Task 1 ( 10 marks)

 

(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). (1 mark)

 

(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). (4 marks)

 

(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.  (5 marks)

 

 

Task 2 (10 marks)

 

Use Excel to produce a Frequency Column Chart (4 marks) and a Relative Frequency Pie-Chart (3 marks) 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? (1 mark)

(b)        Which building type occurs most frequently in your sample?  (1 mark)

(c)        What proportion of properties in your sample consists of weatherboard buildings? (1

           mark)

 

 

Task 3 (10 marks)

 

• Use Excel to sort your sample “Sold Price” data and paste into your MS Word assignment document. (1 mark)
• Use the percentile location formula;

, and the three associated rules (Slide 11 of Week 2 Seminar, Session 1) (1 mark) to determine:

 

Remember to show all working!

(i)         The 70^th percentile. (1 mark)

(ii)        The first and third quartiles. (2 mark)

 

• Briefly explain what the 70^th percentile that you have determined informs you about your sample “Sold Price” data. (2 mark)
• 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. (3 marks)

 

 

 

 

 

Task 4 (10 marks)

 

(a)        Use Excel to produce a Descriptive Statistics table for your sample “Sold Price” data        and paste into your MS Word assignment document. (4 marks)

(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   (1.5 marks)

 

and      IFLL = Q1 – 1.5 x IQR   (1.5 marks)

 

(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, (1 mark)

(ii)        an appropriate measure of dispersion for your sample “Sold Price” data. (1

mark)

 

Provide a brief explanation of the reasoning behind your choice in both cases. (1

           mark)

 

 

Task 5 (10 marks)

 

Remember to show all working! Failure to do so will result in the loss of marks.

 

• From the Descriptive Statistics table obtained in Task 5, identity 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.   ( 2 marks)

 

• 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).   (4 marks)

 

• 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).  (4 marks)

 

 

 

 

Task 6 (10 marks)

 

Remember to show all working! Failure to do so will result in the loss of marks.

 

• 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”. (2 marks) Hence determine:

(i)         A point estimate of the mean “Sold Price” of the population of properties.  (1 mark)

(ii)        A 90% confidence interval estimate of the mean “Sold Price” of the population of properties. (2 marks)

(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. (3 marks)

 

(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. (2 marks)

 

 

 

Task 7 (10 marks)

 

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: (2 marks)

 

(i)         A point estimate of the proportion of brick veneer properties in the population. (1 mark)

(ii)        A 99% confidence interval estimate of the proportion of brick veneer properties in the population. (1 mark)

 

(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. (4 marks)

 

 

(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.  (2 marks)

                                                             SAMPLE SOLUTION

 

Task 2

Figure 1: Frequency column for building type

Figure 2: Pie chart for building type.

Answers to the questions with reference to the visual aid presented for clarity (Frankfort-Nachmias, & Leon-Guerrero, 2015).

1. How many properties in your sample consist of brick buildings?

In the sample brick building consists of 17 properties

2. Which building type occurs most frequently in your sample?

The most frequently occurring building type in my sample was Brick Veneer at 23 properties representing 46%

3. What proportion of properties in your sample consists of weatherboard buildings?

14% of the properties in the sample consist of weatherboard buildings

Task 3

1. Sorted Sold price

Table 1: Sorted Sold price

125	375	435	552	1175
230	385	445	555	1215
270	387.5	453	610	1225
300	400	460	665	1606
319	400	461.25	670	1885
340	415	475	740
346	420.5	481.5	741
350	425	510	785.5
354	425	525	882.5
374	427	544.5	1126

 

1. Using percentile formula
2. Using the formula to find the 70^th Percentile

Replace the values in the formula n=45, P=70

70^th quartile =(45+1)*70/100=32.2

Rounding off to the nearest whole number we get 32 as the position of the 70^th percentile which is $555000

1. First and Third Quartiles

First Quartile = 25^th Percentile, Third quartile =75^th Percentile

Replacing the values we get the following

First Quartile =(45+1)*25/100=46*0.25=11.5

Rounding off to the nearest whole number we get 12 as the position of the 25^th  percentile which is $385,000

Third quartile =(45+1)*75/100=46*0.75=34.5

Rounding off to the nearest whole number we get 35 as the position of the 75^th percentile which is $670000

1. Explaining the 70^th percentile

This show that 70% of the “Sold price” for the sample are below $555,000

1. Determining and explaining the interquartile range

Interquartile range=Quartile 3-Quartile 1

=$670000-$385000=$285000

This shows that the sold price spread between the 25^th percentile and 75^th percentile is $285000