Example of Goodness of Fit Test

The chi-square goodness of fit test is a useful to compare a theoretical model to observed data. This test is a type of the more general chi-square test. As with any topic in mathematics or statistics, it can be helpful to work through an example in order to understand what is happening, through an example of the chi-square goodness of fit test. Consider a standard package of milk chocolate MMs. There are six different colors: red, orange, yellow, green, blue and brown. Suppose that we are curious about the distribution of these colors and ask, do all six colors occur in equal proportion? This is the type of question that can be answered with a goodness of fit test. Setting We begin by noting the setting and why the goodness of fit test is appropriate. Our variable of color is categorical. There are six levels of this variable, corresponding to the six colors that are possible. We will assume that the MMs we count will be a simple random sample from the population of all MMs. Null and Alternative Hypotheses The null and alternative hypotheses for our goodness of fit test reflect the assumption that we are making about the population. Since we are testing whether the colors occur in equal proportions, our null hypothesis will be that all colors occur in the same proportion. More formally, if p1 is the population proportion of red candies, p2 is the population proportion of orange candies, and so on, then the null hypothesis is that p1 p2 . . . p6 1/6. The alternative hypothesis is that at least one of the population proportions is not equal to 1/6. Actual and Expected Counts The actual counts are the number of candies for each of the six colors. The expected count refers to what we would expect if the null hypothesis were true. We will let n be the size of our sample. The expected number of red candies is p1 n or n/6. In fact, for this example, the expected number of candies for each of the six colors is simply n times pi, or n/6. Chi-square Statistic for Goodness of Fit We will now calculate a chi-square statistic for a specific example. Suppose that we have a simple random sample of 600 MM candies with the following distribution: 212 of the candies are blue.147 of the candies are orange.103 of the candies are green.50 of the candies are red.46 of the candies are yellow.42 of the candies are brown. If the null hypothesis were true, then the expected counts for each of these colors would be (1/6) x 600 100. We now use this in our calculation of the chi-square statistic. We calculate the contribution to our statistic from each of the colors. Each is of the form (Actual – Expected)2/Expected.: For blue we have (212 – 100)2/100 125.44For orange we have (147 – 100)2/100 22.09For green we have (103 – 100)2/100 0.09For red we have (50 – 100)2/100 25For yellow we have (46 – 100)2/100 29.16For brown we have (42 – 100)2/100 33.64 We then total all of these contributions and determine that our chi-square statistic is 125.44 22.09 0.09 25 29.16 33.64 235.42. Degrees of Freedom The number of degrees of freedom for a goodness of fit test is simply one less than the number of levels of our variable. Since there were six colors, we have 6 – 1 5 degrees of freedom. Chi-square Table and P-Value The chi-square statistic of 235.42 that we calculated corresponds to a particular location on a chi-square distribution with five degrees of freedom. We now need a p-value, to determines the probability of obtaining a test statistic at least as extreme as 235.42 while assuming that the null hypothesis is true. Microsoft’s Excel can be used for this calculation. We find that our test statistic with five degrees of freedom has a p-value of 7.29 x 10-49. This is an extremely small p-value. Decision Rule We make our decision on whether to reject the null hypothesis based on the size of the p-value. Since we have a very miniscule p-value, we reject the null hypothesis. We conclude that MMs are not evenly distributed among the six different colors. A follow-up analysis could be used to determine a confidence interval for the population proportion of one particular color.

The Death Penalty Is Necessary And Necessary - 1538 Words

The Death penalty debate has had the United States population divided by a great number of elites and citizens in support, and an equally larger number of experts and Americans opposed to it. Internationally, also, countries seem to be having a different stance on the issue of whether to do away with the death penalty or to keep supporting it. In the United States, there are about 33 states that have the death penalty as a legal punishment, but there are about 17 states that have abolished the capital punishment (Banner 60). Those opposed to the death penalty have given reasons that incline a lot towards the morality of the death penalty, claiming that it is against the right to life. However, some reasons make death penalty worthy of†¦show more content†¦Van den Haag explains that keeping criminals who have committed crimes against life is like an insult to the victims because the same victims who are taxpayers will have their money used to sustain an individual who has hur t them (87). Additionally, life imprisonment is examined by economic experts is accumulatively higher compared to death sentence. Many people have opposed this under the claim that a death sentence is expensive as it requires up to $2million and above for the case only. However, proper estimates have it that a case of Life Without Parole can cost between 1.2 to 3.6 million more than a death sentence case (Banner 65). By and large, it is clear that keeping people in the prisons is expensive in terms of food, facilities and maintenance. In support for the death penalty the reduced cost makes it a better and worthy punishment that will also ensure justice for the victims. Again the existence of death penalty acts as a perfect deterrence to those potential criminals who are likely to commit crimes like murder and so on. Advocates for abolition of death penalty have sighted that death penalty does not have any effect in deterring crimes. Actually, they claim that the existence of death penalty leaves the crime rates constant or even higher. However, according to a study done by Van den Haag, the crime rates have increased to more than 10% whenever the death sentence has been abolished (68). Additionally, the same report pointed outShow MoreRelatedThe Death Penalty Is Necessary899 Words   |  4 Pagesdeterrence. As of today, there are thirty-two states which offer the only just punishment for a crime without parallel and eighteen states having abolished the death penalty. The use of the death penalty has brought peace of mind to our citizens. Though through the mid nineteen sixties until the early nineteen eighties only about six death penalties actually took effect. When the number of executions dropped, the murder rate rose from 5.6 per 100,000 people to 10.2 which is almost double the murder rateRead MoreThe Death Penalty Is Necessary858 Words   |  4 PagesThe Death Penalty is a controversial capital punishment which is given against a crime usually involving murder. It is controversial because many people are for it and many people are against it. Many people do not pay attention to the death penalty, because it is only legal in 31 out of the 50 states. Iowa is not one of those states. Life without parole is better, for many reasons. I am against the death penalty not only because it is simply wrong, but because it does not reduce the crime ratesRead MoreIs The Death Penalty Really Necessary?1316 Words   |  6 PagesKyle Kieffer Mrs. Cardell American Lit 06 Mar. 2017 Is the Death Penalty really necessary? Since the very beginning of the growth of the thirteen colonies, to the end product being the United States of America, 15,760 citizens have been executed. Throughout the time span, their methods of executions have gotten more sophisticated, for the good and unfortunately, the bad. The first methods of executions include, but are not limited to: burning on the stake, hangings, or being shot down by a firingRead More The Death Penalty Is Necessary Essay942 Words   |  4 PagesThe death penalty otherwise known as capital punishment, is the most extreme punishment a government can implement on its own people. Presently, only eight-six countries have completely abolished the use of capital punishment, while seventy-four countries still retain some use of the death penalty. Throughout history, the controversy over the necessity of the use of the death penalty has continued. Many oppose the death penalty on basis of moral and ethical grounds, but one must keep in mind thatRead More The Death Penalty: A Necessary Evil Essay893 Words   |  4 Pages The Death Penalty: a Necessary Evil Life is the most wonderful gift that God gives us. He also gives us the power to do what we wish with that life. We can keep it and guard it, or we can take it away. It follows that murder is the worst crime anyone could ever commit. It is a crime that no one can ever make right because once you take a life away you can never give it back. Penalties exacted from criminals are made to fit the crimes committed. The worst crime possible should therefore receiveRead MoreEssay on The Death Penalty Is A Necessary Evil1099 Words   |  5 PagesThe death penalty is a necessary evil that has a positive effect on society today. It is an effective deterrent of crime as well as a safeguard for society. It also helps to keep order in our cities. It is a just and effective punishment for those who have committed crimes heinous enough to deserve death. The death penalty is not a new idea in our world. Its origins date back over 3,700 years to the Babylonian civilization, where it was prescribed for a variety of crimes. (Capital PunishmentRead MoreA Halt On The Death Penalty Is Necessary Since The Cost1265 Words   |  6 Pageson the death penalty is necessary since the cost of maintaining it extends far beyond keeping criminals in prison, it proves to not serve as a deterrent to criminals, and it is inherently racist based on our application to this day. The controversy linked to the expenses of the death penalty compared life in prison is known to be higher. According to Times, the death penalty has three stages. These stages include the cost of prosecution, the cost of defense, and the cost of housing a death penaltyRead MoreThe Death Penalty is Necessary in Modern Society Essay753 Words   |  4 Pagesa more heinous crime has occurred, the convicted person will most likely incur the death penalty. In our modern society it has become necessary to deal out death and judgment to ensure the safety of many. The line is drawn in the sand but in some cases we step over that line to look at each case with strict detail. Even with modern equipment and technology, human error is still inevitable. In some cases, death row inmates have declared their innocence even in their dying moments. With our modernRead More The Death Penalty is a Necessary Deterrent to Crime Essay1712 Words   |  7 PagesThe Death Penalty is a Necessary Deterrent to Crime    Murder and rape are serious crimes, although they arent the only crimes that could be considered serious. Others that might be considered are stealing, which has numerous categories under it such as grand theft auto, etc†¦ The following story is the true account of a young female named Donna. This story tells of Donnas rape and then her murder by a man named McCorquodale and his friend Leroy. The author is telling this story in order to createRead MoreLife Is A Precious Thing, Death Is The Great Evil898 Words   |  4 Pagesâ€Å"Life is a precious thing, death is the great evil†, said by Heinrich Heine who is a famous poet. So we can know that life is the most important thing for every single life entity. There are a lot of words that can modify life, such as important, precious, formidable and so on. The reason why there are so many good vocabulary can modify life is nobody want to lose their own life. It is clear that not only human, but also animals cherish their own life. According to the utterance which Heine said

Wireless Networking and Related Technologies - myassignmenthelp.com

Question: Discuss about theWireless Networking and Related Technologies for Antennas. Answer: Abstract Antennas are essential tools when it comes to wireless communication. The communication systems need a means to convert electronic signals into the system to electromagnetic waves to be transmitted into free space. They are responsible for interconnecting the links involved between the free space and the transmitter and between the receivers and the free space for effective wireless communications. It is therefore not possible for successful wireless communication without thoroughly analyzing the existing antenna technologies before choosing the best as per the needs of the wireless system in the making. If the best antenna is selected regarding its operation, the wireless communication technologies expect a bigger success. The antennas are primarily categorized according to the technology they use and according to their application. The antennas in mobile industries may carry the future since most users in wireless communication technologies are opting mobile devices such as smartph ones and they majorly depend on them. Antenna technologies Based on the direction they radiate the electromagnetic waves; we have two broad categories. Every antenna will fall in either of the two categories. Directional antennas: These are antennas that radiate or receive electromagnetic waves in a specified direction based pattern. They are used when the direction of the other position is not arbitrary to maximize coupling to the electromagnetic field(Johnson, 1961). A good example is a Yagi-Uda antenna used as UHF and VHF frequencies. Omnidirectional antennas: They receive or radiate electronic, magnetic waves from all directions or to all directions. Omnidirectional antennas are best efficient when the position of the other station is not known. A good example is a vehicle antenna. Based on the way they operate; we have the following major types: Aperture: They are constructed with a dipole fixed inside a three-dimensional guiding structure often larger than the wavelength of an aperture responsible for emitting the radio waves. Figure 1: basic horn (Pyramidal) antenna concept. They are mostly used at microwave frequencies and above. A good example is the horn antenna which consists of a flaring metal attached to a waveguide. Monopole: They are similar to dipoles but with only one conductor. The one-rod conductor is fixed to ground or another artificial conductor. Then one side of the feedline of the receiver or the transmitter is connected to the conductor. A good example is a whip majorly used in a vehicle on portable radios and mobile devices such as the walkie-talkie. Their construction is also significantly simple since they just need the metal conductor. Dipole: They are antennas based on two metal rods or wires that can conduct electricity arranged Figure 2: Basic concept of a dipole antenna. In a symmetric way such that the feed line of the transmitter or receiver is attached to them. Antennae based on Dipoles include Yagi. These are used for long distance shortwave communications, television antennae, and point-to-point communication links. The antenna has gains which allow low strength signals to received, a directivity that minimizes interference levels can be easily fixed on poles and is easy to construct since all construction is done from rods. Another dipole is a corner reflector. It is a directional antenna used at UHF frequencies. It is made of a dipole mounted on a reflective metal screen joined at an angle. Its construction is similarly simplified. Travelling wave: These have extensive bandwidth due to non-resonant structures. Travelling of current in the antennas travel in one direction, unlike others where it bounces to and fro forming standing waves. Soon, Aperture antennas will become dominant in medium and long distance wireless links. Aforementioned is because unlike feed antenna, they can be used over a wide frequency range due to their structure of non-resonance. CDMA and FDMA multiplexing techniques. CDMA and FDMA are channel access methods that are used to allow one multi-point transmission medium to transmit for several terminals connected to it while they share its capacity. A multiplexing method allowing several data streams to use one communication channel is needed to produce a good channel access scheme. Media Access Control is used hand in hand with the multiplexing method to cater for assignment of multiplex channels and avoid collisions. It is also responsible for addressing. Frequency-Division Multiple Access and Code Division Multiple Access are therefore similar because they are both used for the mobile and wireless communications. Their aim to is similar, to allow access to channels by different terminals from the same multipoint transmission medium(Hongyi, 1999). Frequency-Division Multiple Access uses frequencies where Code Division Multiple Access uses a unique code for each transmitter. The Frequency-Division Multiple Access multiplexing is done based on the frequency divisions. The total bandwidth available to the system is taken and divided into smaller frequencies. The division ensures that the frequencies do not overlap and they are then assigned to the communicating phones. The frequency band of each data stream is therefore different, and they are assigned different nodes. The FDMA can be used both for analog and digital signals even though all users must share the frequency channel(Naoki Masaak). Each of the users sharing the frequency channel is only allowed to transmit at a single frequency. In Code-Division Multiple Access, the data rates of each of the transmitted bit streams are less than the radio spectrum used in Hertz. It is, therefore, possible to transfer several message signals in the same carrier frequency but with a different spreading code for each. The bandwidth, wide allowing sending of message signals on very weak noise to signal ratios. Unlike the FDMA, the bandwidth here is not divided, and therefore data can be freely sent to any frequency at any time by all the users. Latest advanced wireless technologies Wireless technology is in these times advancing at super levels. The users needs and demands are also rising propelled by the ease and comfort of using the wireless technologies. The technologies already in place spans across all electronic devices including printers, keyboards and mice, Speakers and headphone and display adapters. The devices in demand in the markets are those with integrated wireless technologies. 5G mobile networks: The 5G Cellular network spectrum is one of the latest advances in Wireless networking. 5th generation mobile networks are to give a higher density of mobile wireless networks and fast and reliable device to device communication. It aims at low battery communication and minimal latency. This uses cellular antenna such as Dipole antennas and parabolic reflector antennas to offer data rates of up to 100Mbps in metropolitan areas and up to 1Gbps on an office setup(Osseiran, Monserrat, Marsch, 2016). 5G is giving more bandwidth to all users which are an advantage. Users will have faster access to data. The frequency spectrum, on the other hand, will be an issue due to overcrowding of space not forgetting the smaller coverage expected due to the bigger bandwidth(LaPedus, 2016). GPS: The Global positioning system is another significant advancement in Wireless technology. It provides remote geolocation and time information to the requesting user(Satellite navigation, 2002). It is based on ground based radio-navigation systems. It forms a basis for other beneficial wireless technologies such as autonomous driving which depend on the GPS(Russell Hasik, 2002). The method is advantageous in many ways including its accuracy and the relieved stress of carrying and using maps. It is, however, a disadvantage when it leads a user into an unsuitable path since it does no evaluation of external factors and set it up while on a critical work such as driving. GPS antennas employ circular polarization and helical antennas with different slots. Wi-Fi and Bluetooth: (Lemstra V., 2010) see Wi-Fi as a technology that allows the setup of a Wireless Local Area Network that can connect devices and allow sharing of information. (Kewney, 2004) States that Bluetooth technology allows the exchange of data over short distances over connected devices. Bluetooth antennas operate at frequencies of 2.4 GHz to 2.485 GHz. Satellite communication: Satellite communications operate by amplifying radio telecommunication signals using a device that creates communication channels between transmitters and receivers(Bruno, 1998). Offer a high-speed platform for information sharing although their in-flight communications on airplanes are a disadvantage. These use a variety of antennas based on the applications. The cellular antennas used by the mobile phones and 5G wireless communication Technology will become the dominant players in the future. This is because they operate on a platform where users are increasing day by day. Most people long for technology and mostly begin with cellular networks, e.g., in Mobile phones. References (n.d.). Bruno, P. (1998). Satellite-Based Cellular Communications. McGraw-Hill. Hongyi, F. G. (1999). Capacity Comparison of CDMA and FDMA/TDMA for a LEO Satellite System . 1069-1073. Johnson, R. C. (1961). Antenna Engineering Handbook. McGraw-Hill. Kewney, G. (2004, November 16). High speed Bluetooth comes a step closer. Retrieved from www.newswireless.net LaPedus, M. (2016, June). Waiting for 5G Technology. Retrieved from www.semiengeneering.com/waiting-for-5g-technology/ Lemstra, W., V., H. (2010). The innovation Journey of Wi-Fi. Cambridge University press.(n.d.). Naoki, I., Masaak, i. K. (n.d.). Comparison of CDMA and FDMA/TDMA in non-GEO Satellite Systems. Osseiran, A., Monserrat, J. F., Marsch, P. (2016). 5G mobile and wireless communication technology. Cambridge University Press. Russell, M., Hasik, J. (2002). The precision revolution. PS and the future revolution of aerial warfare. . Naval Institute Press. Satellite navigation. (2002). In N. Bowditch, The American Practical Navigator. United States.

Teenagers, Drugs , and Peer Pressure Essay Example For Students

Teenagers, Drugs , and Peer Pressure Essay Teenagers, Drugs , and Peer Pressure Essay Drug use is an increasing problem among teenagers in todays high schools. Most drug use begins in the teenage years, these years are the most crucial in the maturing process. During these years adolescents are faced with the difficult tasks of discovering their self identity, clarifying their sexual roles, assenting independence, learning to cope with authority figures and searching for goals that would give their lives meaning. Drugs are readily available, adolescents are curious and venerable, and there is peer pressure to experiment, and there is a temptation to escape from conflicts. The use of drugs by teenagers is the result of a combination of factors such as peer pressure, curiosity, and availability. We will write a custom essay on Teenagers, Drugs , and Peer Pressure specifically for you for only $16.38 $13.9/page Order now Drugs addiction among adolescents in turn lead to depression and suicide. One of the most important reasons of teenage drug usage is peer pressure. Peer pressure represents social influences that effect adolescents, it can have a positive or a negative effect, depending on the persons social group. We are greatly influenced by the people around us. In todays schools, drugs are very common, peer pressure usually is the reason for their usage. If the people in your social group use drugs there will be pressure a direct or indirect pressure from them. A person may be offered to try drugs, which is direct pressure. Indirect pressure is when someone sees everyone around him using drugs and he might think that there is nothing wrong with using drugs. Person might try drugs just to fit in the social norms, even if a person has no intentions of using drugs, they might do it just to be considered cool by his/her friends. Today drugs are considered to be acceptable by many teenagers. In todays highs schools the availability and variety of drugs is widespread. There is a demand for drugs and the supply is plentiful. Since drugs are so easy accessible, a natural interest in them may develop. A person may hear about drug experiences, or reactions of drug usage. Examples include, Hey the weed that he sold us was cool, I got stoned man. This response will create a sense of curiosity and may convince the person to try drugs themselves. Many teenagers today believe that their first use of drugs is safe. However even though there is no instant addiction with the first try, youngsters tend to experiment further. Soon a person could actively seek the euphoric effects of drugs. The final and the most disastrous stage is when a person needs drugs in order to function adequately. Therefore availability, curiosity and experimentation could result in drug addiction among teenagers. One of the most devastating side effects of drug addiction and abuse is depression. Depression is the result of chemical imbalance, environmental influence, or a combination of both. Using heavy and very highly addictive drugs as heroin, cocaine, opium and many other will cause sudden mood changes, deterioration of the immune system, nervous breakdowns, unusual flares of temper and many other side effects. Besides physical side effects, drug addiction can create problems in a persons social circles. The person may run into many conflicts with his family and friends, resulting in desire for isolation. This in turn will create more problems since the person will have no social support. Furthermore, drug addiction is a financial strain especially for teenagers. When a person is addicted to drugs he will do anything to obtain money to fulfill his needs. According to previous studies, drug addiction is the results of 3 Is. Teenagers may think of their problems as Inescapable, Interminable and Intolerable. Life may seem bleak and miserable. Seeing no way out, feeling lonely and no prospects for improvement leads to depression. Which can lead to attempted suicide. Many studies have found that drugs are a contributing factor to suicide. Using drugs may reduce inhibitions and impair judgement, suicide is a possibility. .udbe09f16fb758efa5ac064ff45a48323 , .udbe09f16fb758efa5ac064ff45a48323 .postImageUrl , .udbe09f16fb758efa5ac064ff45a48323 .centered-text-area { min-height: 80px; position: relative; } .udbe09f16fb758efa5ac064ff45a48323 , .udbe09f16fb758efa5ac064ff45a48323:hover , .udbe09f16fb758efa5ac064ff45a48323:visited , .udbe09f16fb758efa5ac064ff45a48323:active { border:0!important; } .udbe09f16fb758efa5ac064ff45a48323 .clearfix:after { content: ""; display: table; clear: both; } .udbe09f16fb758efa5ac064ff45a48323 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .udbe09f16fb758efa5ac064ff45a48323:active , .udbe09f16fb758efa5ac064ff45a48323:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .udbe09f16fb758efa5ac064ff45a48323 .centered-text-area { width: 100%; position: relative ; } .udbe09f16fb758efa5ac064ff45a48323 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .udbe09f16fb758efa5ac064ff45a48323 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .udbe09f16fb758efa5ac064ff45a48323 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .udbe09f16fb758efa5ac064ff45a48323:hover .ctaButton { background-color: #34495E!important; } .udbe09f16fb758efa5ac064ff45a48323 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .udbe09f16fb758efa5ac064ff45a48323 .udbe09f16fb758efa5ac064ff45a48323-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .udbe09f16fb758efa5ac064ff45a48323:after { content: ""; display: block; clear: both; } READ: Was Reconstruction a Success? Essay As one statistic illustrates 70% of all young people who attempted suicide used drugs. Illegal drugs, for example, weed, speed, acid, or ecstasy has always been a problem among the younger kids, the problems gets even more serious if it involves additive substances such as cocaine. .