What Is a Plus Four Confidence Interval

In inferential statistics,  confidence intervals for population proportions rely upon the standard normal distribution to  determine unknown parameters of a given population given a statistical  sample of the population. One reason for this is that for suitable sample sizes, the standard normal distribution does an excellent job at estimating a binomial distribution. This is remarkable because although the first distribution is continuous, the second is discrete. There are a number of issues that must be addressed when constructing confidence intervals for proportions. One of these concerns what is known as a â€Å"plus four† confidence interval, which results in a biased estimator. However, this estimator of an unknown population proportion performs better in some situations than unbiased estimators, especially those situations where there are no successes or failures in the data. In most cases, the best attempt to estimate a population proportion is to use a corresponding sample proportion. We suppose that there is a population with an unknown proportion p of its individuals containing a certain trait, then we form a simple random sample of size n from this population. Of these n individuals, we count the number of them Y that possess the trait we are curious about. Now we estimate p by using our sample. The sample proportion Y/n is an unbiased estimator of p. When to Use the Plus Four Confidence Interval When we use a plus four interval, we modify the estimator of p. We do this by adding four to the total number of observations, thus explaining the phrase â€Å"plus four. We then split these four observations between two hypothetical successes and two failures, which means that we add two to the total number of successes. The end result is that we replace every instance of Y/n  with (Y 2)/(n 4), and sometimes this fraction is denoted by  p with a tilde above it. The sample proportion typically works very well at estimating a population proportion. However, there are some situations in which we need to modify our estimator slightly. Statistical practice and mathematical theory show that the modification of the plus four interval is appropriate to accomplish this goal. One situation that should cause us to consider a plus four interval is a lopsided sample. Many times, due to the population proportion being so small or so large, the sample proportion is also very close to 0 or very close to 1. In this  type of situation, we should consider a plus four interval. Another reason for using a plus four interval is if we have a small sample size.  A plus four interval in this situation provides a better estimate for a population proportion than using the typical confidence interval for a proportion. Rules for Using the Plus Four Confidence Interval The plus four confidence interval is an almost magical way to calculate inferential  statistics more accurately in that simply adding in four imaginary observations to any given data set, two successes and two failures, it is able to more accurately predict the proportion of a data set which fits the parameters. However, the plus-four confidence interval isnt always applicable to every problem. It can only be used when the confidence interval of a data set is above 90% and the sample size of the population is at least 10. However, the data set can contain any number of successes and failures, though it does work better when there are either no successes or no failures in any given populations data. Keep in mind that unlike the calculations of regular statistics, inferential statistics calculations  rely on a sampling of data to determine the most likely results within a population. Though the plus four confidence interval corrects for a larger margin of error, this margin must still be factored in to provide the most accurate statistical observation.

Anne Style Of Anne Francis Robbins - 894 Words

Anne Francis Robbins was born in New York City on July 6th, 1921. Anne’s early life seemed like it would not lead to be anything nearly as successful as it did. Early on in her life Anne would acquire the name Nancy. When Nancy was born her father left her and her mother. Nancy’s mother Edith, who was a young actress, sent Nancy to go live with her aunt and uncle in Maryland. Here she attended a community school titled Sidwell Friends School. Nancy would regularly travel with her aunt to see her mother in New York City. Nancy’s mother would go on to marry a very prominent neurosurgeon from Chicago. Nancy would then move back in with her mother and her new stepfather who adopted her. Nancy now went from poor/middle class to very wealthy.†¦show more content†¦After being in three films and a couple guest spots, Nancy decided quit acting and focus on raising their family. They then had another kid, counting Ronald’s two other kids, made four in total. In 1967, Ronald was elected as the governor of California. Nancy immediately took the role as her beloved state. She was quickly criticized after speaking out about governor’s mansion calling it a â€Å"fire trap† before moving her family to a Sacramento suburb. The press and Ronald’s political opponents recognized her as snobbish, though she had only moved for the safety of her family. Her reputation soon healed itself after becoming involved in the foster grandparents program. She was than known as a â€Å"model first lady.† In 1980 Ronald was elected president of the United States, after a failed campaign in 1976. In 1982 she championed a drug abuse awareness and education program. She spread the awareness by traveling throughout the U.S. and other foreign countries. In 1985 the â€Å"Just Say No† campaign took off, but was criticized by some as simplistic. Though the criticism was still in affect, the National Crusade for a Drug Free America act was finalized by President Reagan in 1986. â€Å"The president’s personal protector† was said to be Nancy’s most important role as the first lady. When there was an assassination attempt on President Reagan, Nancy took it as her concern to make sure she knows what he’sShow MoreRelatedStephen P. Robbins Timothy A. Judge (2011) Organizational Behaviour 15th Edition New Jersey: Prentice Hall393164 Words   |  1573 PagesOrganizational Behavior This page intentionally left blank Organizational Behavior EDITION 15 Stephen P. Robbins —San Diego State University Timothy A. Judge —University of Notre Dame i3iEi35Bj! Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Editorial Director: Sally Yagan Director of Editorial Services:

Americas War on Terror Essay - 1677 Words

With the September 11 terrorist attacks in New York City, the United States adopted radical changes to its foreign policy and its response to terrorist threat. With the swift implementation of the USA PATRIOT Act shortly after the attacks (Uniting and Strengthening America by Providing Appropriate Tools Required to Intercept and Obstruct Terrorism Act), and intervention in Afghanistan, the United States had begun its War on Terror. This war was shepherded by then President George W. Bush. These actions marked the beginning of the War on Terror, and laid the groundwork for the problems experienced by the Obama administration almost ten years later. The USA PATRIOT Act was a statute designed to unburden law enforcement agencies from privacy†¦show more content†¦conduct in the ‘war on terror,’ especially the use of Guantanamo to circumvent legal protections of the rights of prisoners detained there† (Lowenthal 2009: 19). The United States initiated Operation Iraqi Freedom on 20 March 2003, without NATO approval, beginning with targeted bombing of Iraq, and soon a full-scale invasion. This has proved to become an unpopular war, for some because of the motivations behind it or because of the perceived lack of progress in Iraq, attributed to â€Å"enemy body counts and casualty ratio data† which â€Å"is quantifiable and commonly viewed by the public as a reasonable indicator of success (or, more likely, failure)† (Boettcher and Cobb 2006: 833). It also damaged the United States’ international standing because the war in Afghanistan â€Å"was followed by the deeply controversial Iraqi war of shock and awe which fractured the international legal order so carefully crafted in the crucible of Lake Success in 1945† (Steyn 2004: 7). To the present day, the United States remains engaged in Afghanistan and Iraq; and continues to operate military camps outside of legal jurisdiction in Guantanamo Bay. These actions and decisions have formed the cornerstone of the USA’s response to terrorism. Barack Obama was elected President of the United States in the 2008 election, promising to close Guantanamo Bay’s military camps and provide a timeline for the withdrawal of troops from Iraq. Both of these promises are yet to be met, however theShow MoreRelatedPresident Obama s Foreign Policy758 Words   |  4 PagesLindsay (2011), President Bush’s foreign policy was dominated, first by the ‘war on terror’, and second by his ‘freedom agenda.’ This suggests that President Bush’s foreign policy was largely driven by ideology. Lindsay (2011:766) argues that during the war on terror â€Å"fighting terrorism became not just a priority, but the priority† of American foreign policy. The war on terror was the rationale behind America’s decisions to go to war with Afghanistan and Iraq. According to Lindsay (2011), America invadedRead MoreCharles Krauthammer The 9 / 11 Synthesis Summary840 Words   |  4 PagesIn â€Å"The 9/11 â€Å"Overreaction†? Nonsense.†, Charles Krauthammer selects the supporting side of The United States of America’s reaction to the terrorist attack of September 11th, 2001. Throughout the essay, Krauthammer succeeds in persuading his target audience of conservatives and general Americans that not only was Americas reaction to the 9/11 terrorist attack justified, but it also brought adequate results. Krauthammer utilizes various strategies such as the rhetorical triangle, stylistic techniquesRead MoreTaken Hostage By David Farber1083 Words   |  5 Pagesinforms us of America’s first encounter with radical Islam and what had caused the conflict between them. For four hundred and forty-four days, President Carter tried to put effort into resolving the issues but he failed on releasing the hostages. Since the American people paid close attention to this issue, they were highly disappointed with President Carter and his processes. From our class lectures and throughout the tensions illustrated in Farber’s book, we learn of how the role of Cold War policy hadRead MoreGeorge W. Bush s Foreign Policy Successful1601 Words   |  7 Pagesthe foundation of America. These acts shatter steel, but they cannot dent the steel American resolve† - George. W. Bush Prior to World War I, the United States’ foreign policy remained predominantly isolated. However, upon the end of the war, American foreign policy saw a pragmatic shift from its original isolationistic nature to XXXXX . America’s policy then was calling for American to avoid entangling political alliance. The new policy of the United States differed from the original inRead MoreChomsky And The War On Terror1277 Words   |  6 Pagespolitical commentator, social justice activist, and anarcho-syndicalist advocate does an elaborate job in his speech given at Harvard University, to make us question if there really is a war on terror. Chomsky calls everybody a hypocrite and uses the U.S. Army Manual definition of terrorism to argue that there can’t be a war on terrorism because the U.S. is also a terrorist group itself. We can’t fight something if we ourselves do that same thing. Chomsky backs up his claim with many pieces of evidenceRead MoreThe United States And The Islamic State Of Iraq1080 Words   |  5 PagesSuccessful nations allow conflict to arise within and outside of the nation. War is the offspring of such political intercourse. The intention to gain power and control serve as enablers for national and international wars. Attaining power and control expand potential competition from a regional to a global level. The United States have involved itself in such terrorists attacks due to the desire to possess such resources, power and control. The Islamic State of Iraq also commonly known as ‘ISIS’Read MoreThe Realism Theory Of The War On Afghanistan1648 Words   |  7 Pagesthe realism theory in examining the War in Afghanistan. For example, realism explicitly applies to relations between nations and consequently, war between countries. This was not the case, since the war did and still does not involve conflict between America and Afghanistan. Rather the war was between America and the Taliban government that sup ported the infamous terror group, al Qaeda. For this reason, realist theory does not explain this highly controversial war. Another aspect that contravenes realismRead MoreAmerica Is A Great Nation959 Words   |  4 Pagesnumbers don’t feel like people. With numbers, comes distance. To truly understand the severity of any situation, we must take in account the statistics and numbers. But we cannot forget what is precious. On September 11th, 2001, a horrific act of terror struck our nation to the core. Fear, devastating and humbling, lodged into our blessed lives. Over 2,800 American civilians were murdered in cold blood when two planes were hijacked and flown directly into the twin towers (Anderson 3). This atrociousRead MoreThe Us Strategy For Winning The Global War On Terrorism1157 Words   |  5 PagesIn light of this, it should be mentioned that â€Å"the US strategy for winning the Global War on Terrorism is predicated on creating an international environment inhospitable to terrorists and all those who support them† (Fogarty 2001). Meaning, that the fight against terrorism heavily relies on international cooperation. In order to achieve such a feat, nevertheless, America must be amiable by fellow governments and their citizens. 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Panera Bread free essay sample

The driving concept behind Panera Bread is to provide a premium specialty bakery and cafe experience to urban workers and suburban dwellers. Panera Breads distinctive menu, signature cafe design, inviting ambience, operating systems and unit location strategy allowed it to compete successfully in five submarkets of the food away from home industry: breakfast, lunch, daytime â€Å"chill out†, light evening eat in or take out, and take home bread. In his letter to shareholders, in the company’s 2005 annual report, Panera chairman and CEO Ron Shaich said: â€Å"we think our continued commitment to providing crave-able food that people trust, served in a warm, community gathering place by associates who make our guests feel comfortable, really matters. † Panera’s target market are urban workers and suburban dwellers who are looking for quick service meals and a more aesthetically pleasing dining experience than that offered by traditional fast food vendors. The competitive strategy which most closely fit the competitive approach of Panera Bread is the broad differentiation strategy. This unique position has contributed to its success by adding a bonus to the mix-specialty food, opening for breakfast, lunch, and dinner also offer hand-tossed salads, signature sandwiches, and hearty soups served in edible sourdough bread bowls along with hot and cold coffee drinks. In addition, providing catering services through its via Panera catering business, suggesting a new time of day to eat specialty foods, calling the time between lunch and dinner †chill-out† time. Moreover, the unique position also has providing an inviting neighborly atmosphere adding to their appeal as well. Yes, Panera Bread will reach its goal of becoming a leading national brand in the restaurant industry because the company is counting on its unique positioning strategy, its signature foods, and savvy execution to make this goal a reality. Q2) Porter’s Five Forces Competitors: The main competition Panera Bread Co. experiences is from coffee shops such as Starbucks and Caribou Coffee, along with specialty restaurants such as Chipotle Mexican Grill. Starbucks is a global company with superior market share and brand awareness. Caribou coffee is closer in scale to Panera Bread Co. ; both have high growth outlooks and are currently expanding. Chipotle competes with Panera Bread at lunch and dinner, whereas Starbucks and Caribou compete with Panera Bread in the mornings and at non-traditional dining hours. Panera Bread Co. ’s free Wi-Fi network gives the company a considerable competitive advantage. Substitutes: Small, privately owned local coffee shops or delis could be substitutes for a chain restaurant such as Panera Bread. The small neighborhood atmosphere that â€Å"mom and pop shops† offer could potentially be eliminated. Panera Bread Co. has the ability to offer a wider array of goods and services than substitutes such as these. Since Panera Bread offers a broad assortment of goods on its menu, the threat of substitutes is not of large concern. Potential Entrants: The specialty restaurant industry is by no means mature and has plenty of room for growth, as seen by Caribou and Panera Bread Co. ’s expansion into new markets. In researching competitors, there were few companies with an identical structure and strategy as Panera Bread Co. , which exhibits its belief that there is room for profit in the specialty restaurant industry. As seen through Chipotle’s success, the specialty chain restaurant model can work and the threat of new entrants to the industry is possible. However, the current restaurant market is experiencing commodity and labor inflation that could contract the current margins in the industry and inhibit new entrants. Power of Suppliers: Since many of Panera Bread’s items on the menu are directly correlated to commodity prices such as wheat and dairy prices, the suppliers are quite powerful in this industry. A recent shift Panera Bread made was attaining some its baked goods from external vendors instead of being produced by its own fresh dough facilities (FDF’s), which again increases the power of suppliers. Customers: Patrons love Panera Bread for the wonderful smells and flavors that fill its stylish and very relaxed bakery/cafe shops. The place tends to be a hotspot for the â€Å"soccer mom† crowd, but with the largest free Wi-Fi network in the country, it looks as though businesspeople may become regulars. Its customers have substitutes in the specialty restaurant industry but Panera Bread Co. tends to have loyal customers. Panera Bread’s strategy is â€Å"to provide a premium specialty bakery and cafe xperience to urban workers and suburban dwellers. The concept is a mix between fast food and casual dining, or fast casual. By choosing this strategy, Panera is attempting to achieve competitive advantage in the unique offerings it provides, offering that rivals don’t have and can’t afford to match. In this case, delicious handcrafted bread arriving fresh daily, served in an inviting atmosphere is the company’s competitive advantage and core competen cy. Q3) Barriers to entry that Panera Bread has created for potential competitor are product differentiation and cost advantages independent of size. The barrier for Panera Bread is low. In product differentiation, Panera Bread very proud for their business because they can delivers high quality of food and products with faster speed compare to other casual dining. Besides, the barrier of cost advantages independent of size is the emergence of fast casual which is the new category in the restaurant industry. The owners of Au Bon Pain and Saint Louis Bread Company felt that they could help pioneer this new category. The maintenance cost is low, there are less competitors. It is necessary to consider entry barriers when assessing dominance, when determining whether unilateral conduct might deter new firms from participating in a market, and when analyzing the likely competitive effects of mergers. Entry barriers because competition will not be reduced if new firms could enter easily, quickly, significantly. Q4) Panera Bread’s primary sources of competitive advantage are its position in the restaurant industry, the atmosphere of its restaurants, the distinctive products, brand strength, customer loyalty, and financial performance. The advantages for position in the industry are avoid from arising of competition, success in positioning and execution, positioning strategy of various restaurant chains and also snack time. Besides, the atmosphere are franchised outlets have been operated, convenience, customer attraction, and also expansions. The next is distinctive products which provides product differentiation and offers various kinds of foods. For brand strength is special in brands and foods and also fast-casual category. Furthermore, the customers loyalty which is teamwork and manager-customer relationship. Lastly, the financial performance can avoid threats to profitability and increase of sales. References 1. Panera Bread position, research from: http://www. antiessays. com/free-essays/421278. html 2. Porter’s five forces, research from: www. trinity. edu/smf/inc/reports/PNRA. oc 3. Panera Bread position, advantages of primary sources, research from: https://docs. google. com/viewer? a=vamp;q=cache:2Ow6jb9_g-EJ:eshare. stut. edu. tw/EshareFile/2011_12/2011_12_41a57d4a. ppt+Do+you+think+Panera+Bread+will+reach+its+goal+of+becoming+a+leading+national+brand+in+the+restaurantamp;hl=enamp;gl=myamp;pid=blamp;srcid=ADGEEShBx7Llys8yZ-7i2-500tGOybggsozWXzUjym1Ueg4idLVJlFVzIc_bqVOJ_rhmrzmDSU4RvhjFpTE-RVxp_9Q6KYVHp9f4 2sK72ODpq5J0FJQ2J-pMjyZyafaF1SHZ_sy8K9amp;sig=AHIEtbRos7KiryelsJM71tuaW5YP9SXS9A