INSTRUCTIONS FOR OBTAINING EXCEL OUTPUTS FOR PART III
(Tasks 6 – 9) OF THE STAT 11048 ASSIGNMENT.
The following step by step instructions are provided for you so that you are able to obtain the Excel outputs required for completing Part III of the Essential Statistics assignment tasks due in week10.
Note that the specifics of these instructions, and hence the resulting outputs, refer to a demonstration set of sample data contained in columns A to I, rows 1 to51 (including column headings) of an MS Excel assignment data file. Because of this, the Excel outputs that you obtain using your data will, with almost complete certainty, be different to what you see in the demonstrations that follow.
As you perform the steps for each assignment task make sure you pay particular attention to instructions regarding spreadsheet cell locations, modifying them where necessary to suit your particular data set. This is important so that subsequent work on the assignment flows consistently. Also, make sure that when you conclude an assignment work session you progressively save your spreadsheet work and continue on with the saved file once you recommence work in your next assignment work session.
Open your Excel file SamplePropertyData.xls which you created after the assessment 2 part 1. The variables contained in this data file 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)
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.
Normal Probability Distribution and Estimation of Population mean and proportion
Task 6 (7 marks)
In Task 6 you are required to use Excel to determine a point estimate and a 99% confidence interval estimate of the mean “Land Size” of the population of properties.
In order to achieve this we will need to obtain a descriptive statistics table (as per Assignment Task 5) except that this time we will need to ensure that the table includes information suitable for constructing the confidence interval estimate.
Although the following steps demonstrate how to do this, note that the Excel outputs you obtain will be different to what follows, as you will almost certainly be using different data to that used in this demonstration.
Step 1:
Obtain a descriptive statistics table for the “Land Size” sample data.
Repeat the procedure described in Steps 1 and 2 of Assignment Task 5 to obtain the descriptive statistics table for the “Land Size” sample data.
In the Descriptive Statistics dialogue box you will need to tick the Confidence Level for Mean box and change the Confidence Level from the default 95% to the required 99% level.
The descriptive statistics table resulting from this process is:
Note: The “Confidence Level(99.0%)” information, now provided in the descriptive statistics table, enables us to construct, in this instance, a 99% confidence interval estimate of the mean “Land Size” of the population of properties. This value (95.539), for the data that forms the basis of this demonstration, has been rounded to three decimal places for consistency with the sample mean rounding as suggested in Step 2 of Assignment Task 5.
Step 2:
Deduce the point estimate and the 99% confidence interval estimate of the mean “Land Size” of the population of properties from the sample “Mean” value and the “Confidence Level” information provided in the descriptive statistics table.
Remember that the “Mean” information provided in the descriptive statistics table is the mean of the sample data. You are required, in Assignment Task 7, to obtain two estimates, a point estimate and an interval estimate, of the mean “Land Size” of the population of properties.
Further, note that the “Confidence Level” information, from the lecture material of week 7, is the value of “e” (error bound) that is subtracted and added to the sample mean to obtain the lower confidence limit (LCL) and upper confidence limit (UCL) respectively, of the appropriate confidence interval.
Step 3:
Copy the tabular output into a MS Word document to form part of your completed assignment.
Left click on cell A1 of the descriptive statistics table and then drag to highlight the entire contents of columns A and B. Then select the Copy icon from the Home menu and paste into your Word document as described in Step 3 of Assignment Task 5.
Assignment Task 7
In Task 7 you are required to use Excel to determine a point estimate and a 90% confidence interval estimate of the proportion of properties Sold at auction in the population.
In order to achieve this we will need to obtain a descriptive statistics table, as per Assignment Task 6 above, but this time for a “new” set of sample data designed specifically to distinguish Sold at auction from non-Sold at auction propertiesin your sample.
Although the following steps demonstrate how to do this, note that the Excel outputs you obtain will be different to what follows, as you will almost certainly be using different data to that used in this demonstration.
Step 1:
Transform the sample “Sales Result” data (V3) into a “new” set of sample data designed specifically to distinguish brick veneer from non-brick veneer properties (including vacant land) in your sample.
Note that there are a number of techniques for doing this ranging from basic to the more sophisticated. The basic technique simply involves manually re-coding the values of variable V3 such that Sold at auction properties are recorded as “1” and non-Sold at auction properties are recorded as “0”. A slightly more sophisticated technique might employ the use of the conditional “IF” function to achieve the same result.
The method employed in this demonstration will be the manual re-coding technique but feel free to use alternative methods if you so desire when completing the task for your data.
To make the manual process a little less tedious we will first sort the “Sales Result” data (V3).
With your Excel workbook open at the sample data worksheet, click on cell E2 and then drag down to highlight the entire contents of column E, rows 2 to 51 (your sample “Building Type” (V3) data).
From the Home menu select the Copy icon and then paste the contents of cells D2 to D51 into any unused column, say, T1 to T50 (by activating cell T1 and then selecting the Paste icon).
With cells T1 to T50 highlighted, from the Data menu, Sort and Filter grouping, select the Sort Smallest to Largest ( ) icon at which point the initial contents of cells T1 to T50 (your sample V4 values) will be sorted into ascending order.
Now, adjacent to the first “1” in column T (if there is one), type “0” in column U and press “Enter”. Immediately re-activate that cell and then moving the mouse cursor over the right hand bottom corner of it click on it when the cursor turns to a black cross and then drag vertically down column U until all the empty cells adjacent to cells with a “1” in column T have “0” copied into them.
Repeat this process for any cells in column U adjacent to cells in column T containing “3” or “4” in them at which point all non-brick veneer properties will be recorded in column U as “0”.
The “Sales Result” data transformation is completed by following the process above for the first “2” appearing in column T but typing “1” in the adjacent empty cell in column U and then “clicking and dragging” to copy a “1” in all remaining empty cells of column U.
Data range U1:U50 will then contain values “0” and “1” only with the former representing non-Sold At auction properties and the latter representing Sold At auction properties.
Step 2:
Obtain a descriptive statistics table for the transformed “Sales Result” sample data.
Repeat the procedure described in Step 1 of Assignment Task 7 above to obtain the descriptive statistics table suitable for constructing a point estimate and 90% confidence interval estimate for the proportion of Sold at auction properties in the population.
In the Descriptive Statistics dialogue box you will need to specify, in the Input Range, the cell locations of the transformed sample “Sales Result” variable i.e. u1:u50.
The Confidence Level for Mean box has been ticked and adjusted for 90% confidence.
The descriptive statistics table (with confidence interval estimation information included) resulting from this process is:
Note: That the decimal values in this table have been rounded to, at most, two decimal places since the data being summarised in this table is whole number data (0’s and 1’s). This is consistent with the suggestion in Step 2 of Assignment Task 5.
At this stage you may be a little concerned that we have produced an Excel output that is going to provide information about a mean rather than a proportion.
The special feature to note here is that the transformed “Sales Result” data consists entirely of 0’s and 1’s and because of this the “Sum” (in this case 40) actually represents the number of brick veneer properties (each represented by the number 1) in the sample of size fifty.
The “Mean” then, calculated as40/50 = 0.8, as well as providing the arithmetic mean of the fifty data values (consisting of twenty-one 1’s and twenty-nine 0’s), also provides the percentage (40/50 = 80%) or proportion of sold at auction properties in the sample of size fifty.
Step 3:
Deduce the point estimate and the 90% confidence interval estimate of the proportion of Sold at acution properties in the population from the sample “Mean” value and the “Confidence Level” information provided in the descriptive statistics table.
As explained above the “Mean” information provided in the descriptive statistics table for a data set consisting entirely of 0’s and 1’s also provides the proportion of 1’s in the sample data. You are required, in Assignment Task7, to obtain two estimates, a point estimate and an interval estimate, of the proportion of Sold at auction properties in the population.
Further, note that the “Confidence Level” information, from the lecture material of week 7, is the value of “e” (error bound) that is subtracted and added to the sample proportion to obtain the lower confidence limit (LCL) and upper confidence limit (UCL) respectively, of the appropriate confidence interval.
Step 4:
Copy the tabular output into a MS Word document to form part of your completed assignment.
Repeat the procedure described in Step 3 of Assignment Task 6 above.
Assignment Task 8
In Task 8 you are required to use Excel to produce a single sample hypothesis test output, to test, at the 1% level of significance, the hypothesis that for properties in the population which were “Sold at auction” the mean “Advertised Price” is greater than 600 ($000s).
The use of a “dummy variable”, consisting of all zeros, will be necessary in order to complete the following procedure.
We are focussing on the properties in the population which were sold at auction. Note that this will necessitate the preliminary sorting of your sample data according to “1-Sold at auction ”. The other difference is that this time you are required to perform the hypothesis test using the method of comparing the calculated t-value with the critical t-value.
We will obtain a t-Test: Paired Two Sample for Means output to enable you to perform this single sample hypothesis test.
Although the following steps demonstrate how to do this, note that the Excel outputs you obtain will be different to what follows, as you will almost certainly be using different data to that used in this demonstration.
Step 1:
Sort the entire sample data according to variable, “Sales Result”, V3.
This is necessary so that the properties with sold at auction result can be readily identified and, in particular, so that the mean Sold Price can be calculated by Excel for such properties.
Sort the sample data from smallest to largest. You will need to make the specification of the variable in the Column Sort by drop down list. You will need to specify V3 (Sale result).
When you have completed this sorting procedure you will observe that all the properties in your sample will have been sorted according to the sale result they contain. You will notice from the V3 variable values that the properties sold at auction can now be readily identified
Step 2:
Create another variable of “Sold Price” sample data, V11, specifically relating to properties with more than 3 rooms.
Type the new variable name, V11, at the top of any unused column, say for example in cell, Y1.
Examine the listing of “Sold Price”, V7, data (for properties with more than 3 rooms) for any blank cells (properties that did not sell) and copy the contents of the non-blank cells (“Sold Price” data) into column Y from cell Y2 down.
For the data forming the basis of this demonstration, cells Y2 to Y41 eventually contained the “Sold Price” data for properties sold at auction
Once again the necessity for doing this is that the t-Test: Paired Two Sample for Means process requires the specification of the “Sold Price” data under consideration without any blank cells.
Step 3:
Obtain a t-Test: Paired Two Sample for Means output for the “Sold Price” sample data for properties sold at auction, and, the dummy variable sample data (all 0’s) for the same properties.
From the Analysis grouping of the Data menu select Data Analysis.
Select t-Test: Paired Two Sample for Means from the Data Analysis Tools list and then select OK.
In the t-Test: Paired Two Sample for Means dialogue box you will need to specify, in the Variable 1 Range, the cell locations of the “Sold Price” variable, V11, for properties that were sold at auction (for the data forming the basis of this demonstration y2 to y41).
You will also need to specify, in the Variable 2 Range, the cell locations of the corresponding dummy variable (V9) values (all 0’s) – for the data forming the basis of this demonstration Z2 to Z41.
Specify the Hypothesized Mean Difference. This is, once again, the value specified by the equality in the null hypothesis for this particular hypothesis test (in this case 600).
Specify Alpha (α) – in this case 0.01 and select New Worksheet Ply (if not specified by default) so that the output will appear on a new worksheet of the MS Excel workbook.
Select OK to obtain the t test: Paired Two Sample for Means output.
Note: The t test: Paired Two Sample for Means output provided by Excel at this point is, once again, in need of modification so as to provide more clarity in the information provided.
Step 4:
Modify the t test: Paired Two Sample for Means output provided by Excel to provide more clarity in the information provided.
Repeat the procedure described in Step 5 of Assignment Task 9 to obtain the t test: Paired Two Sample for Means output with enhanced clarity of information provided.
Step 5:
Copy the t-Test: Paired Two Sample for Means output into a MS Word document to form part of your completed assignment.
Left click on cell A1 of the t test: Paired Two Sample for Means output and then drag to highlight the entire contents of columns A, B and C. Then select the Copy icon from the Home menu and paste in to your Word document.
Step 6:
Identify the location of the information contained in the t-Test: Paired Two Sample for Means output necessary for carrying out the single sample hypothesis test.
In this task you are required to perform the single sample hypothesis test using the method of comparing the calculated t-value with the critical t-value.
For this purpose MS Excel provides the calculated t-value (t Stat) together with the magnitudes of the t Critical one-tail value and the t Critical two-tail value for performing the required hypothesis test.
Step 7:
Perform the required hypothesis test.
You will need to determine whether you are dealing with a one-tailed or a two-tailed test.
If you are dealing with a one-tailed test, it will once again be important to determine whether the sample evidence is consistent with the alternative hypothesis before you proceed further with the test.
If this is not the case the null hypothesis cannot be rejected.
Since you are required to perform the test by comparing the calculated t-value with the critical t-value, you will need to allocate an appropriate sign (+ or −) to the relevant critical t-value before you proceed with the test. Remember that the t Critical one-tail value and the t Critical two-tail values provided by Excel in this output are “magnitudes”. The “signs” of these values need to be determined before the comparison with the calculated t-value is performed.
If the test is one-tailed positive, the Critical one-tail value is the relevant comparison value and should be assigned a positive value.
If the test is one-tailed negative, the Critical one-tail value remains the relevant comparison value but this time should be assigned a negative value.
If the test is two-tailed, the Critical two-tail value is the relevant comparison value and should be assigned the same sign as the t Stat value.
Assignment Task 9
In Task 9 you are required to use Excel to produce a paired/dependent samples hypothesis test output to test, at the 5% level of significance, the hypothesis that the mean “Sold Price” of a property in the population is different to the mean “Advertised Price”.
Note that this time we are performing a paired/dependent samples hypothesis test, because the sub-sample providing data relevant to the “Sold Price” of properties is the same ((i.e. not independent) as that for the “Advertised Price” of properties.
Although the following steps demonstrate how to do this, note that the Excel outputs you obtain will be different to what follows, as you will almost certainly be using different data to that used in this demonstration.
Step 1:
Sort the entire sample data according to “Sold Price”, V7.
This is necessary so that the “Sold Price” data for properties that did sell, together with the corresponding “Advertised Price” data for the same properties, can be easily specified, and, in particular, so that the mean “Sold Price” and “Advertised Price” can be separately calculated by Excel for these properties.
Repeat the procedure described in Step 2 of Assignment Task 8, this time to sort the sample data according to “Sold Price”. The only variation you will need to make to the procedure described in Task 8 is with the specification of the variable in the Column Sort by drop down list. This time you will need to specify V7 (Sold Price).
When you have completed this sorting procedure you will observe that all the properties in your sample will have been sorted according to the sold price of the property and, in particular, that properties that did not sell (blank V7 cells) have been filtered to the bottom of column H.
For the data forming the basis of this demonstration, cells H2 to H46 contained the sold price of properties that in fact did sell (non-blank V7 cells).
You will then need to identify the cell locations of the “Advertised Price” variable, V8, for the corresponding properties that you have just identified as having sold. This will be readily achieved since these advertised prices will be located in column I adjacent to the non-blank cell locations in column H.
Step 2:
Obtain a t-Test: Paired Two Sample for Means output for the “Sold price” and the “Advertised Price” sample data (for properties that sold).
From the Analysis grouping of the Data menu select Data Analysis.
Select t-Test: Paired Two Sample for Means from the Data Analysis Tools list and then select OK. Note that a “t-test” is appropriate in this situation because the relevant population variances are unknown.
In the t-Test: Paired Two Sample for Means dialogue box you will need to specify the non-blank cell locations of the “Sold Price” variable, V7, and the corresponding locations of the “Advertised Price” variable, V8, for the same properties.
Once again we recommend, particularly when dealing with one-tail hypothesis tests, that you specify the locations of these two variables in the same order as they are referred to in the formal recording of the alternative hypothesis (Variable 1 Range for the variable referred to first and Variable 2 Range for the variable referred to second).
In this case we have chosen to specify the non-blank cell locations of the “Sold Price” variable (i.e. h2:h49) in the Variable 1 Range. And, we have specified the corresponding cell locations of the “Advertised Price” variable (i.e. i2:i49) in the Variable 2 Range.
Specify the Hypothesized Mean Difference. This is the value specified by the equality in the null hypothesis (expressed as a difference) for this particular hypothesis test (in this case again 0).
Specify Alpha, the level of significance of the hypothesis test (α) – in this case 0.05 and select New Worksheet Ply (if not specified by default) so that the output will appear on a new worksheet of the MS Excel workbook.
Select OK to obtain the t test: Paired Two Sample for Means output.
Note: The t test: Paired Two Sample for Means output provided by Excel at this point is, once again, in need of modification so as to provide more clarity in the information provided.
Step 3:
Modify the t test: Paired Two Sample for Means output provided by Excel to provide more clarity in the information provided.
Follow the procedure described in Step 5 of Assignment Task 8 to obtain the t test: Paired Two Sample for Means output with enhanced clarity of information provided.
In this instance we will replace “Variable 1” and Variable 2” with “Sold Price ($000’s)” and “Advt. Price ($000’s)” respectively, so as to make explicit reference to the variables of interest.
The number of decimal places quoted in the output has been adjusted in accordance with the guidelines described in Step 5 of Assignment Task 8
.
Note: The use of Scientific (or Exponential) Notation in this case in the recording of the two probability (P) values. Particular care will need to be taken not to misinterpret these two numerical values (are they small or large in comparison to α?).
Step 4:
Copy the t-Test: Paired Two Sample for Means output into a MS Word document to form part of your completed assignment.
Left click on cell A1 of the t test: Paired Two Sample for Means output and then drag to highlight the entire contents of columns A, B and C. Then select the Copy icon from the Home menu and paste in to your Word document.
Step 5:
Identify the location of the information contained in the t-Test: Paired Two Sample for Means output necessary for carrying out the two sample hypothesis test.
In this task you are required to perform the two sample hypothesis test using the P-value approach.
Once again, MS Excel provides two P values, the P(T<=t) one-tail – for one-tailed hypothesis tests and P(T<=t) two-tail – for two-tailed hypothesis tests.
Step 6:
Perform the required hypothesis test.
You will need to determine whether you are dealing with a one-tailed or two-tailed test.
If you are dealing with a one-tailed test, and particularly since you are required to perform this hypothesis test using the P-value approach, it is important to determine whether the sample evidence is consistent with the alternative hypothesis before you proceed with the test.
This can be achieved by comparing the means obtained from the samples with the statement of the alternative hypothesis. Alternatively you can check that, for a one-tail positive test, t Stat is positive and for a one-tail negative test, t Stat is negative.
Remember that if the sample evidence is not consistent with the alternative hypothesis the null hypothesis cannot be rejected.
Don’t forget to save your Excel worksheet, SamplePropertyData.xls, on which you have completed the above work and recommence future work (Part III) on the assignment using this same file.
PN V1 V2 V3 V4 V5 V6 V7 V8
107 1 1 2 2 8 879 1200
111 1 1 1 3 5 650 440 374
115 3 1 2 2 5 613 450
116 3 1 1 1 5 845 1800 1681
117 3 0 1 1 6 880 827
127 1 0 1 2 5 319 255
136 3 1 3 2 6 512 552 490
142 2 1 3 2 8 885 425 363
143 2 1 1 1 7 636 542 486
144 2 1 1 3 6 585 552 480
146 4 1 1 3 3 248 615 554
156 3 1 2 2 10 645 1150
161 2 1 4 3 4 296 633 564
163 2 3 4 1085 132 105
171 2 1 1 3 6 535 465 406
173 2 1 2 1 4 280 750
181 3 0 4 1 5 936 803
184 2 1 4 1 4 200 460 407
186 3 1 1 1 5 319 805 736
191 2 1 1 2 7 650 270 253
198 2 3 4 560 112 87
199 3 0 1 1 3 420.5 367
201 1 1 1 2 7 20000 1010 826
204 1 1 2 2 5 531 550
212 3 1 1 2 5 578 718 662
215 1 1 1 3 5 412 379 313
220 2 1 3 3 4 236 610 541
222 3 1 1 2 6 730 650 590
223 3 1 4 1450 1360 1208
225 3 1 4 2 5 796 900 850
228 3 1 1 1 4 435 596 536
232 2 0 1 2 6 670 610
241 4 1 1 1 4 125 782 716
257 1 1 3 2 6 697 505 447
268 1 0 1 2 4 441 381
276 2 1 1 2 5 380 363 289
279 4 0 1 1 4 865 814
284 4 1 4 1 4 167 675 618
293 1 1 1 3 5 712 631 577
301 1 1 1 2 5 446 432.5 369
305 1 0 4 2 4 351 279
318 3 1 1 3 6 703 501 433
325 3 0 1 2 6 605 536
327 3 1 3 2 7 700 845 788
354 3 0 1 1 3 409 359
359 1 1 4 1 7 725 645.55 593
364 2 1 1 3 5 450 418 363
368 2 1 1 3 5 630 426 366
370 2 1 4 3 6 635 450 400
371 2 3 4 1160 265 238
_________________________________________________________________________
The complete STAT 11048 assignment (all three parts) accounts for 20% of the overall assessment in the unit.
This third part of the STAT 11048 assignment is to be completed and submitted for correction in the tutorial of week 11. No time extensions will be granted although special consideration applications may be accepted from students unable to satisfy submission requirements due to extenuating circumstances.
As for Parts I and ll, Part III of the assignment must be submitted in hard copy form accompanied by a completed Assessment Declaration (see the Assessment Information page of the unit website).
Although you will be provided with guidance with regard to addressing the assignment tasks, you will need to complete the tasks in your own time. The document “Instructions for Obtaining Excel Outputs for Part III of the STAT 11048 Assignment” (see the Assessment Information page on the unit website) provides “step by step” instructions for obtaining the Excel outputs that are necessary in any of the of the assignment tasks.
To avoid any complications associated with misplaced assignments, make a photocopy of your assignment before you hand in the original to your tutor for correction.
Presentation
• Your answers must be presented in task number order and be clearly labelled with the appropriate task number. Answers to each task must start on a new page.
• Your assignment must be presented in Microsoft (MS) Word. Copy and paste any relevant Excel outputs to this document immediately above or below your written answers to each task.
• If you are unfamiliar with the use of the MS Word Equations Editor, you may write algebraic/mathematical/statistical symbols and notation in neat handwritten form.
• Your answers must be clear. You must highlight relevant items on the output and make reference to them in your assignment.
• Completed assignments are to be presented for correction on A4 paper, stapled in the top left hand corner. Please print on one side of the paper only.
• Do not submit the assignment with fancy bindings, folders or plastic envelopes.
• An Assessment Declaration (see the Assessment Information page on the unit website) is required and must be stapled to the front of your assignment.
• Do not include the assignment questions with your solutions nor the population data.
• You are permitted to consult your textbook and notes and to communicate with other students. However, the work you hand in for correction must be that of your own group. Be aware that the University penalties for plagiarism are severe.
Introduction
In Part I of the assignment you have selected a random sample of 50 properties each containing observations, where appropriate, of the eight variables V1 to V8.
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)
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.
You should continue the required work on Part III of the assignment using the Excel worksheet, SampleData.xls, that you were working on at the completion of Part II of the assignment.
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. Part III of the assignment requires 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 two tasks in Part III of the assignment. Each task is worth 6 marks. 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.
The total mark available for the entire assignment is 60. The total mark you receive for your assignment will be converted to a mark out of 20 before being aggregated with your test and examination marks to produce your final result for the unit
Task 6 (7 marks)
(a) Use Excel to produce a Descriptive Statistics table for the “Land Size” variable in your sample suitable for constructing an interval estimate of the population mean “Land Size”. Hence determine:
(i) A point estimate of the mean “Land Size” of the population of properties.
(ii) A 99% confidence interval estimate of the mean “Land Size” 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 “Land Size” is actually 750 square meters, would you consider the interval estimate obtained in (a), to be satisfactory? Explain why or why not.
(d) If you are asked to construct the 95% confidence interval what will happen to precision of the interval estimate in comparison to the 99% confidence interval constructed in (a)
Task 7 (6 marks)
Use Excel to produce a Descriptive Statistics table for the properties Sold at auction in your sample suitable for constructing an interval estimate of the population proportion of properties Sold at auction.
(a) Hence determine:
(i) A point estimate of the proportion of properties Sold at auction in the population.
(ii) A 90% confidence interval estimate of the proportion of properties Sold at auction 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 properties Sold at auction is actually 80%, would you consider the interval estimate obtained in (a), to be satisfactory? Explain why or why
Task 8 (7 marks)
(a) Use Excel and your sample data file to produce a single sample hypothesis test output, to test at the 1% level of significance, the hypothesis that, for properties in the population which were “Sold at auction” the mean “Advertised Price” is greater than 600 ($000s).
(b) Write, in symbolic form, the null and alternative hypotheses.
(c) Is this a one-tailed or two-tailed test?
(d) By comparing the calculated t statistic from the Excel output with the critical t-value, state whether you would reject the null hypothesis or not, and why.
(e) Make a brief statistical conclusion in the context of the variables in this hypothesis test.
Task 9 (7 marks)
Use Excel and your sample data file to produce a paired/dependent samples hypothesis test output to test at the 5% level of significance, the hypothesis that the mean “Sold Price” of a property in the population is different to the mean “Advertised Price”.
(b) Write the null and alternative hypotheses.
(a) Is this a one-tailed or two-tailed test?
(b) Using the p-value approach, state why you would reject the null hypothesis or not.
(e) Make a brief statistical conclusion in the context of the variables in this hypothesis test.
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