(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.
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.
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?
(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) (1 mark) to determine:
(i) The 70th percentile. (1 mark)
(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.
(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;
IFUL = Q3 + 1.5 x IQR
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, (1 mark)
(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.
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 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.
(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 bound for 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).
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”. (2 marks) 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.
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:
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.
(i) Advise Josie whether there is a binding contract with Sam.
In this part of the question, advice needs to be given to Josie if she had entered into a violent contact with Sam. The reason behind this issue is that when Sam visited Josie's studio, a particularly like a painting of sunflowers. The painting was displayed in the studio along with its price that was mentioned as $900. But Sam made an offer to purchase the painting for $700. However, Josie said that they will sell the painting for at least $800. Therefore, although Sam was ready to purchase the painting, but he said that he wanted the approval of his wife before purchasing the painting. As a result, Josie wrote it down that she had made an offer to sell the painting to Sam for $800 and at the same time, it was also mentioned by Josie that the painting will not be sold till Tuesday midnight. But Wendy, an avid art enthusiast visited the studio on Monday itself and offer to purchase the painting for $900. Therefore Josie sold the painting to Wendy on Monday itself. She left a message on the answering machine of Sam, but he could not get this message. Therefore, Sam called Josie on the phone to accept the offer, but the call got disconnected therefore he posted a letter in which he accepted the offer on Tuesday.
In this context, the law of contract provides that the presence of certain elements is essential for the formation of a legally enforceable contract. On the other hand, if even a single element does not present, the contract cannot be enforced in the court. Hence, the first requirement is that an offer should be made. For this purpose, the presence of at least two parties is required in the agreement. However, the law of contract provides that an offer can also be made to the whole world. An example of the case where it was held that the offer was made to the world at large is present in Carlill v Carbolic Smoke Ball Co. in this case the Court had held that the company's offer was open to the whole world. It is also necessary that the offeror should intend to be bound by the terms mentioned in the offer. In the same way, the differences present between an offer and invitation to deal. Generally, advertisements are considered as invitations to deal. In the same way, the goods that have been displayed in the windows of shops, along with their price are also treated as invitations to deal. Therefore in such a case, the customer has to make the offer and the owner of the goods has to decide if he wants to accept the offer or not. As mentioned above, generally it is visited that an advertisement is an offer to deal but there can be certain circumstances where even advertisement amounts to an offer (Carlill v Carbolic Smoke Ball Co., 1893). For example in the present case, the painting made by Josie had been displayed in the studio along with its price. Therefore it can be considered as an invitation to deal.
When Josie wrote the note, she had stated that the painting will not be sold till Tuesday midnight. However, she sold the painting to Wendy on Monday. As a result, it has to be seen if Sam can enforce this promise against Josie. In order to deal with such cases, the law provides that the promise made by one party in which it has been mentioned that the offer will remain open for a particular time needs to be supported by consideration. But in the present case, no consideration has been supplied by Sam in return of Josie's promise not to sell the painting. It has been mentioned in Dickinson v Dodds. In this case, an offer was made by the defendant to sell his house. At the same time, the defendant also promised that the offer will remain open until Friday. However, the defendant sold the house on Thursday and informed the plaintiff through a friend. But the plaintiff decided to accept the offer on Friday morning, and then we could not do so, he brought a claim in the court seeking specific performance of this promise.
The application of postal acceptance rule also needs to be considered. Therefore, it has to be considered if you do the application of postal acceptance rule, Sam can be allowed to claim that the offer needs to be considered as accepted when he had placed the acceptance letter in the mail box. The postal rule was stated by the court in Adam v Lindsell. It is considered as an exception to the general rule, which provides that an offer can be withdrawn at any time before its acceptance. However in the present scenario, the postal rule is not applicable. The reason behind this position is that before the acceptance of the offer by Sam, Josie had revoked the offer. The painting had been sold to Wendy and Josie had also left a message on Sam's answering machine. As a result, it can be said that a valid contract is not present between Josie and Sam.
(ii) The remedies that might be available
In this question, the issue deals with the remedies that is available to the innocent party, when the terms of the contract have been breached. In this context, the court may grant the remedies of damages, specific performance and injunctions. The court provides the remedy of damages to the innocent party as a substitute for the failure to perform the contract. Consequently, damages are granted with a view to place the innocent party in the similar position in which such party would have been if the terms of the contract would have been perform properly. As a result, generally punitive damages are not awarded by the courts. It also needs to be seen by granting the remedy of damages if the loss caused to the other party is the direct result of such a breach. The court may award liquidated damages when such a clause has been mentioned in the contract. It is stated in such a clause that a particular amount will be payable in case of a breach of contract provided the sum is not mentioned as a penalty.
Among the equitable remedies that can be granted by the court for breach of contract include specific performance and injunctions. The remedy of specific performance is granted by the court when it is ordered by the court that the contract should be performed by the other party. However such order is generally made only in the case where adequate compensation cannot be provided by damages. The remedy of specific performance is not granted in case of contracts involving personal service. On the other hand, injunctions are the orders that direct a party not to do something, for example. The party may be directed not to continue with the breach.
The rule in Pinnel’s case:
There are certain problems that are associated with the application of the rule provided in Pinnel's case. This rule provides that the payment of a lesser amount cannot be treated as the complete discharge of the debt obligations. The rule was provided as the promise of the creditor to refrain from suing the debtor for the remaining amount is not supported by consideration. Therefore, such a promise is not enforceable against the debtor. Therefore in Pinnel's case, the court was of the opinion that by paying an amount that is less than the debt on the date due is not to be treated as the complete satisfaction of the debt. On the other hand, if the debtor had gifted horse, hawk, robe etc, it can be considered as the complete satisfaction of the debt. In this regard, it was stated by the court that in this case the gift can be more beneficial for the creditor as against money otherwise the creditor would have refused to accept the gift and treat it as the complete satisfaction of the debt. However, the court stated that the payment of a lesser amount on a date before the date due to repeat the debt can also be treated as valid consideration. The reason given in favor of this position was that in this case, the early repayment of debt may amount to something more than necessary under the original agreement. The court had also mentioned this principle in Foakes v Beer.
But the rule provided in Pinnel's case has also faced much criticism. Experts have claimed that due to this rule, the creditors are permitted to go by from their promise and still claim the remaining amount. An example of this criticism was seen in Couldery v Bartrum where Jessel MR pointed out that under the common law, a thing may be accepted as the complete satisfaction of debt, but not the lesser amount. Hence, accredited may accept a horse or a canary, and it would be considered as the complete satisfaction of the debt. However due to a peculiar situation, the debtors are not allowed by the common law to accept a smaller amount in liue of the whole debt.
As a result of the problems associated with this rule and the criticism faced by this rule, the courts came up with certain exceptions to the application of this rule. Therefore, now it is, provided that this rule will not be applicable:-
- When a smaller amount has been accepted by the credited, as well as something different in kind;
- When the payment is made before the due date, at the request made by the creditor;
- When the payment of a smaller amount has been made a different place or in different currency;
- When any other act has been performed by the debtor that was not required under the original agreement;
- When it would result in a fraud on third-party; or
- When the defense of promissory estoppel is available.
While the traditional estoppel only applied in cases where a representation has been made regarding an existing fact and consequently it does not cover the representations that have been made in the context of future intentions. In this way the application of traditional estoppel was confined to their presentations that were made in context of present facts. However, the application of this doctrine had been extended to cover the representations made in context of future intentions by the court in Central London. The comments that have been made by Denning J had played a significant role, because the other judges consider that a solution was available in these comments regarding the problems that arose while applying the Pinnel's rule.
In this way, if in a particular case, the court finds out that the application of the Pinnel's rule will not be fair, there are certain exceptions available to the application of this rule.
Graw, Parker, Whitford, Sangkuhl, 2015, Understanding Business Law 7th ed LexisNexis Butterworths
Stephen Graw, 2011, An Introduction to the Law of Contract, 7th Ed., Thomson Reuters
Sweeney, O’Reilly & Coleman, 2013, Law in Commerce, 5th Ed., LexisNexis
Adams v Lindsell ( 1 B
Carlill v Carbolic Smoke Ball co  1 QB 25
Central London Property Trust Ltd. v high Trees house Ltd (1947) KB 130
Couldery v Bartrum (1881) 19 Ch D 394
Dickinson v Dodds (1876) 2 Ch D 463
Foakes v Beer (1884) 9 App Cas 605
Harvey v Facey  UKPC 1
Partridge v Crittenden  1 WLR 1204
Pinnel's case (1602) 77 ER, 237
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