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The variables in the data set are as follows:
V1 = Region around Melbourne 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 simply 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 for the 400 properties.
Assignment Tasks (Part III)
Answers to the assignment tasks must be based on the sample data file that you created in Part I of the assignment. As for Part II, most tasks in Part III of the 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.
There are four tasks in Part III of the assignment. You must meet all task requirements to receive full marks. No marks will be awarded to a task that requires an Excel output, if a print copy of the output has not been included with your answer. No marks will be awarded if only the Excel outputs are submitted without comments, explanations or the analysis required in the task.
Task 6
(a) By reference to numerical summary measures in the Descriptive Statistics table obtained in Task 5, provide three pieces of distinct evidence that might suggest that your sample “Sold Price” data has been obtained from a normally distributed population. What is your conclusion? Note: Make sure your three pieces of distinct evidence only contain one relating to the shape of the sample data.
(b) Regardless of your conclusion in (a), assume your sample “Sold Price” data have been obtained from a normally distributed population, and calculate, using Standard Normal tables, approximately how many “Sold Price” data values in your sample you would expect to lie within 1.5 standard deviations of the mean (i.e. between z = –1.5 and z = +1.5).
(c) Use your sorted “Sold Price” sample data from Task 4, and the mean and standard deviation from the Descriptive Statistics table of Task 5, to manually count the number of “Sold Price” data values in your sample that lie within 1.5 standard deviations of the mean. State whether this count matches, approximately, your answer to (b) and hence whether this result confirms (or not) your conclusion in (a).
Task 7
(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.
(b) Make a brief verbal statement explaining the meaning of the confidence interval estimate obtained in (a) in the context of the variable in this task.
(c) 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 8
(a) By reference to the Descriptive Statistics table obtained in Task 7, determine a 99% confidence interval estimate of the mean “Sold Price” of the population of properties using the following formula:
(sample statistic) ± (critical z or t) × (standard error of the sample statistic)
(b) Comment on the precision of this interval, in particular, compare the precision associated with this interval with that obtained in Task 7. Explain why the direction of the change in precision that you have observed in these two intervals ought to be obvious prior to constructing the two intervals.
Task 9
(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) Make a brief verbal statement explaining the meaning of the confidence interval estimate obtained in (a) in the context of the variable in this task.
(c) If the population proportion of brick veneer properties is actually 42%, would you consider the interval estimate obtained in (a), to be satisfactory? Explain why or why not.
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