 = Advertised Price ($000s)
Column A (PN), contains the property identification numbers from 001 to 400 properties.
Selecting your Random Sample and Creating your Sample Data File
To select your random sample, you need:
- A printed copy of the Random Number Table handy.
- Open the PopulationPropertyData.xls file on computer screen.
- Create a SamplePropertyData Excel file and keep it open on computer screen.
In order to select the sample data that will form the basis of your assignment you will need to make use of the random number table provided as a pdf file (RandomNumbers.pdf) on the Assessment Information page of the unit website. The provided table of random numbers is, as the title suggests, a sequence of randomly generated numerical digits (0 to 9). These digits are arranged in a table with ten columns (numbered 0 to 9) and one hundred rows (numbered 01 to 00) spread over two pages. The entries in each column of each row consist of six single digits.
Your first task is to select 50 three-digit random (property) numbers ranging from 001 to 400 from the table of random numbers. The type of simple random sampling that we will be engaged in here is termed "without replacement" because we specifically do not want to allow a property number to be selected more than once. If we allowed this to occur we would run the risk of the sample being biased and so not representative of the population. In the population, a particular property only occurs once and so it would not do to allow a particular property to occur more than once in your sample. In this way we can be more assured that the sample is typical of the population and so perform inferential statistical analyses about the population with some confidence.
In order to select your 50 random property numbers you will need to first go to a starting position row and column in the random number table (Note ~ not the population property data) defined by the last three digits of your VU student identification number (the assignment marker will check your student ID number against the three digits number you use to collect the random sample). The last two digits of your VU ID number identifies the row and the third last digit identifies the column of your (relatively) "unique" starting position.
Assignment Part I -
Part I of the assignment simply requires the submission of a hard copy of your sample property data presented in a maximum of no more than 3 printed pages in total. (See the Assignment Part I Model Answer). This sample data set will form the basis of the statistical presentation and analysis tasks contained in Part II of the assignment.
Task 1 -
(a) Make a hard copy of your Random Number Table containing the following:
(i) The highlight of the starting row and starting column of the sample selection process. (Refer to the Assignment Part I Model Answer).
(ii) The strikethrough/mark on the three digits good numbers and the cross-out of the repeated number(s). (Refer to the Assignment Part I Model Answer).
(b) Print a hard copy (see note below) of your sample property data (9 columns x 51 rows of data plus the column headings row) from the Excel file (SamplePropertyData) obtained per the above instructions.
Assignment Part II -
Answers to the six assignment tasks in Part II must be based on the sample data file that you have created in Part I. All tasks in this assignment require you to obtain an Excel output prior to performing some analysis. Copy and Paste these outputs to your assignment MS- Word document immediately preceding any subsequent analysis. Explanations must be precise and to the point. Charts and tables must have appropriate titles and numerical values must be rounded to an appropriate number of decimal places and accompanied by the correct units of measure.
Task 2 - Use Excel to produce a Frequency Column Chart and a Relative Frequency Pie-Chart for your sample to show the number and proportion, respectively, of each building type.
Use these graphical summaries to answer the following questions:
(a) How many properties in your sample consist of brick buildings?
(b) Which building type occurs most frequently in your sample?
(c) What proportion of properties in your sample consists of weatherboard buildings?
Task 3 -
(a) Use Excel to sort your sample "Sold Price" data and paste into your MS Word assignment document.
(b) Use the percentile location formula; and the three associated rules (Slide 11 of Week 2 Seminar, Session 1) to determine:
Remember to show all working!
(i) The 70th percentile.
(ii) The first and third quartiles.
(c) Briefly explain what the 70th percentile that you have determined informs you about your sample "Sold Price" data.
(d) Determine the Inter-Quartile Range of your sample "Sold Price" data and provide a brief explanation of what information this statistic provides about your sample data.
Task 4 -
(a) Use Excel to produce a Descriptive Statistics table for your sample "Sold Price" data and paste into your MS Word assignment document.
(b) Use results from Task 3 to determine manually for this data, the upper and lower inner fence limits;
Remember to show all working!
IFUL = Q3 + 1.5 x IQR
and IFLL = Q1 - 1.5 x IQR
(c) Based on the limits calculated in (b), choose from the numerical summary measures provided in the Descriptive Statistics table, and/or measures calculated previously in Task 3;
(i) an appropriate measure of central tendency, and,
(ii) an appropriate measure of dispersion for your sample "Sold Price" data.
Provide a brief explanation of the reasoning behind your choice in both cases.
Task 5 - Remember to show all working! Failure to do so will result in the loss of marks.
(a) From the Descriptive Statistics table obtained in Task 4, identify three pieces of evidence that indicate whether your sample "Sold Price" data has been obtained from a normally distributed population or not. What is your conclusion? Note: Make sure only one piece of evidence relates to the shape of the sample data.
(b) Regardless of your conclusion in above, assume the "Sold Price" population data is normally distributed. Applying the Standard Normal tables, calculate how many "Sold Price" observations in your sample would expect to lie within 1.5 standard deviations of the mean (i.e. between z = -1.5 and z = +1.5).
(c) Use the mean and standard deviation from the Descriptive Statistics table of Task 5 to calculate the boundfor 1.5 standard deviation spread from the mean. Using the "Sold Price" sample data, manually count the number of observations fall within the bound. State whether this count matches, approximately, your answer to (b) and hence whether this result confirms (or not) your conclusion in (a).
Task 6 - Remember to show all working! Failure to do so will result in the loss of marks.
(a) Use Excel to produce a Descriptive Statistics table for the "Sold Price" variable in your sample suitable for constructing an interval estimate of the population mean "Sold Price". Hence determine:
(i) A point estimate of the mean "Sold Price" of the population of properties.
(ii) A 90% confidence interval estimate of the mean "Sold Price" of the population of properties.
(iii) Make a brief verbal statement explaining the meaning of the confidence interval estimate obtained in (ii) in the context of the variable in this task.
(b) If the population mean "Sold Price" is actually 650 ($000s), would you consider the interval estimate obtained in (a), to be satisfactory? Explain why or why not.
Task 7 - Remember to show all working! Failure to do so will result in the loss of marks.
(a) Use Excel to produce a Descriptive Statistics table for the brick veneer properties in your sample suitable for constructing an interval estimate of the population proportion of brick veneer properties. Hence determine:
(i) A point estimate of the proportion of brick veneer properties in the population.
(ii) A 99% confidence interval estimate of the proportion of brick veneer properties in the population.
(b) Using the following formula: (sample statistic) ± (critical z or t) ´ (standard error of the sample statistic)
Use the rule of thumb for good normal approximation (Slide 3 of Week 7 Session 2) for proportion, then the Empirical Rule (Slide 8 of Week 5 Session 1) for a Normal distribution to determine a 95% confidence interval estimate of the proportion of brick veneer properties in the population.
(c) Compare, in terms of the precision, the interval manually calculated in (b) with the interval obtained from the Descriptive Statistics table in (a). Explain why the direction of the change in precision is expected.
Attachment:- Assignment File.rar