FORMULAS / STRATEGY FOR STATISTICS Essay Example For Students

FORMULAS / STRATEGY FOR STATISTICS Essay Probability Complement Law P(A) = 1 P(A) Laws Of Addition -P(A B) = P(A) + P(B) P(A B), if A and B not mutually exclusive P(A B) = P(A) + P(B), if A and B are mutually exclusive Conditional Probability P(A|B) = P(A B) P(B) Independent Condition If A and B are independent, P(A B) = P(A) x P(B) Laws Of Multiplication If A and B are dependent, P(A B) = P(A) x P(B|A) or P(A B) = P(B) x P(A|B) Descriptive Statistics Population Mean, m= all values N Sample Mean, x = all values n Population Variance, s2 = (X m)2 N Sample Variance, S2 = (x x)2 n-1 Standard Deviation = square root of s2 or S2 Probability Distribution Expected Value, E(x) = all x P(xi = x) = m Properties of E(x), E(a) = a E(ax) = aE(x) E(ax b) = aE(x) b E(x1 x2) = E(x1) E(x2) E(x2) = all x2 P(xi = x) Variance, Var(x) = E(x m)2 or Var(x) = E(x2) n(x)2 Properties of Var(x), Var(a) = 0 Var(ax) = a2Var(x) Var(ax b) = a2E(x) Var(x1 x2) = Var(x1) + Var(x2) E(x2) = all x2 P(xi = x) Standard Deviation = square root of var(x) Binomial Distribution x ~ Bin (n , p) Characteristics, Experiment consist of a number of trials Results of trials are only either success or failure Probability of each test between trials are the same E(x) = np Var(x) = npq Continuous Distribution x ~ N(m , s2) Standardising, z = x m s Normal Approximation to Binomial Distribution x ~ N(np , npq) Conditions, Number of trials n > 50 Must use continuity correction Joint Probability Conditional Mean E(x | y=y1) = all x P(xi | y) E(XY) = all x all y P(xi = x and yi = y) When x and y are independent, E(XY) = E(X) E(Y) Covariance of 2 random variables, sxy Cov(XY) = E(XY) E(X)E(Y) When X and Y are independent, Cov(XY) = 0, since E(XY) = E(X)E(Y) Correlation Coefficient, r = Cov(XY),-1 r 1 Var(x) Var(y) Formula for Variance of linear combinations of 2 dependent variables Var(X Y) = Var(X) + Var (Y) 2Cov(XY) Var(aX bY) = a2Var(X) + b2Var (Y) 2abCov(XY) Distribution Of Sample Mean Sample Proportion Let X denote the population variable. m the population mean and s2 the population variance. then, x ~ N(m,s2/n) Let P denote the population proportion with proportion P with n, the number of samples, then P ~ N { p , p (1-p)/n } if P is unknown, P ~ N { P , P (1-P)/n } approx. where P is the sample proportion with the use of continuity correction x (1/2n) Theory Of Estimation Mean Square Error MSE = E(V q)2 where V is the value of the estimator from the true value q Best estimator of the true value is the one that yields the lowest MSE Confidence Interval The interval of which the true value is probable to be included. 3 Cases Of Formula For Confidence Interval For population mean where m, s2 given,-m = x (s2/n)1/2 Zsig level m given but s2 unknown, samples size n > 50-m = x (S2/n)1/2 Zsig level m given but s2 unknown, samples size n < 50-m = x (S2/n)1/2 tsig level For difference in population means mx my where m, s2 given,- mD = (x y) (sx2/nx + sy2/ny)1/2 Zsig level m given but s2 unknown, samples size n > 50- mD = (x y) (Sx2/nx + Sy2/ny)1/2 Zsig level m given but s2 unknown, samples size n < 50- mD = (x y) (Sp2/nx + Sp2/ny)1/2 tsig level where pooled variance, Sp2 = S(x-x)2 + S(y-y)2 nx + ny - 2 Sp2 = Sx2(nx-1) + Sy2(ny-1) nx + ny - 2 Paired Samples- mD = D (SD2/nD)1/2 tsig level where D is the difference between the paired samples. For Population Proportion, p ~ N { p, p(1-p)/n } p not given, then it is estimated with variance P(1-P)/n, in the confidence interval of p = P (P(1-P)/n)1/2 Zsig level Hypothesis Testing Procedure: State Null and Alternate hypothesis Determine one or two sided test Find Ztest or ttest and compare the result with Zcritical and Tcritical respectively Decision Rule, |Ztest| < Zcritical or |ttest| < Tcritical then null hypothesis is true Conclude in relation to hypothesis / question e.g., Ztest = x - m s/n P-value - Decision Rule Reject H0 if p-value < level of significance Accept H0 if p-value level of significance .u39460ac9855cae49de3f21ea69457c87 , .u39460ac9855cae49de3f21ea69457c87 .postImageUrl , .u39460ac9855cae49de3f21ea69457c87 .centered-text-area { min-height: 80px; position: relative; } .u39460ac9855cae49de3f21ea69457c87 , .u39460ac9855cae49de3f21ea69457c87:hover , .u39460ac9855cae49de3f21ea69457c87:visited , .u39460ac9855cae49de3f21ea69457c87:active { border:0!important; } .u39460ac9855cae49de3f21ea69457c87 .clearfix:after { content: ""; display: table; clear: both; } .u39460ac9855cae49de3f21ea69457c87 { 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; } .u39460ac9855cae49de3f21ea69457c87:active , .u39460ac9855cae49de3f21ea69457c87:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u39460ac9855cae49de3f21ea69457c87 .centered-text-area { width: 100%; position: relative ; } .u39460ac9855cae49de3f21ea69457c87 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u39460ac9855cae49de3f21ea69457c87 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u39460ac9855cae49de3f21ea69457c87 .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; } .u39460ac9855cae49de3f21ea69457c87:hover .ctaButton { background-color: #34495E!important; } .u39460ac9855cae49de3f21ea69457c87 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u39460ac9855cae49de3f21ea69457c87 .u39460ac9855cae49de3f21ea69457c87-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u39460ac9855cae49de3f21ea69457c87:after { content: ""; display: block; clear: both; } READ: Banning Child Labour in Developing Countries Essay Type I Error - The error of rejecting H0 when H0 is true P(type I error) = the level of significance Type II Error, b .

The Tension Between the Apology and Crito Essays -

Every once in a while, someone will say something at a certain point in life and later on life say something that contradicts the first statement. In most cases, these statements get unnoticed or overlooked because we are all human and may have different opinions at different instances in time. We could also say that the person who contradicted themselves did not fully develop their thoughts and that is why they were inconsistent in their thoughts. In the case of Socrates, there is an inconsistency problem between two texts because he appears to say one thing in the Apology and the opposite in Crito. It is documented that in one text he says that no matter the case one must always obey the law and in the other text he says one must disobey the law if unjust. At first glance, it seems that Socrates is contradictory and in the case of philosophy contradiction is unacceptable unless justified. Due to the fact that Socrates is such brilliant mind and a famous philosopher we must explore this problem to the deep roots in order to resolve the problem. After delving into this topic further, I will explain that the inconsistency problem is solved by Socrates consistent belief in the leadership of god. In what follows, I will describe why there is tension between the two texts and give you my interpretation of Socrates beliefs. Let us begin by developing the background of the story and then summarizing what was said by Socrates in both passages. We do not have the exact account of what happened because there were no records kept during his lifetime but we do have what is thought to be a very accurate portrayal. It is said, Socrates was accused of both formal and informal charges. The formal charges against him are for corrupting the youth and worshipping false gods. The informal charges accuse him of being a Sophist. As a result of the formal charges, Socrates is put on trial and given a chance to plead his case. During the trial Socrates is trying to convince the jury that he is not a Sophist and explains he does not except payment for opening the minds of others. He goes on to defend himself by discrediting his accusers and expresses his loyalty to Apollo. During Socrates defense in the Apology, he states ?Suppose ? you were to say to me, ?Socrates, we will not obey Anytus this time. Instead, we are prepa red to let you go. But on the following condition: that you spend no more time on this investigation and don?t practice philosophy, and if you?re caught doing so, you?ll die.? Well, as I just said, if you were to let me go on these terms, I?d reply to you, ?I?ve the utmost respect and affection for you, men of Athens, but I?ll obey the god rather than you, and as long as I draw breath and am able, I won?t give up practicing philosophy? (29c-d). This statement reads that if Socrates were ordered by law to stop practicing philosophy that he would disobey orders and not follow the law. At the end of the trial, Socrates is found guilty and sentenced to death. After being sentenced, Socrates is sent to be held imprisoned until it is time for his execution. During his captivity, Crito; a loyal friend of Socrates comes to visit and shares the news with Socrates that his execution day in is the very near future. Crito then says that he has a plan to help Socrates escape, flee the city, and avoid his execution. He states that he and others are willing to accept the consequences whatever they may be to save the life of their dear friend Socrates. Though he contemplates escaping, Socrates makes the decision it is unjust to disobey the law and in Crito says, ?in war and in law courts, and everywhere else, [you must] do whatever your city or father land commands or else persuade it as to what is really just? (51b-c). This statement reads that whatever it is that the courts orders are supreme and the law must be followed in all circumstances unless you can persuade the

Writing a Tk Sample Essay

Writing a Tk Sample EssayTk sample essay is a great way to get your ideas across to the reader in a way that doesn't require lengthy explanations. It is a great idea to make sure that you have some samples of what you are talking about because some people just aren't capable of understanding long passages. If you have an introduction, then it will be easy for the reader to get up to speed on what you are trying to say.There are lots of books that you can use as a basis for your Tk sample essay. If you're writing from a list of ideas, you can write the list down and work out the ideas in your head in a more abstract fashion. You should be able to develop your own unique style, and there will always be room for variety. It is important to remember that your Tk sample essay should be unique to you and not plagiarize the ideas of another person.The best place to get your Tk example essay is online. There are a lot of sites that offer free essay writing tips, and you can try them out and see if they suit you or not. When it comes to Tk, your passion is more important than anything else.People who write essays regularly often find themselves overwhelmed with all the information that they need to fit into their Tk sample essay. This is especially true for beginners and even experienced writers who are still learning the art of writing essays. Don't panic and just keep on going until you are happy with the way you are writing your Tk example essay.When you are creating your Tk sample essay, it's important to keep your ideas short and concise. You don't want to lose the reader by taking too much time on a complex subject. If you're not sure how to phrase a certain idea, then check out the tutorials for some ideas.One of the key ideas in writing your Tk example essay is to choose the topic that you are going to write about. Decide which topic you want to focus on and start writing. You should begin by getting an idea of what you are trying to convey in your essay. Once y ou've got your focus, you can then start to outline your ideas and put them in order.Your idea should be clear, but the question you should ask yourself when brainstorming 'Is this going to be something that people will be able to understand easily?' You don't want to be overcomplicating your topic to make it sound too complicated. Just keep your Tk sample essay simple and you will be able to get past the 'analysis paralysis' syndrome that many students get at this stage.If you're not sure about how to start, you should try and get yourself as far as you can before trying to move onto the next level. After you have read some of the examples, you should have a good idea of how to create a Tk sample essay.

International Space Station essays

International Space Station essays The International Space Station is an idea for an international cooperative scientific environment. The station maintains a low orbit around the Earth. This is 217 to 285 miles above the Earth. The station itself is under construction while in orbit. Construction started in 1998 and will take years to complete. It is estimated to be completed by the year 2006. Sixteen separate nations are working together to complete this massive laboratory. The United States is working with Russia, Japan, Canada, Brazil, the United Kingdom, France, Germany, Belgium, Italy, the Netherlands, Denmark, Norway, Spain, Switzerland, and Sweden. Each country is contributing to the construction of the station. The station is made up of more than 100 components and will take 44 more trips with the three main space vessels to complete it. It will take nearly 2000 man-hours and nearly 60 space walks to construct and maintain the station. After completion, the estimated lifespan of the station is close to ten years. The estimated cost of the station will be between 35 and 37 billion dollars. Once completed, the station will have several pressurized living modules and will The station will be comprised of several major components, such as the Control Module. This contains two rocket engines with command and control systems. Three Nodes on the station connect the sections of the station together. A Service Module contains the life support systems and the living space for the crew during assembly. Six different Scientific Laboratories contain the scientific equipment and controls a robotic arm on the exterior of the station. This arm can manipulate the cargo of incoming shuttles. A Laboratory Module is where the scientific experiments take place. The low gravity makes many experiments possible; in the fields of microgravity, life sciences, Earth sciences, and Space sciences. The Truss is a long spine used ...

Workforce Management of Singapore Airlines Essay

Workforce Management of Singapore Airlines - Essay Example The cabin crews in Singapore Airlines are recruited keeping in mind some basic objectives like not only being graciously presentable but also to reflect the feelings of warmth and friendliness. On the other hand, it also wanted to radiate a sense of authority and confidence in the pattern of their in-flight service. The recruitment function was carried along different ethnic groups from China, Malaysia, India and Eurasian communities. Cabin crews were recruited for both male and female within an age group of 20 to 25 years. The recruitment function contained stress and emotional interview rounds to judge the applicant’s ability to face such. Other parameters considered were communication, grace and posture and work experience. The need for a younger creed of cabin crew dismissed the recruitment of older people. This need to undergo a change for older crewmembers would mean less hassle in the functions of recruitment, selection, and training. Further, the taking of skilled and experienced new crewmembers also increased the chances of job-hopping by them. An interview conducted revealed that the crewmembers were not interested to suggest their brothers and sisters join Singapore Airlines for it did not provide a secured career.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   The training program for the young recruits was an extensive one. It covered not only the theoretical base in providing guidelines on professional and personal etiquettes but also had a practical part. The practical training was imparted to make the recruits familiar with handling several amenities but also in the preparation and serving of beverages and dishes on board. Punctuality was taken as an integral factor in the program where a person thrice late was debarred from attending.

Common Assessment Term Paper Example | Topics and Well Written Essays - 1000 words

Common Assessment - Term Paper Example The Financial crisis has severely affected the personnel of the organizations. There have been several instances of employees’ retrenchment, downsizing as well as cutting the workforce to reduce the fixed overheads. This has resulted in the organizations left with only a fewer employees to meet the obligations and this causes the organizations to suffer not only in producing more products but also in producing quality products. (Skipper, 2009, pp.3-5; Basu, n.d, pp.205-207; Shah, 2010) The paper will assess the situation where the executives have been trying to redesign the jobs for employees and thereby facing a loss of employees every time they attempt to change the structure. Boosting Employee moral: An organization should look at effectively protecting the morale of the employee and constantly monitor the employee morale because the organizations have to realize at first the growth, the productivity of the organization rest mainly on the employees’ expertise. So the organization must be clear and lucid to the point of the scope of each and every employee. Giving a clear and transparent job specification to each and every employee is highly essential. Proper and effective communication is also highly important as clear communication addresses many complex issues. The employee should be given enough space for expressing ideas in a particular matter the employee is expert. The employee should be given in hand training for the particular job and should be given adequate feedback for their improvement such that the employee can get accustomed to the job requirement as needed by the employer. (Bruce, 2002, pp.69-74; Martocchio, 2004, pp.163-164) Designing crisis management: During the times of recession, the executives have been involved in restructuring the jobs, the situation during the crisis have gone to such extent that the employees working in a particular domain had to work on other domains simultaneously. There have been several instances wh en an employee working in a higher designation has to work for much lower designation profiles which have acted to a huge impediment to the morale up gradation of the employee. During the crisis period the situation has gone to such a level that in an IT organizations employees working as software developers for the organization even had to do marketing jobs which is a completely different profile for those employees. Moreover, employees working in higher designations to the level of floor managers or middle level managers in an organizational structure had to do works like depositing funds or withdrawal of funds from banks which are simply clerical jobs. So in different high esteemed organizations employees of higher repute and working in much senior positions had to do simple clerical jobs mainly to make up for the jobs of the employees who have been retrenched during the crisis. This has caused a huge moral degradation of the employees. On the other hand this has severely increas ed the work load on the employees as they had to take multidimensional roles in their work. This has caused a major setback in the employees’ moral. This has again resulted in employees resigning their positions as not

Unit 3 Essay Example | Topics and Well Written Essays - 500 words

Unit 3 - Essay Example Age and can possibly provide an example for this relationship. As one ages, resistance to diseases decreases. This means that the increase in age negatively affect resistance to diseases. Correlation studies can take many forms. Let us consider non-experimental correlation studies and quasi-experimental studies. Non-experimental studies involve measuring things as the objects appear. In non-experimental studies, the methods used include observation, case history, and surveys. It is it is unethical to manipulate independent variables. Non-experimental values are used to provide solutions to problems and question existing realities. Lawrence Lisa (2011), conducted a non-experimental descriptive correlation study to examine the relationship amongst four variables, moral distress, education level, CRP and work ethics and how these variables affected nurses work engagement. The study found out that there was a positive direct relationship between CRP and work engagement and a negative correlation moral distress and work engagement. According to Ramos-Alvarez, Moreno Fernandez, Valdez Conroy, & Catena (2008), quasi experiments are evaluations that attempt to determine whether a program or intervention has an expected effect on the participants. Quasi experiments take different forms but usually lack aspects of true experiments. This is the reason quasi experiments are not ideal for dissertation work. In a true experiment, there must be pre-test and posttest design, treatment group, control group and random assignment. For quasi experiment, either one or two of these aspects are lacking. Raanas, Grindel & Herting (2012) conducted a quasi experiment study to examine the health advantages of a bedroom window observethe natural background for patients undergoing a rehabilitation program. The funding for this research was that a blocked view appeared to influence negative physical health changes in women. For men, blocked views