The Central Limit Theorem Essay Example for Free

The Central Limit Theorem Essay The Central Limit Theorem for a Mean state that for a random sample of size n from a population with mean  µ and standard deviation ? , as the sample size increases the distribution of the sample mean approaches a normal distribution with mean  µ and standard deviation . On the other hand, if the population is normal, the distribution of the sample mean is normal regardless of sample size (Doane Seward, 2007). Now, suppose a random sample of size n is taken from a population with mean 100 and standard deviation 10. The sampling error or standard error of mean for samples of n = 1, n = 4, n = 9, n = 16, n = 25, n =100 will be For n = 1, For n = 1, For n = 1, For n = 1, For n = 1, For n = 1, From above it can be seen that as the sample size increases, the sampling error reduces. Further, the histogram (if plotted) of samples means approaches a normal distribution. Therefore, while on cannot get rid of sampling error the results from one’s statistical work can be still useful as the sampling error will be less for larger sample size. References: Doane D. P. Seward L. E. (2007). Applied Statistics in Business and Economics. McGraw-Hill/Irwin: New York DQ2-WK3 What is the difference between a sample and a population? When can the same information (e. g. the age of each of the ten students in our class) be considered both sample data and population data? A sample involves looking only at some items from the population. For example, if a survey is to be taken from student of XYZ College for their choices, than the population will be consist of taking survey of all the students in XYZ College and a sample will be taking survey for only some of the students selected based on sampling method. For small population, there is little (or no) reason to sample. Similarly, if the data are on disk, than 100% of the cases can be examined easily (Doane Seward, 2007). Therefore, the same information can be considered both sample data and population data if the population is small or can be taken easily with no additional cost for analysis purpose. For example, in a class of 30 students, if the average age is to be determined, than the population is entire class that is all 30 students. In this case, the population is small; therefore, there is no need to sample and therefore, the age of all 30 students can be considered both sample data and population data. References: Doane D. P. Seward L. E. (2007). Applied Statistics in Business and Economics. McGraw-Hill/Irwin: New York DQ3-WK3 When would you use ANOVA at your place of employment, in your education, or in politics? Please share the WORDS that would lead you to the null hypothesis for a specific and simple example and, then, show the null and alternative hypothesis in symbols. Analysis of variance (commonly referred to as ANOVA) is used for comparison of more than two means simultaneously and to trace sources of variation to potential explanatory factors (Doane Seward, 2007). For example, if sample data for 15 days of manufacturing defect rates for automotive parts manufactured at four plant locations is collected (or available). Than, ANOVA can be used to answer questions such as are the observed differences in the plants’ sample mean defect rates merely due to random variation? Alternatively, are the observed differences between the plants’ defect rates too great to be attributed to chance? This can be written as null and alternate hypothesis as , i. e. at all four plants mean defect rate are the same. , i. e. at least one mean differs from the other. Now, if the null hypothesis is not rejected than it can be concluded that the observations within each treatment or group actually have a common mean ? (ibid). References: Doane D. P. Seward L. E. (2007). Applied Statistics in Business and Economics. McGraw-Hill/Irwin: New York

Daniel Defoe :: Essays Papers

Daniel Defoe Daniel Defoe (1660?-1731), English journalist and novelist, whose work reflects his diverse experiences in many countries and in many walks of life. Besides being a brilliant journalist, novelist, and social thinker, Defoe was an outstanding author, producing more than 500 pieces of literature. Defoe was born in London about 1660, the son of a candle merchant named Foe. Daniel added "De" to his name about 1700. He was educated for the Presbyterian ministry but decided to go into business in 1685. He became a hosiery merchant, and his business gave him frequent opportunities to travel throughout western Europe. An opponent of the Roman Catholic King James II, in 1685 Defoe took an active part in the unsuccessful rebellion led by the Duke of Monmouth against the king. In 1692 his business went into bankruptcy, but subsequently he acquired control of a tile and brick factory. He obtained a government post in 1695 and the same year wrote "An Essay upon Projects", a remarkable writing of matters of public concern, such as the education of women. Especially noteworthy among his writings during the next several years was the satiric poem "The True-born Englishman" (1701), an attack on beliefs in racial or national superiority, which was directed particularly toward those English people who resented the new king, William III, for being Dutch. The next year Defoe anonymously published a tract entitled "The Shortest Way with the Dissenters", which satirized religious intolerance by pretending to share the prejudices of the Anglican church against nonconformists. In 1703, when it was found that Defoe had written the tract, he was arrested and punished with an indeterminate term in jail. Robert Harley, the speaker of the House of Commons, gave Defoe his release in November 1703, on the condition that he agree to become a secret agent and public propagandist for the government. During his time in prison Defoe's business had been ruined, so he turned to journalism for his living. From 1704 to 1713 he issued a triweekly news journal entitled "The Review", for which he did most of the writing. Its opinions and interpretations were often independent, but generally, "The Review" leaned toward the government in power. Defoe wrote strongly in favor of union with Scotland, and his duties as secret agent may have included other activities on behalf of union, which was achieved in 1707. In 1709 he wrote a History of the Union.

Journal on Hamlet’s quote Essay

Hamlet is one of Shakespeares most discussed plays. The drama has a lot of figurative language to be interpreted in various meanings. Among the famous quotes taken from Hamlet, perhaps the one bringing a wide range of different opinions is the line Hamlet said to his friends Rosencrantz and Guildenstern Why, then, tis none to you; for there is nothing either good or bad, but thinking makes it so: to me it is a prison. (Shakespeare, Hamlet, II, ii, 249.) There is a deep concept in this saying, which perfectly represents the reality and the values of right and wrong. In the context, despite Hamlet saying this line does not refer to the moral values in the society; it does reflect the theme of the play. In this scene when Rosencrantz and Guildenstern, his old friends directed by King Claudius to come and check on his madness, Hamlet simply is mocking his fake friends naiveness. However, this quote does not only have this joking effect, but also foretells the theme of the play. Hamlet is the play of revenge, of finding the truth, of defining what is right and what is wrong. The way the prince thinks about life is going to help him deciding on his actions. . . . for there is nothing either good or bad implies in this world, nothing being is given a low or high value, a righteous or foul reason to exist. The way people look at it, react to it, and perceive it make it good, or bad. For instance, killing is always considered a horrible crime, but in the play Hamlet has to decide to murder his own uncle. However in that situation it is not completely a crime. It may either be right or wrong, depends on each persons view on what is more meaningful, a life, or the elimination of bad deeds. The decision to defy something as right or wrong also depends on a lot of different background like historical, cultural and other aspects. Hamlet considers the marriage between his mom and his uncle two months after King Hamlets death is unethical. The truth is in other nations, relatives do get royal marriage right after death of a family member to remain the stability within the royal clan, which is considered great wisdom and of great moral. In each persons view, an event has various personal relations to his belief and moral conception; therefore the definitions of right and wrong, good and bad vary among people. The argument of right and wrong, or good and bad, perhaps is the main theme  of the play. Is revenge a good excuse for murder? Is Hamlet not doing the same thing as Claudius did to his father? The answers lay upon each audience and his own opinion, as the truth lays in thinking makes it so Work Cited Shakespeare, William. Hamlet. Rpt. in Compact Literature Reading Reacting Writing. By Kirszner and Mandell. 6th ed. 2007.

St Clement s Retreat And Conference Centre - 1615 Words

St Clement’s Retreat Conference Centre is located at Galong, where is between Yass and Harden NSW. There is nearly one and a half hour’s drive from Canberra. Also it is close to train routes. It covers an area of 800 acres in a peaceful place where also has picturesque scenery [1]. This retreat and conference centre can offer air conditioned accommodation with modern facilities. It is an ideal center for prayer, study and reflection. Figure 1 shows the map of St Clement’s Retreat and Conference center. This retreat and conference center includes accommodation, prayer rooms, dining rooms, chapels, pool, library and other living facilities. St Clement’s history can go back to 1918, it was the home for priests of Redemptorist Congregation.†¦show more content†¦In order to meet the energy demand and a sustainable future, renewable energy is a better way to achieve it. Commonly, renewable energy is defined as energy which is able to be captured from existing natural resources that are replenished rapidly, such as flowing water, sunshine, wind, geothermal heat flows and ocean [2]. Renewable energy technologies are required to provide technologies to use one or several renewable energy resources. There are some different types of renewable energy technologies, which include solar energy, bioenergy, hydropower, wind energy, geothermal energy and tidal energy. This thesis project will focus on the solar photovoltaic which is currently one of types of solar energy technologies, and this technology using photovoltaic cells to converts sunlight directly into electricity.Solar photovoltaic system can generate electricity from sunlight through using PV modules, and the system can be integrated into building designs, installed on rooftops, or large scale power plant. With the development of photovoltaic technologies, solar photovoltaic capacity has been incr eased from 3.7 GW (2004) to 177GW (2014) [3]. Figure 2 shows this change from 2004 to 2014, there is a big trend of increase in these years. The increase of PV capacity can reduce the carbon emission and provides more job opportunities. It also helps to reduce air pollution and make a friendly environment for living. One of the common PV system is