How to Find Critical Values with a Chi-Square Table

How to Find Critical Values with a Chi-Square Table The use of statistical tables is a common topic in many statistics courses. Although software does calculations, the skill of reading tables is still an important one to have. We will see how to use a table of values for a chi-square distribution to determine a critical value. The table that we will use is located here, however other chi-square tables are laid out in ways that are very similar to this one. Critical Value The use of a chi-square table that we will examine is to determine a critical value. Critical values are important in both hypothesis tests and confidence intervals. For hypothesis tests, a critical value tells us the boundary of how extreme a test statistic we need to reject the null hypothesis. For confidence intervals, a critical value is one of the ingredients that goes into the calculation of a margin of error. To determine a critical value, we need to know three things: The number of degrees of freedomThe number and type of tailsThe level of significance. Degrees of Freedom The first item of importance is the number of degrees of freedom. This number tells us which of the countably infinitely many chi-square distributions we are to use in our problem. The way that we determine this number depends upon the precise problem that we are using our chi-square distribution with. Three common examples follow. If we are doing a goodness of fit test, then the number of degrees of freedom is one less than the number of outcomes for our model.If we are constructing a confidence interval for a population variance, then the number of degrees of freedom is one less than the number of values in our sample.For a chi-square test of the independence of two categorical variables, we have a two-way contingency table with r rows and c columns. The number of degrees of freedom is (r - 1)(c - 1). In this table, the number of degrees of freedom corresponds to the row that we will use. If the table that we are working with does not display the exact number of degrees of freedom our problem calls for, then there is a rule of thumb that we use. We round the number of degrees of freedom down to the highest tabled value. For example, suppose that we have 59 degrees of freedom. If our table only has lines for 50 and 60 degrees of freedom, then we use the line with 50 degrees of freedom. Tails The next thing that we need to consider is the number and type of tails being used. A chi-square distribution is skewed to the right, and so one-sided tests involving the right tail are commonly used. However, if we are calculating a two-sided confidence interval, then we would need to consider a two-tailed test with both a right and left tail in our chi-square distribution. Level of Confidence The final piece of information that we need to know is the level of confidence or significance. This is a probability that is typically denoted by alpha. We then must translate this probability (along with the information regarding our tails) into the correct column to use with our table. Many times this step depends upon how our table is constructed. Example For example, we will consider a goodness of fit test for a twelve-sided die. Our null hypothesis is that all sides are equally likely to be rolled, and so each side has a probability of 1/12 of being rolled. Since there are 12 outcomes, there are 12 -1 11 degrees of freedom. This means that we will use the row marked 11 for our calculations. A goodness of fit test is a one-tailed test. The tail that we use for this is the right tail. Suppose that the level of significance is 0.05 5%. This is the probability in the right tail of the distribution. Our table is set up for probability in the left tail. So the left of our critical value should be 1 – 0.05 0.95. This means that we use the column corresponding to 0.95 and row 11 to give a critical value of 19.675. If the chi-square statistic that we calculate from our data is greater than or equal to19.675, then we reject the null hypothesis at 5% significance. If our chi-square statistic is less than 19.675, then we fail to reject the null hypothesis.

Film analysis with historical theme Research Paper

Film analysis with historical theme - Research Paper Example ty in the United States in comparison to the poverty of South America and the resulting desperation, the film does open up the discussion and provide a beginning toward the hope of a solution to the problems of labor abuses and poverty. Maria’s journey is an example of the hard choices that must be made when economic pressure leaves one vulnerable to exploitation. The story of Maria Full of Grace follows the journey of a young, teenage woman who is pregnant and chooses to act as a mule for drug runners after losing her job due to unfair treatment by her boss, in order to provide an income for herself, her coming child, and the rest of her family in Columbia. After a brush with authorities at the airport, she and the other mules who came with her are taken to a motel room where one of the women experiences a rupture of one of the drug balloons and dies. The drug runners cut open her body to retrieve the drugs, and in fear Maria and another mule escape from the room, taking with them the drugs. Ultimately, Maria decides to stay within the United States in order to give her child and herself a chance through the opportunities that she perceives that do not exist in her own country. The film portrays the economic climate of Columbia where drug cartels rule the nation. The drug trade is the core of the nature of economic stability in Columbia and once in the United States, the characters find themselves facing the hope of opportunity that they did not have in their home country. According to Boyd, the director was attempting to â€Å"perceive as the link between history and biography and the relationship between the two in society, our personal troubles, and the social structures† (140). A criticism that Boyd discusses, however, is that no connection between the complicity of the United States to the drug trade in Columbia, as well as fully explore the state of exploited women within the dynamic of that atmosphere. Boyd states that â€Å"Poor and racialized women are

International Dimension for Business Essay Example | Topics and Well Written Essays - 3000 words

International Dimension for Business - Essay Example With the opening up of world economy, nearly all the business entities big or small, old or new are getting inspired in taking their business to the international level (Aswathappa, 2010, p.6). Companies are getting determined in their decision to operate across the globe. The shifting of organisations from a domestic viewpoint to a level of internationalization gives rise to a number of challenges for the firm (Turner & Johnson, 2009, p.2). The challenges may be in the form of setting up of infrastructure in the foreign market, purchasing the materials from overseas suppliers and the biggest challenge is to sell it to the foreign customers. One of the biggest trends of the recent times has been the lowering of international trade barriers. Different organisations such as World Trade Organisation, GATT and IMF are constantly working towards the intensification of globalised trade. In the recent past globalisation has been a catchphrase for the business organisations. Globalisation is a global phenomenon which can be defined as the movement of goods, services, resources, funds and labour around the world in a harmonized and synchronized way. In this process a global relation among the countries gets developed and ensures efficacy in using the scares resources of the world (Milward, 2003, p.10-16). The present study deals with the international dimension of business or in other words the other avenue to conduct business apart from the local listings. The study will reveal the international market entry strategies such as foreign direct investment, franchising, licensing and exporting. The study will also try to analyse the foreign market entry strategy of Volkswagen. The reason for choosing this organisation for conducting the study is because it is amongst prime multinational companies. A multinational company is described as the company which operates in its home country as well as in foreign market. The factors which contributed towards choosing this company a re its rich history, brand image and also considering the fact that it is the biggest car manufacturing & marketing company of the world. Company History The history of the company dates back to 1937, when the company was known as ‘Gesellschaft zur Vorbereitung des Deutschen Volkswagens mbH’. In the next year the company is renamed to ‘Volkswagenwerk GmbH’. The construction of the plant for manufacturing cars started on 1938 at Wolfsburg, Germany. During the period of 2nd world war the production of the company switched to weapons and arms. At around 20000 forced labours, prisoners were working at the plant. After the end of World War II the responsibility of Volkswagenwerk was placed on to the hands of British military government. During that era mass production of volkswagon beetle was started. During the 1950s the product line of the company was increased. In the meantime the production of Volkswagon bus was initialized. The bus is still popular even in this century for its multi-functionality and is popularly known as VB bully. As the wheels rolls on the company slowly touched the milestone of producing one million Volkswagon beetle cars. The employees and dealers from the country and overseas celebrated this memorable day in a special comportment. In 1972 the company has broken the all time record of car production with the figure touching mammoth 15,007,034 units. The company slowly moved towards the production of new age cars during 1973 with its model ‘passat’. With that initiation the company moved towards the production of varieties new age cars. That was the time when Golf was built inside the industrial units of the company. The

The Harlem Renaissance and Its Role in American Literature Essay Example for Free

The Harlem Renaissance and Its Role in American Literature Essay Historically, the African American experience is defined by the constant struggle to be recognized, to assert identity, and to rise from the stereotypes and negativity of racism and discrimination. While it took some time before these issues were resolved, the contributions coming from the African American culture’s collective and individual experiences have formed a profound body of work, from then until now. One of the most renowned eras of African American literature is the Harlem Renaissance. Originally known as the New Negro Movement, the Harlem Renaissance saw an incredible influx of activity within the community of black writers that started during the early 1920s (McElrath, par. 1). The movement began with the holding of literary discussions series in both lower and upper Manhattan, specifically Greenwich Village and Harlem. Much of the credit was given to Charles Spurgeon Johnson, an editor who called on young and aspiring African American writers to bring their creative talents to New York in order to form an unprecedented membership of black creative artists. The call was heeded, and the next few years saw the arrival of black writers from all over America and even from the Caribbean, coinciding with the cultural phenomenon of the black urban migration. The Harlem Renaissance was soon born, and its roster included then-unknown names that would rise to exemplary heights in a short time (â€Å"Harlem Literature†, pars. 1-2). II. Themes Within the Harlem Renaissance More than a specific form or style, the Harlem Renaissance was characterized by its embracing of all styles and elements arising from culture and experience. The black signature in the emergent jazz and blues music also made its impact on the literature produced, since many of the themes covered by music also resonated within the writing community. Slavery and the production of identity, the complexities of life as African Americans in the modernity of the urban North, and the issues concerning the writing and performance for white audiences were some of the more prevalent themes appropriated by writers of the Harlem Renaissance. Racial pride and the reference to African history were found within the lines of black writers’ works, as well as a marked desire to achieve political and social equality within the greater American society. Yet more than anything. the Harlem Renaissance was defined by its upholding of diversity—in style, voice, and expression (â€Å"Harlem Renaissance†, pars. 1-2). Langston Hughes and Claude McKay, both poets, paved the way for the showcase of the African American mindset, particularly in Hughes’ appropriation of the ghetto life, and in the militant tone and passion against racial violence and for cultural pride in McKay’s â€Å"If We Must Die†. Other writers followed suit, and most notable was the membership of women in this elite circle. III. The Men and Harlem African American writers have come a long way since the efforts of Frederick Douglass on his text opposing slavery (Malvasi, par. 4), and the premier list of the Harlem Renaissance included many names, but always topped by three: Hughes, McKay, and Countee Cullen. Unlike the other two, Cullen had lived all his life in New York City, and viewed poetry as ‘raceless’, though he did acknowledge the presence of racism in America. However, the tackling of racist themes and injustice in his iconic poem â€Å"Yet I Do Marvel† apparently changed this passive outlook. Hughes, on the other hand, was quite experienced and well-traveled, a fact that appears in the use of the outdoors as a literary device in his profound poem â€Å"Negro Speaks of Rivers†. Finally, Claude McKay promoted a more irreverent method of fighting inequality and racism, the nature of which answers the anger and fear instilled in the hearts of African Americans. His abovementioned poem, â€Å"If We Must Die†, calls for honorable death in the face of the various forms of torture and persecution against blacks (McCrone 2-3). IV. The Writing Women of the Harlem Renaissance Perhaps the most marginalized among an already marginalized community are the women, most of whom are relegated to traditional roles limited to domesticity and child-rearing. While these were—and still are—values deemed important and significant, much must be credited to the African American women writers of the era, who had more to contribute on top of the collective experience of slavery and injustice. Editor Jessie Fauset, teacher Dorothy Peterson, and writers Ethel Ray Nance, Regina Anderson, and Georgia Douglas Johnson were some of the first women to claim part of the Harlem Renaissance for the interests of the female voice. Included in their activities were discussion and writing group organization, promotion of black authors in their respective communities, and the publication of African American writing in various magazines where they served as editors. But most of all, the women of the Harlem Renaissance made their mark by writing about fear and violence, as well as gender and tradition, within the context of the black experience. Names such as Dorothy West, Hallie Quinn, and Zora Neale Hurston were active in this group, women who would later make their literary voices resound even louder than those of their male counterparts (Lewis, pars. 13-17). V. Criticism Notwithstanding the great proliferation of creativity and intellectualism, the Harlem Renaissance and its impact on American literature was not without flaws or criticism. Because of the newness of the concept of freedom, specially in the realm of writing, many black writers resorted to crafting their works in styles commonly identified with white literary standards. Even worse, some of them appropriated images of blacks that agree with the racial stereotypes propagated by the whites. The goal to promote African American identity was not always successful, perhaps due to the still flimsy grasp on freedom and equality—concepts that are alive and well in this era. Works Cited â€Å"Harlem Literature†. Harlem Renaissance Multimedia Resource. 2009. John Carroll University. 17 March 2009 http://www. jcu. edu/harlem/Literature/Page_1. htm. â€Å"Harlem Renaissance†. Spiritus-Temporis. com. 2005. 16 March 2009 http://www. spiritus-temporis. com/harlem-renaissance/diverse-and-common-themes. html. Lewis, Jone Johnson. â€Å"†Harlem Renaissance Women: African American Women Dreaming in Color†. Women’s History. 2009. About. com. 17 March 2009 http://womenshistory. about. com/od/harlemrenaissance/a/dreaming_color. htm. Malvasi, Meg Greene. â€Å"Soul Deep: African American Literature and Music†. Suite101. com. 2004. 16 March 2009 http://www. suite101. com/article. cfm/harlem_renaissance/98190. McCrone, Audrey. â€Å"Three Harlem Renaissance Writers (Hughes, McKay, Cullen)†. Essays on American Literature. 2001. 17 March 2009 http://www. suite101. com/article. cfm/american_literature_essays/78581/3. McElrath, Jessica. â€Å"Harlem Renaissance: The New Negro Movement†. Afro-American History. 2009. About. com. 17 March 2009 http://afroamhistory. about. com/cs/harlemrenaissance/a/harlemren. htm.

Viewer Response - The Graduate Essay -- essays research papers

In The Graduate, the director, Mike Nichols’, emphasizes the mysterious tone of the film with his overuse of lighting, camera angles, and shadows. The uncertainty Benjamin Braddock feels can be seen right from the start as he stands on the moving sidewalk at the airport. He is positioned at the right hand side of the screen moving forward. You can see a large area to the left where the credits appear. I think the director chose this technique for the opening credits to symbolize how this graduate is arriving at a new destination & has much uncertainty in front of him.   Ã‚  Ã‚  Ã‚  Ã‚  Dark rooms with shadows are used heavily in this film. The director shows Benjamin’s room as dark and shadowy to parallel his personality. This is also seen in the Robinson house. Shad...

StockTrak

If we compare our Bear and Bull spreads to short and long stock positions respectively we can actually show how options are highly levered financial instruments, increasing profits, but also losses tremendously. If we had shorted a Cataracts stock our profit from the price decline would have been 6. 50% per share, while with our Bear Spread we made a profit of ten times the cost of building the spread. On the other hand, If we had held a Nikkei stock we would have had a loss of 6. 27% per share from the price cline, whereas our loss with the bull spread was 74. 8% if we compare it to the cost of building the spread. This figures show how option trading is cheaper relative to stock trading, but profits or losses are much higher in percentage terms. For our Butterfly, Strangle and Straddle strategies we chose Pfizer, which based on our analysis, presented Itself as a very stable stock, with a 6-months average price of $30. 66 and a current price of $31. 12 (March 13th). We wanted to be t on very low volatility and make a profit from very low fluctuations from Pfizer stock.Our Butterfly parade consisted on shorting two 32-strike calls and taking a long position on 31- strike and 33-strike calls. The center strike price of our butterfly was the exercise price of the Straddle and also lied exactly in the middle of the $31. 5-strike put and $32. 5-strike call for our Strangle. In the end, our Butterfly spread turned out to be for our spread (see Graph 3). 2. ) The article posted referrers to â€Å"covered call writing† as taking a long position on stock and writing a call that is significantly out-of-the money.With his strategy, if the call option is exercised and the investor has to sell his hares, he is covered by holding the underlying. If we compared the covered call strategy to a short naked call we can clearly see that the risk for the naked position is unlimited if the price of the stock increases. With the covered call, by going long on the underlying, we cap our profit but we also limit our loss, whereas with the naked short call we are completely exposed. The analog position using puts, I. E â€Å"covered put writing† would mean writing a put and shorting the underlying.To execute such a strategy is possible, but the risk embedded in it is very high, because the potential asses from a price increase in the stock are unlimited. The premium gained from the put writing might not be large enough to cover the losses from the short position if the price increase is high. 3. ) For our collar strategy we selected Apple stock. To execute such a trade we bought 1,000 shares at $527. 49, went long one thousand 535-strike puts and shorted the same number of 540-strike calls; both option contracts expired on April 25.Our collar was as close to zero as possible, where the put options had a price of $16. 5 and the call options were priced at $17. 25. If the rice of Apple had stayed between the two designated strikes, our profit would ha ve been the value of the stock plus the $0. 75-differential between the option prices. At maturity Apple closed at $571. 94, meaning that the call option was exercised and we lost $41. 94, but we also gained $44. 45 on the price appreciation of the shares, leaving us with a net profit of (44. 45 – 41. 94 + 0. 75) $3. 26 per share. 4. To execute the stop- loss and delta-hedge strategies we wrote 100 at-the-money call option contracts on Backbone and Google. Our initial position to hedge both strategies was long the hares of both companies. For Backbone we used the stop-loss strategy and set arbitrary times to check our positions and hedge it. The initial cash inflow of shorting these options was $35,500 and the cost of hedging this position went up to $174,312. 51. On the other hand, with the Google options we used the delta-hedge strategy and checked the stock price 3 times a day.The initial cash inflow from shorting the calls was $54,000 and the costs related to hedging reac hed a total of $1 The amount spent for hedging the FEB.. Shares was 5 times larger than he value of the options we sold, while for Google the ratio was 20 to 1 . After seeing these figures we can observe that hedging strategies are extremely costly, but are essential to protect short positions against risk and prevent higher losses. 5. ) To create the â€Å"synthetic† rep we bought Gold at spot price of $1,296 on March 27 and shorted Gold futures expiring in April; the average of the ask and bid prices for this contract was $1 ,302.Executing this transaction, we locked in our prices for a return of 0. 463%. The I-month treasury bills from the U. S. Federal Reserve website is quoted at 0. 0167%, which is essentially 0%. Comparing the return rate from our futures contract with the I-month T-bill rate, there is an arbitrage opportunity. To exploit this opportunity we would borrow money at the T-bill rate of and use it to buy gold at the spot price, in addition to these transacti ons, we would short Gold futures to make a final profit of 0. 613%. 6. ) current pence of BIBB: $ 290. 54 price of put @ 290: 10. 30 price of call @ 290: 13. 00 Deep in the money calls: price of call 0280: 9. 40 pence of put 0280: 5. 42 Deep in the money puts: price of call @300: 7. 72 pence of put 0300: 16. 8 If we look at at-the-money options and, considering that the risk free rate is essentially zero, the stock price and the present value of the strike price are practically equal, so in order for UT Call Parity to obey, the put and call price should be identical.As we can see in the quoted prices above, parity doesn't hold; the call price is higher than the put. We could exploit this opportunity by going long on the put and the share, shorting the call and borrowing the present value of K. When it comes to deep in-the-money calls the share price is higher than the present value of K, so the call price should be higher than the put price by the same amount as the price differenti al between S and IV (K). We can see from the prices above that the call is undervalued in relation to the put.To exploit this arbitrage opportunity we would buy a call, invest IV (K) and short the put and the share. Finally, for deep in-the- money puts, the share price is lower than the present value of K, so the put price should be higher than the call price by the same amount as the price differential between S and IV (K). We can see that the put is undervalued in relation to the call. To exploit this arbitrage opportunity we would buy the put and the share, borrow IV (K) and short the call. 7. When looking at the overall performance of our portfolio and its relative risk we can conclude that it was much riskier relative to the S and also had a lower return. If we look at the summary figures of our portfolio we can see that it had an overall return of 0. 63%, whereas the SPY IETF had a percentage return of 1 . 19% (see Graph 4). We believe that the reason for the lower return and higher risk of our portfolio comes from several trades involving silver and platinum futures entrants that we performed to experiment with the platform and observe how these contracts behaved.In general we think that such a project is a very useful and enjoyable way to get to know the trading world. Performing actual trades allowed us to â€Å"get our hands dirty' and truly understand how to build spreads and implement investment strategies. This project gave us the opportunity to go beyond the theory and realize that trading can sometimes be more complicated that it seems on paper, but can also become much clearer once the theory is implemented in a â€Å"real world† setting. We very much enjoyed working on this project.

How Service Learning Can Be Utilized Throughout Your...

Service Learning is defined as a type of teaching and learning strategy that combines community service with reflection and instruction to help enhance the learning experience and as well as strengthen communities. Some examples of service learning are; working with political organizations, neighborhood associations and a tutor elementary or secondary students are a variety of subjects. Service Learning can be implemented into many majors, such as psychology majors, nursing majors, and health and food science majors -- just to name a few. The benefits of service learning can be utilized throughout your lifetime time; some benefits include 21st century skills such as critical thinking, problem solving, communication, decision making, as well as leadership skills. Not only will you gain these helpful benefits, but also some real life experience in any internship or community service practices. An added benefit to your social being is also having a greater sense in learning. It can help improve one’s academic outcome. You will gain a better attention to learning and how service learning also helps the community and the students you interact with. Just like the intern, the students will also gain some helpful benefits as well as life experiences. Most importantly, service learning also helps students gain knowledgeable practices in real world scenarios. Service learning is important and beneficial for students because it provides them with opportunities to develop civicShow MoreRelatedThe Learning Approach For Lea rning1184 Words   |  5 Pagesi. At one time or another, in an individuals’ working life, they will be expected to learn about at least one aspect of operations the of the company in which they are employed with. 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