Assignment Internal Cash Control Essay Example for Free

Task Internal Cash Control Essay The shortcomings in the inner power over money distributions are, there ought to be just a single individual responsible for composing the checks for each errand, and there ought to be numbered checks for the two individuals with the goal that the assets spend can be followed simpler, the cupboards were the checks are put away ought to be two bolted cupboards, one for every individual who composes the checks. Reminder: I would prescribe that to have a superior power over cash paid and things bought, that you begin having numbered checks in two separate records, one record for the treasurer and one record for the buying operator. This strategy will make it simpler for moth gatherings to maintain a strategic distance from errors, and it will likewise be simpler to confirm cash spent and gotten. P4-1A The inward control standards executed by the Guard Dog Company are, numbered checks with the goal that the organization has a number path to screen money dispersment. Each check must have endorsement from Jane Bell, and Dennis Kurt before a check can be given, this is a foundation of obligation to guarantee that not simply anybody particle the organization can compose checks. Checks must be marked by either Tom Kimball, the treasurer, or Karen Thews, the associate treasurer. Prior to marking a check, the underwriter is relied upon to contrast the measures of the check and the sums on the receipt, this is likewise a type of foundation of duty and both of these strategies are an utilization of documentation methods. In the wake of marking a check, the underwriter stamps the receipt â€Å"paid† and embeds inside the stamp, the date, check number, and measure of the check. The â€Å"paid† receipt is then sent to the bookkeeping division for recording. By doing this it is a method of checking organization money dispersment and documentation control. Limitless tickets to ride are put away in a safe in the treasurer’s office. The blend to the safe is known by just the treasurer and right hand treasurer. By securing the checks a protected it sets up obligation regarding the checks, and uses a Physical, mechanical, and electronic controls to limit any check issues to one source. Every month the bank proclamation is accommodated with the bank balance per books by the associate boss bookkeeper. By doing this it sets up report control, along these lines any inconsistencies in the sum paid can be checked. Show the shortcomings in interior bookkeeping control in the treatment of assortments. The shortcomings in the treatment of assortments are the manner in which the cash is saved, the manner in which the looks at are made and the manner in which the cash is confirmed and saved. P4-2A List the enhancements in interior control systems that you intend to make at the following gathering of the review group for (1) the attendants, (2) the head usher, (3) the money related secretary, and (4) the fund panel. The upgrades the attendants need to make is that after each offering they ought to independently check their own gathered bins and log there sum in a contribution log book, so that there is less space for mistake in the subsequent stage. By giving all the bins to the head usher without tallying the cash themselves, the head usher can offer any sum on his last store. The upgrades the head usher needs to make is to ensure that each usher tallies their crates, and that the head usher checks all the bins and checks for disparities to ensure that nobody is taking any cash. The head usher ought to likewise check the sum given to him/her against what is written in the contribution log. Have a book to log the measure of cash that is placed into the safe with the goal that it is signed in a manner that can be checked by the board of trustees, a note is definitely not a sheltered strategy since it very well may be tossed out, by signing in a book it is simpler to discover were the inconsistencies originated from. The upgrades the money related secretary should make is that he/she ought to have a rundown of what should be paid and make a log of the sums that need paid and to ensure the receipts are logged alongside whatever bills or administrations that should have been paid that week. The monetary secretary ought to likewise check the measure of cash in the safe against the log that is kept by the attendants. The money related board of trustees should show an increasingly itemized rundown of what consumptions are required every month with the goal that the budgetary secretary comprehends what is required for installment that month. They ought to likewise be engaged with confirming the places of worship salary. To improve interior control the congregation ought to have a log for cash got during contributions, they should advise the gathering to make the checks payable to the congregation or to the record holder that the registers are kept with, in light of the fact that anybody can money a look at made to â€Å"cash†. The congregation ought to likewise confirm that any cash not saved from the contribution was spent appropriately and not utilized for individual things. Incorporate how an organization could utilize the five essential standards of money the board to expand exactness for a business. An organization can expand the assortment of receivables by offering motivating forces for snappy installment from their clients. An organization can postpone the installment of liabilities and bills to near the due date of the risk or bill, so that if any use is required before the due date they won't have gone through the cash too soon. An organization can keep stock low on the product that doesn't sell rapidly, with the goal that the organization has cash for the product that is well known and selling quick. An organization that desire to extend should hold up until they have abundance cash in a moderate season with the goal that they can grow their business and possess new areas open in energy for their bustling season. An organization ought to put cash that is sitting inactive into okay companies’, the most widely recognized type of fluid speculations is enthusiasm paying U. S. government protections.

Controversial Supreme Court Case Roper V. Simmons Essay Example

Questionable Supreme Court Case Roper V. Simmons Essay Example Questionable Supreme Court Case Roper V. Simmons Paper Questionable Supreme Court Case Roper V. Simmons Paper Article Topic: Questionable The Death Penalty is a questionable theme all alone. Be that as it may, on the off chance that you include the chance of a minor accepting capital punishment it gets considerably all the more intriguing. The Supreme Court instance of Roper v. Simmons was an ideal case of that. Roper v. Simmons gave the Supreme Court two inquiries: 1) regardless of whether the execution of the individuals who were sixteen or seventeen at the hour of a wrongdoing is brutal and bizarre rebuffed and 2) does is damage the Eighth and Fourteenth Amendment. The principle crowd for this specific case is the general American populace, and explicitly influences the adolescent populace. Christopher Simmons, seven months short of his eighteenth birthday celebration, arranged and executed the homicide of a guiltless lady. Portrayals of the homicide are completely chilling. Reports uncovered that Simmons and an assistant bound the lady in tape and dropped her off an extension, suffocating her in the waters underneath. Simmons later admitted to the wrongdoing and even took an interest in a recorded reenactment of it. On the off chance that he had been a grown-up at the hour of the homicide, Simmons’ case would not bring up any sacred issues. Yet, because of his age, the issue under the steady gaze of the court was whether the Eighth and Fourteenth Amendments permitted the United States to â€Å"execute an adolescent wrongdoer who was more established then 15 however more youthful than 18 when he carried out a capital wrongdoing. † Justice Kennedy insisted the past decision in the Missouri Supreme Court. Therefore, Simmons couldn't be considered for capital punishment because of his age, and his sentence stayed at life in jail without any chance to appeal. Equity Kennedy proceeded to state, â€Å"it is the court’s thinking that puts forth this defense questionable, due to advancing gauges of decency† (ROPER v. SIMMONS, (03-633) 543 U. S. 551 2005) since the decision in Stanford v. Kentucky (1989), the Court has grounds to govern against the adolescent capital punishment. In the Stanford managing, the Court held that adolescents younger than 15 couldn't be executed, â€Å"due to sees that have been communicated by regarded proficient associations, and driving individuals from the Western European people group. † (STANFORD v. KENTUCKY, 492 U. S. 361 1989) The Court later governed in Atkins v. Virginia (2002) that, â€Å"mentally hindered people were absolved from capital punishment too, a further indication of society’s evolving gauges. † (ATKINS v. VIRGINIA, 536 U. S. 320 2002) The choice in Atkins disclosed that because of their debilitations, â€Å"it is exceptionally far-fetched that such guilty parties would ever merit the death penalty. † (ATKINS v. VIRGINIA, 536 U. S. 320 2002) The thinking in Atkins is applied to the Simmons choice. Kennedy contends that since people under 18 are completely less chargeable than the normal lawbreaker, they ought not merit capital punishment. Kennedy includes that there are three contrasts between adolescents under 18 and grown-up guilty parties. To begin with, â€Å"juveniles regularly come up short on the development found in grown-ups, an attribute that is reasonable among the youthful and teenagers are overrepresented factually in for all intents and purposes each class of crazy conduct. † (ROPER v. SIMMONS, (03-633) 543 U. S. 551 2005) The subsequent contrast is, â€Å"that they are progressively defenseless against negative impacts or outside weights and this could prompt degenerate conduct. † (ROPER v. SIMMONS, (03-633) 543 U. S. 51 2005) Lastly, Kennedy declares that â€Å"the character of an adolescent isn't too framed as a grown-up and that character qualities in young people are momentary. † (ROPER v. SIMMONS, (03-633) 543 U. S. 551 2005) Moreover, in view of the relative youthfulness and untrustworthiness of such individuals, Kennedy coherently noticed that almost every state bars individu als under 18 from casting a ballot, serving on juries or wedding without parental assent. If so, they ought to likewise be excluded from capital punishment, since adolescents have a more prominent case than grown-ups to be pardoned of conditions that can prompt wrongdoing and freak conduct. Likewise, the guard presented mental and neurological proof demonstrating that young people, including sixteen-and seventeen-year-olds, need adequate mind and social advancement to have the essential culpability. In spite of the fact that the Court perceived that adolescents are less experienced, instructed, and insightful than grown-ups in Thompson, the Roper Court is, â€Å"unlikely to discover the insufficiencies of adolescents as extraordinary as those of the intellectually impeded. † (THOMPSON v. OKLAHOMA, 487 U. S. 15 1988) Furthermore, Stanford’s express dissatisfaction with logical confirmation proposing that adolescents are less guilty shows that the Court is probably going to discover reprisal can be adequately served. At long last, â€Å"juveniles will probably be seen as reasonably discouraged by the danger of capital punishment, particularly since the equivalent subjective and conduct capacities at issue in Stanford are getting looked at in Roper. † (ATKINS v. VIRGINIA, 536 U. S. at 320. Pp. 5-17) Justice Stevens concurred with the lion's share pinion, yet felt constrained to take note of that in light of the fact that our comprehension of the Constitution changes now and again, the Court could properly inspect the adjustment in measures to decipher the Eighth Amendment. However Justices O’Connor and Scalia felt that there were clear issues with the Court’s cover administering. They were particularly worried that the Court felt a â€Å"national consensus† against the adolescent capital punishment existed. An enormous number of the American populace are hostile to capital punishment and much increasingly enthusiastic against it with regards to adolescents confronting this sentence. As indicated by Justice Kennedy, 30 states presently preclude the adolescent capital punishment †12 that have killed the death penalty by and large and 18 that bar adolescents from its range. However Justice Scalia impacts this contention taking note of, â€Å"that none of the Court’s past cases that managed claimed established constraint upon capital punishment has tallied states that have dispensed with capital punishment altogether. † (ROPER v. SIMMONS, (03-633) 543 U. S. 51 2005) Justice O’Connor includes that the â€Å"halting pace of change† in this circumstance is far unique in relation to the â€Å"extraordinary wave of authoritative action† that went before the court’s administering in Atkins. This gives the protesters â€Å"reason to pause,† in light of the fact that the national slant doesn't appear as concrete as Justice Kennedy attests. Be that as it may, the 5-4 Supreme Court choice in Roper v. Simmons now forestalls anybody younger than 18 from being executed. The disagreeing conclusions additionally centered around the Court’s thinking that adolescents are â€Å"categorically less at fault than the normal lawbreaker. The two Justices can't help contradicting this thinking, and Justice O’Connor calls attention to that however a multi year old killer is ordinarily less capable than a grown-up, doesn't mean he could be adequately guilty to justify capital punishment. O’Connor calls attention to that Simmons boasted he could â€Å"get away with murder† due to his age. Giving an indication that he was not hindered by the possibility of the death penalty. The way that everything about arranged ahead of time clarifies how Simmons has an awareness tangibly more debased than that of the normal killer. Equity Scalia refers to an amicus brief by the American Psychological Association, which contended, â€Å"Adolescents had successful abilities in thinking about good quandaries and understanding social guidelines and laws†¦ and could settle on choices like having a premature birth without parental endorsement. † (APA 2004) Surely, if adolescents are full grown enough to settle on a premature birth, they can be sufficiently developed to submit murder. Moreover, Scalia talked about the amici briefs portray, â€Å"Additional instances of murders submitted by people under 18 that include really massive acts. (APA 2004) While adolescent executions are uncommon, Justices O’Connor and Scalia accept that it was an error to boycott them totally. In their brain, not exclusively are a few young people equipped for grievous acts, they ought to be rebuffed in like manner. References American Psychological Association. Roper. D. P. v. Simmons, C. (2004). Brief from the Psycholo gical Association, Missouri Psychological Association. as Amici Curiae supporting respondent July 2004. Recovered May 20, 2011 from apa. organization/about/workplaces/ogc/amicus/roper. pdf ATKINS v. VIRGINIA, 536 U. S. 320 (2002) Retrieved May 20, 2011 from FindLaw: http://caselaw. findlaw. com/va-preeminent court/1427407. html ROPER v. SIMMONS, (03-633) 543 U. S. 551 (2005) 112 S. W. 3d 397, avowed Retrieved May 20, 2011 from law. cornell. edu/supct/html/03-633. ZD1. html STANFORD v. KENTUCKY, 492 U. S. 361 (1989) Retrieved May 20, 2011 from FindLaw: http://laws. findlaw. com/us/492/361. html THOMPSON v. OKLAHOMA, 487 U. S. 815 (1988) Retrieved May 20, 2011 from FindLaw: http://laws. findlaw. com/us/487/815. html

Literature of The Long White Cloud Books from Aotearoa New Zealand

Literature of The Long White Cloud Books from Aotearoa New Zealand Aotearoa New Zealand. The Land of The Long White Cloud. Middle Earth. Home to Taika Waititi, Lorde, Badass Librarians, and Flight of the Concords. New Zealand is a tiny little island in the middle of the ocean, but from it comes a literary canon of vast and varied voices. Its a place of wonder and beauty and its a country in which the roots run deep. These books are from my homeland, so although you may never visit, or listen to me wax lyrical about the mountains and lakes and trees, you can at least experience the best of New Zealand literature in the pages of a book. The Bone People  by Keri Hulme A harrowing and heartbreaking novel that explores post-colonial New Zealand. Kerewin is an a-sexual woman from  Maori descent who is fiercely independent and headstrong, her lonely life is disrupted when a mute orphan arrives at her home one stormy night. Raising questions about race, sexuality, and abuse The Bone People is morally ambiguous and will fuck you up. The Whale Rider  by Witi Ihimaera The tale of a young girl growing up in a patriarchal world, The  Whale Rider questions cultural and indigenous sexism. Set on the rugged coast of New Zealand, the novel expertly intertwines past with present creating a sense of hope for the future. White Lies by Witi Ihimaera Originally titled The Medicine Woman, White Lies is a clash of culture and tradition when a  Maori Medicine Woman is asked to keep a secret by a wealthy white woman. The Luminaries by Eleanor Catton The world was focused on New Zealand literary scene when Catton won the 2013 Man Booker Prize for her 800 page novel,  The Luminaries.  This novel is a commitment so make time for it, but with its intricate structure and intriguing mystery,  The Luminaries  is worth the weight. The Rehearsal by Eleanor Catton Often eclipsed by its more famous older sister, Cattons  The Rehearsal  is a quietly powerful debut novel. Combining sexuality, music, identity, and drama, its a novel I will never tire of reading. I Am Not Esther by Fleur Beale Everyone loves a story about a cult and this is one of the best. A young girl finds herself raised by relatives who are in a religious cult. Her name is changed to Esther and she is forced to live a life that suppresses all she knows to be true. Obsessive, terrifying, fascinating. Baby by  Annaleese Jochems Baby makes me feel like Im reading about a Murakamiesque ennui musing on celebrity culture, money, social media, and narcissism, its blunt and urgent.  Baby is a  truly millennial novel complete with a millennial pink cover. Can You Tolerate This? by  Ashleigh Young Wicked smart personal essays exploring punk rock, growing up in the 90s, and mental health. Ive read so many essay collections, but one that is seeped in the culture and history of New Zealand allows me to see elements of my own story reflected in literary non-fiction. Wild Pork and Watercress by Barry Crump In the midst of the worlds obsession with Taika Waititi, readers will be pleased to know his film  Hunt for the Wilderpeople  is based on Crumps Wild Pork and Watercress. The Chimes by Anna Smaill Longlisted for the 2016 Man Booker Prize,  The Chimes  is set in a world where words are forbidden and memories are absent, in their absence music and objects form a way of communication and power. Wake  by Elizabeth Knox A disturbing novel with an excellent cover,  Wake  is about a community who are overcome with insanity, commit mass homicide, and then are left with the gory aftermath. Lewisville by Alexandra Tidswell Based on true events,  Lewisville  is a  historical novel spanning decades and continents. Anchored by a secret, the plot chronicles the reinvention of a young woman and the secrets we keep in order to remake ourselves. Potiki by Patricia Grace The question of ownership is at the heart of every colonised nation. And, it is a question that continues to be debated and discussed in New Zealand politics today. Graces  Potiki  speaks to this question and looks at ownership itself is the land something to be owned? And if so, by who? Tu  by Patricia Grace Named for the  Maori God of War, Tu was a solider in the  Maori Battalion in Italy during World War II.  Tu speaks of  war, survival, brotherhood, and sacrifice. Incidentally, one of Taika Waititi early short films  Tama Tu is about this very Battalion. Hera Lindsay Bird by Hera Lindsay Bird A collection of confessional poetry from young poet Hera Lindsay Bird. In 2016 her poem  Keats Is Dead So Fuck Me From Behind went viral, and in true form the rest of Birds poetry is just as raw and raunchy. Who Was That Woman, Anyway? by Aorewa McLeod A feminist navigation of a male world,  Who Was That Woman, Anyway?  jumps from party to dorm room to classrooms to covens in search of sexual identity and belonging.

Important Events in the European History That Changed the...

Essay 3 The changes are an integral part of progress and development. It is a well-known fact that in order to gain a new level the society should go through the series of different transformation. These transformations are not always pleasant and peaceful but, in general, they are useful for the society and help it to become a better one. In this work I am going to explain how, the European world changed dramatically as a result of a series of stresses in the late 13th to the mid 15th centuries and how such events as Black Plague, the One Hundred Years War and the collapse of Papal Power influenced the Medieval European society. The transformation of the Medieval society was long and painful process, which lasted approximately 150†¦show more content†¦The second effect was lack of laborers. The level of trust to the Church also decreased. The One Hundred Years’ War was another historical even, which influenced on the society in the Middle Ages. It â€Å"was a long s truggle between England and France over succession to the French throne. It lasted from 1337 to 1453, so it might more accurately be called the â€Å"116 Years War† (Wheeler, â€Å"The Hundred Years’ War†). Actually, it was the series of smaller wars and included several battles. The war involved two countries, England and France, which were among the leading ones in Europe during the Middle Ages. Nothing special, that such a massive struggle, which involved a large amount of people during the extremely long period of time, resulted into the drastic demographic, economical and political changes. England lost most of its continental territories and the insanity of the King brought it into the series of internal conflicts. On the contrary, France was able to strengthen its positions. The third important point, which initiated the changes in the European society and brought it to the new era of development, was the collapse of Papal Power. In the Middle Ages the be lief that there is one Pope, who rules the church, was extremely strong. That is why the division of the Papacy into the two ruling points, one in Avignon, France and one in Rome was a great tragedy for many people asShow MoreRelatedInfluence Of Science And Religion1564 Words   |  7 Pagesof the human experience since time began. Both science and religion have influenced human thought and civilization. When a question could not be answered by time and observation, people fell back on spiritual explanations. The need to resolve important everyday questions, such as; what controlled their environment, or, what system of morality is needed to best promote the stability of the tribe, meant that for early peoples, some response was required, so some people within started to come up withRead MoreHow the Columbian Exchange Changed Our World Forever810 Words   |  3 Pagesto the Old World and vice versa. This exchange had an enormous influence on the world: without the Columbian exch ange, the world would not be the same as the one we know today. In his essay, Charles C. Mann (2007) called the exchange the most important event after the death of the dinosaurs. Firstly, the Columbian exchange dramatically transformed the American ecological environment. Charles C. Man (2007) explained that, due to the success of Rolfe’s tobacco plantation in Jamestown, English earthwormsRead MorePrimary Source Evaluation Essay1018 Words   |  5 Pagessubstantially after the events described took place. The time gap did not seriously affect the main content of the material because the events he describes were very serious and unforgettable ones. He wrote the material at the time he had already been a member of the Anti- Slavery Society leaving room for a little suspicion of his tendency to exaggerate some descriptions in his narrative. 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The Aims of Social Networks Assignment Example

Essays on The Aims of Social Networks Assignment The paper "The Aims of Social Networks" is a good example of an essay on technology. Social networking can be termed as an act of getting connected to and participating in a network of users connected virtually via a network. The network is often established by a portal or a website that enables users to create their profile on it and lets them get connected to all the other users who are logged into the site. This network of virtual individuals is tremendously large in magnitude and is a source of a number of advantages and disadvantages.   Examples of platforms supporting social web profiles are Facebook, Twitter, Orkut LinkedIn, etc. The globalization of today’s world sees it as such that virtually every human being is connected to the web in one way or the other. AIMS AND SCOPE: The aims of Social Networks are numerous. They can be summarized as follows: The spreading out of information and that too in an efficient and timely manner. The maintenance of timely runtime contact with individuals across the globe irrespective of their physical locations etc. The connections via social networks can be used to interconnect individuals whether it may be for personal or professional purposes. The scope of social networks varies extensively. From personal updates to the marketing of your officially launched professional product, the social network does it all for you. Its usage in E-Commerce and specifically E-Marketing is widespread as well. CONCLUSION AND RECOMMENDATIONS The increasing popularity of social networks d emands that social ethics be made prevalent on social networks. If the cons are administered social networks are inevitable from the lives of humans. Recommendations for social networks are primarily for youngsters. Youngsters are advised not to share their personal information with strangers on public social networks.

All Contracts Are Agreements but Not All Agreements Free Essays

According to section 2(a) of Indian Contract Act states that, â€Å"every promise on every set of promises forming the consideration for each other an agreement. An agreement is a form of cross reference between different parties, which may be written, oral and lies upon the honor of the parties for its fulfillment rather than being in any way enforceable. It is also a fact that an agreement is a proposal and its acceptance, by which two or more person or parties promises to do abstain from doing an act. We will write a custom essay sample on All Contracts Are Agreements but Not All Agreements or any similar topic only for you Order Now But a contract according to section 2(h) of the Indian Contract Act, â€Å"An agreement enforceable by law is a contract. It is clear these definitions that the two elements of a contract are: (a) Agreement Contractual Obligation (b) Enforceability by Law. For Example: X invites his friend to coffee and the latter accepts the invitation. This is a social agreement not a contract because it does not imply any legal obligation. We can say that: (a) All contracts are agreements, (b) But all agreements are not contracts. (a) All Contracts are Agreements For a Contract to be there an agreement is essential; without an agreement, there can be no contract. As the saying goes, â€Å"where there is smoke, there is fire; for without fire, there can be no smoke†. It could be said, â€Å"Where there is contract, there is agreement without an agreement there can be no contract†. Just as a fire gives birth to smoke, in the same way, an agreement gives birth to a contract. Another essential element of a contract is the legal obligation for the parties to the contract; there are many agreements that do not entail any legal obligations. As such, these agreements cannot be called contracts. For Example: A gives his car to B for repair and B asks for Ksh. 2000 for the repair works. A agrees to pay the price and B agrees to repair the car. The agreement imposes an obligation on both. The third element of a contract is that the agreement must be enforceable by Law. If one party fails to keep his promise, the other has the right to go the court and force the defaulter to keep his promises. There are other elements are: 1. Offer and acceptance, 2. Legal obligation, 3. Lawful consideration, 4. Valid object, 5. Agreement not being declared void by Law, 6. Free consent, 7. Agreement being written and registered, 8. Capacity to contract, 9. Possibility of performance from what has been discussed. It is clear that all contracts are agreements. (b) All Agreements are not Contracts: An agreement is termed a contract only when it is enforceable by law. All agreements are not necessarily legally enforceable. It can rightly be said that an agreement has a much wider scope than a contract. For example that agreements are not legally binding are an invitation to dinner or to go for a walk and its acceptance. These are agreements not contracts. An agreement does not necessarily imply a legal obligation on the parties to the agreement. It is import here to clarify what exactly is an obligation. Obligation is a legal tie which imposes upon a person or persons the necessity of doing or abstaining from doing definite act or acts. An agreement need not necessarily be within the framework of law and be legally enforceable. If it is, then it is a contract. A promises B to do physical harm to C whom, the latter does not like and B promises to pay A Ksh. 1000 to do that, it cannot be termed as a contract because such an act would be against the law. Any agreement of which the object or consideration is unlawful is void and cannot be called a contract. It would be clear from what has been said so far that an agreement has a much wider scope than a contract. An Agreement implies fulfilling some agreed condition. It does not necessarily imply that the stipulated conditions conform to the law and are enforceable by it. It may be said that an agreement is the genus of which contract is the species. It also makes it clear that all agreements are not contracts but all contracts are agreements. How to cite All Contracts Are Agreements but Not All Agreements, Essay examples

S1 Task A Measurements Essay Example

S1 Task A: Measurements Essay My aim is that within the limits of a small-scale survey I will collect sample data of a population, and by using estimation techniques I will determine the populations parameters (such as the mean and the variance). My population is smarties, and in this investigation I am looking at the individual weight of random smarties, which will be my sample. I decided to stick with weight, as it is a property that will vary a lot, I think, and so I hope will prove an interesting investigation. An important factor to help me decide on how large my sample should be is that the size of the sample must be quite small, because it is stated so in my aim. However, to make accurate estimates of population parameters the sample must be large enough. Therefore to help me decide on the size of my sample, I have accordingly looked at the Central Limit Theorem, which states that: * If the sample size is large enough, the distribution of the sample mean is approximately Normal. * The variance of the distribution of the sample mean is equal to the variance of the sample mean divided by the sample size. We will write a custom essay sample on S1 Task A: Measurements specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on S1 Task A: Measurements specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on S1 Task A: Measurements specifically for you FOR ONLY $16.38 $13.9/page Hire Writer The Central Limit Theorem allows predictions to be made about the distribution of the sample mean without any knowledge of the distribution of the parent population, as long as the sample is large enough. For this reason, the sample size will be set at fifty, which I consider large enough for the distribution of its mean to be normal (according to the Central Limit Theorem). It should not be larger because the aim of this investigation is to carry out a small scale survey. The sample. The sample will be of the weight of fifty smarties. To be a good sample I must make sure that the results are valid and not biased in any way, which means that these smarties must be collected randomly, because the sample must be random for the Central Limit Theorem to be in effect, which would provide a Normal distribution of its mean which will allow me to make predictions of the parent population. I have decided to collect my sample data in a group, in order to lower he costs of the investigation, and also to provide assistance with greater accuracy to collecting the sample. Five tubes of smarties will be bought, each from a different shop, and ten smarties will be selected at random from each tube to be used in the survey. This should produce a nice sample, which I am fairly confident will be random. Calculations. In this investigation I will need to calculate a few things in order to come to my conclusion. This is a quick plan of what I will be calculating. * The mean, standard deviation and variance of the sample. * These will be used to estimate the variance and standard deviation of the parent population of smarties. * This in turn, will be used to estimate the standard error (the standard deviation of the sample mean distribution). * And, this will be used along with the mean of the sample to create confidence intervals for the mean of the parent population of smarties. Accuracy of measurements. My group will randomly select the required smarties from the packets and one after the other, they will be weighed on an electronic balance that will be reset to zero after each measurement, which will reduce the chance of any inaccuracies that might arise from small pieces of smartie being left on the balance. The balance we have used has a high degree of accuracy, as the measurements are given in grams to three decimal places. However, if the difference in the weight of smarties is too small to be detected on this balance, either a more accurate balance must be found or a survey of something with a higher variance must be carried out. Results (sample data). There is a table of the sample I have collected in my group. Weight of smartie (g) 0.898 0.939 0.921 0.941 1.004 0.994 0.922 0.934 0.893 0.934 0.954 0.998 1.042 1.009 0.957 1.013 1.110 0.972 1.034 1.041 1.042 0.949 0.952 0.964 0.953 0.867 0.932 1.011 0.955 0.959 0.982 0.913 0.939 0.954 1.061 0.906 0.955 0.901 0.957 1.081 0.994 1.044 0.955 0.950 1.014 1.027 1.050 1.045 1.047 0.915 Stem and leaf diagram of sample data. 1.11 0 1.10 1.09 1.08 1 1.07 1.06 1 1.05 0 1.04 122457 1.03 4 1.02 7 1.01 134 1.00 49 0.99 448 0.98 2 0.97 2 0.96 4 0.95 02344555779 0.94 19 0.93 24499 0.92 12 0.91 35 0.90 16 0.89 38 0.88 0.87 0.86 7 Although not necessary, I thought it would be somewhat useful to depict my sample data onto a stem and leaf diagram. Other information about the sample includes the lowest value, which is 0.867g, the highest is 1.110g, and the range is 0.243g. Sample Parameters. Mean. Using the total sum of the fifty smarties and dividing it by fifty to obtain the mean. Variance. The formula for variance states that you take the Mean of the squares minus the square of the mean. Standard Deviation. The standard deviation is found by finding the square root of the variance. Population Parameters. Estimate of the Mean of the population of smarties. The mean is an unbiased estimator, that is, the mean of its distribution is equal to the mean of the parent population. For this reason it can be used as an estimator for the mean of the population of smarties. As the mean of my sample is 0.976, then an estimate of the mean of the population of smarties is therefore: Estimate of the Variance of the population of smarties. The variance of the sample is a biased estimator. A biased estimator is one for which the mean of its distribution is not equal to the population value it is estimating. Therefore it must be converted to an unbiased estimator, by multiplying the sample variance by the number of smarties. You can see that the estimate of the variance of the population is slightly larger, than the variance of the sample. This is because within each sample some values are larger and smaller then the population mean, overall these cancel out and the mean of each sample would be closer to the population mean than the individual item. Estimate of the Standard Deviation of the population of smarties. Standard Error. The standard error is the standard deviation of the sample mean. According to the central limit theorem, the standard error can be calculated by performing a square root of the variance of the mean. This can be demonstrated algebraically: The standard error calculated above is quite small. This means that the variance of the sample mean is low, and this shows that one can be quite confident that the actual mean of the population is around 0.976. However this is not a very mathematical or user friendly method of showing how confident one is about the accuracy of the estimate made. This introduces the use of Confidence Intervals. Confidence Intervals Background. To calculate how confident one is about the estimate of the population mean, one can use confidence intervals. These tell you how confident (as a percentage) you can be that the mean of the population falls within a given range. How they work is explained in the following. Example Sample Mean Distribution: According to the Central Limit Theorem, the sample mean is distributed Normally. The mean of the sample mean (the centre of the curve) is equal to the population mean. The shaded area in the diagram shows the population mean à ¯Ã‚ ¿Ã‚ ½ 1 standard error. According to the tables for the normal function, this comprises of 68% of the curve. This means that there is a 68% chance that the mean of the sample is within one standard error of the mean of the population. This probability can be written algebraically as an inequality: However, as m is not known when sampling, the above inequality is useless, as it is not known to which number to add or subtract the standard error from. So the inequality is rearranged into this: This shows that the probability that the population mean is within 1 standard error of the sample mean is 68%. In other words you can be 68% confident that the population mean is within 1 s.e. of the sample mean. This idea can be used to calculate the confidence intervals that allow you to be 90%, 95% and 99% sure of the range where the population mean is found. 90% Confidence Interval. To work out a 90% confidence interval, you must work out how many standard errors from the mean contain 90% of the area under the curve (shown by the 0.9 in the shaded area above, as the are under the whole curve is equal to 1). The table of the Normal function shows areas to the left of points on the x-axis. This means that to work out the z score (the number of standard errors), you must calculate the total area to the left of the z, and look that up in the table to find the z score. This then allows you to calculate the confidence interval: The formula again to calculate confidence interval is here: The k value for 90% is 1.645, which I will use in the formula to find the confidence interval. This in words means that you can be 90% confident that the mean weight of the population lies between 0.963g and 0.989g. 95% Confidence Interval. The k value for 95% is 1.960, which I will use in the formula to find the confidence interval. This means that you can be 95% confident that the population mean is between 0.961g and 0.991g. This is a larger range than that of the 90% confidence interval, because to be more confident, the possible range must increase. 99% Confidence Interval. The k value for 99% is , which I will use in the formula to find the confidence interval. This means that you can be 99% confident that the population mean is between 0.956g and 0.996g. Validation. I must test my confidence intervals, and check if another sample will fit, and therefore show whether my investigation has been successful. For this quick test my group collected another ten results from two further packets of smarties. We used the same method for data collection as before. The Data we collected for the second (test) sample: Weight of smartie (g) 1.105 0.933 0.921 0.848 1.100 0.952 0.870 0.853 1.091 0.997 Mean. Looking back at my confidence intervals, this new sample mean actually fits in each of the confidence statements I made. Conclusion. After using the estimation techniques of the Central Limit Theorem I have estimated the following population parameters for the weights of smarties (three significant figures): Mean = 0.976g Variance = 0.00292 Standard Deviation = 0.0547g Using the Confidence Interval technique I have produced the following confidence: 90% = 0.963g ; m ;0.989g 95% = 0.961g ; m ; 0.991g 99% = 0.956g ; m ; 0.996g Also, my second sample data has proved my confidence intervals correctly, and the mean of 0.967g fit into the ranges that I calculated. I suppose there is no real conclusion, and I could not have set myself a hypothesis, as the investigation did not really call for one. The limiting factors meant I could not carry out a more detailed investigation, as for example if I based my sample on how many of each colour of smarty per tube, I would need a sample of about fifty tubes of smarties, which would have been impractical for me, as I would have had a time and a cost burden. Limitations. The size of the sample was small. The calculations that relied upon the data collected are therefore inaccurate to some extent, looking at how many smarties and packets of smarties there are in the world, a sample of fifty is completely dwarfed. To be more accurate a large sample must be collected. The sample might have been a fluke I might have got all the big smarties, or all the small ones. However there is not much to do to eliminate the possibility of this apart from to weigh every single smartie. This is extremely impractical. The smarties gathered were from my groups immediate area. Even though they were taken from different shops and different packets, they do not necessarily represent all the smarties in the world, only ones in my area. The results may be unreliable because the company that produces smarties may be changing, or have changed the mean weight setting for the smarties. They may be trying to slowly lower the weight while keeping the price the same. This could mean that the actual population parameters are somewhat different to the ones estimated here. But this may be unlikely. I found that the actual investigation may have been very limited from the start, by choosing the weight from random packets it meant I could not analyse the ratio of smarties per packet, or the mean weight per packet, as to collect a sample for those types of investigation I would need to have collected about fifty packets of smarties, which not only may have been expensive but would have been very tedious to measure each smarty from fifty packets, and would have been very impractical to carry out. Possible Extension. A statistical analysis of entire tubes of smarties could be carried out. The actual weight of the smarties could be compared to the price on the tube to determine whether the manufacturers are lying about how much smartie there is in their packets. Also similar investigations looking at how many smarties per packet, average weights of packets, etc. Weighing smarties of different colours could also be done to find if there are any differences between them. Or even counting how many smarties of different colours you get in different packets. But yet again an investigation like this would be harder to carry out, as you would need at least fifty packets of smarties to carry out a small scale investigation Also, a larger sample size could be taken to determine the mean and variance more accurately, a lot more accurately in fact. Lastly, I could have extended my confidence interval calculations; I could have included a 99% confidence of the mean varying only à ¯Ã‚ ¿Ã‚ ½ 0.001g, which would have shown I would have needed a massive sample, possibly over 20,000 to get that much confidence in such a small interval.