An Introduction to Hypothesis Testing

An Introduction to Hypothesis Testing Hypothesis testing is a topic at the heart of statistics. This technique belongs to a realm known as inferential statistics. Researchers from all sorts of different areas, such as psychology, marketing, and medicine, formulate hypotheses or claims about a population being studied. The ultimate goal of the research is to determine the validity of these claims. Carefully designed statistical experiments obtain sample data from the population. The data is in turn used to test the accuracy of a hypothesis concerning a population. The Rare Event Rule Hypothesis tests are based upon the field of mathematics known as probability. Probability gives us a way to quantify how likely it is for an event to occur. The underlying assumption for all inferential statistics deals with rare events, which is why probability is used so extensively. The rare event rule states that if an assumption is made and the probability of a certain observed event is very small, then the assumption is most likely incorrect. The basic idea here is that we test a claim by distinguishing between two different things: An event that easily occurs by chance.An event that is highly unlikely to occur by chance. If a highly unlikely event occurs, then we explain this by stating that a rare event really did take place, or that the assumption we started with was not true. Prognosticators and Probability As an example to intuitively grasp the ideas behind hypothesis testing, we’ll consider the following story. It’s a beautiful day outside so you decided to go on a walk. While you are walking you are confronted by a mysterious stranger. â€Å"Do not be alarmed,† he says, â€Å"this is your lucky day. I am a seer of seers and a prognosticator of prognosticators. I can predict the future, and do it with greater accuracy than anyone else. In fact, 95% of the time I’m right. For a mere $1000, I will give you the winning lottery ticket numbers for the next ten weeks. You‘ll be almost sure of winning once, and probably several times.† This sounds too good to be true, but you are intrigued. â€Å"Prove it,† you reply. â€Å"Show me that you really can predict the future, then I’ll consider your offer.† â€Å"Of course. I can‘t give you any winning lottery numbers for free though. But I will show you my powers as follows. In this sealed envelope is a sheet of paper numbered 1 through 100, with heads or tails written after each of them. When you go home, flip a coin 100 times and record the results in the order that you get them. Then open the envelope and compare the two lists. My list will accurately match at least 95 of your coin tosses.† You take the envelope with a skeptical look. â€Å"I will be here tomorrow at this same time if you decide to take me up on my offer.† As you walk back home, you assume that the stranger has thought up a creative way to con people out of their money. Nevertheless, when you get back home, you flip a coin and write down which tosses give you heads, and which ones are tails. Then you open the envelope and compare the two lists. If the lists only match in 49 places, you would conclude that the stranger is at best deluded and at worse conducting some sort of scam. After all, chance alone would result in being correct about one half of the time. If this is the case, you would probably change your walking route for a few weeks. On the other hand, what if the lists matched 96 times? The likelihood of this occurring by chance is extremely small. Due to the fact that predicting 96 of 100 coin tosses is exceptionally improbable, you conclude that your assumption about the stranger was incorrect and he can indeed predict the future. The Formal Procedure This example illustrates the idea behind hypothesis testing and is a good introduction to further study. The exact procedure requires specialized terminology and a step by step procedure, but the thinking is the same. The rare event rule provides the ammunition to reject one hypothesis and accept an alternate one.

Pietro Lorenzetti essays

Pietro Lorenzetti essays The first work that I visited was Pietro Lorenzettis panels from an altarpiece showing the Enthroned Virgin and Child, with kneeling donor and angels. The piece immediately caught my eye because of its resemblance to two other works from the Pre-Renaissance, Cimabues Madonna Enthroned and Giottos Madonna Enthroned. Pietro Lorenzettis piece is from Siena during the 1320s. It is about 30 x 60 inches and done in tempera and tooled gold on a wooden panel. Through a dark outer room, the piece is visible through a doorway with a stone archway. The architecture of the room and surrounding rooms emphasizes the Gothic influence of the period and brings and pieces together nicely in that historical setting. In the room there are also other altarpieces from the same pre-Renaissance period. The background of the piece was done primarily in the tooled gold. There is molding in the shape of a triple bubble above the heads of Madonna and Child. She is seated on a throne, Child on knee, and you can see by looking at her hand that the proportions are not quite right because it is larger than it should be. Her dress is detailed in gold. The golden halos around the heads are circular despite the direction in which the head is turned. The brush strokes for these halos are done circularly and contrast the brush strokes on the rest of the panel. Most subject matter of art in the Proto-Renaissance was limited to religion and more specifically, Christianity. The paintings were not realistic, with images looking flat and somewhat abstract. This was due to the fact that priorities were to communicate the religious subject matter and not to critique naturalistic style. As Ive mentioned, Lorenzettis piece shares many similarities with Cimabues and Giottos pieces. During this time there was the beginnings of a naturalistic emphasis, but artists lacked the knowledge o...

Cell Phones Research Paper Example | Topics and Well Written Essays - 750 words

Cell Phones - Research Paper Example The main reasons for this monumental change over such a short, time are the abilities that science and technology has conferred to modern phones, particularly mobile devices. Today, a phone has acquired such a wide variety of uses that a phone without the ability to call, while it would be dysfunctional, would still be a viable communication device. On the other hand, a 1990s phone would be useless if one could not make or receive calls on it. While the early phones were expensive gadgets and the reserve for the rich and educated, today they can be owned by almost anyone and one needs only the most basic education to use a phone. Mobile phone companies are competing to see whose device can hold and use the most applications and offer the best services other than calling. One can use their mobile phone to browse the internet, and as such access pertinent information from virtually anywhere in the world, provided they have a good signal. As a result, millions of people many of them you ths spend hundreds of hours every week using their phones on nonverbal interaction and social networking, indeed, the time spent making phone calls pales in comparison to the time spent on Facebook, tweeter, instant messaging or in related activities. Many mobile phones offer the user a capacity to do any of these activities especially the smart phones, described as â€Å"clever gadgets,† which are more than just phones, (McKendrick, 2011). This is because of their many features that transcend what ordinary mobile phones can do including a variety of user friendly applications that allow users to carry out a range of tasks such as; reading EBooks, teleconferencing, reading, and creating emails. Mobile phones can also be used in time of emergencies; to call for help, or look for directions when one is lost because some of them have gotten applications like Google maps, which enable users to look for direction, and pinpoint their current location. Furthermore, mobile companies use the technology to help the police trace lost people or criminals by tracing their signals. Indeed a lost person can be traced even if their phone is switched off (Siegel, 2008). Other security futures include sending distress messages without having to make a phone call, for instance with some Samsung phones one only need to press the volume key thrice, and a discrete text is sent to a pre-determined number notifying the recipient that the sender is in danger. Mobile devices are also used as/alongside baby monitors, using certain IPhones applications parents use their Smartphone to keep an â€Å"eye† on their infants. For instance, one can use an application that automatically sends a message to their phone whenever the child makes noise or cries (Associated Press, 2009). A more rudimentary albeit expensive tactic, which can be used, is to leave one phone in the baby crib with an active connection to another phone, possibly with a headpiece so one can listen to the baby w ithout being present. Mobiles phones today have an immense entertainment role and are competing with mainstream media such as Television and radios. Several phone types allow one to listen to radio and watch television on the move. Teens and young adults (13-24) are the leading users of mobile devices for these functions (chiff.com