Calculating a Confidence Interval for a Mean

Inferential statistics concerns the process of beginning with a statistical sample and then arriving at the value of a population parameter that is unknown. The unknown value is not determined directly. Rather we end up with an estimate that falls into a range of values. This range is known in mathematical terms an interval of real numbers and is specifically referred to as a confidence interval. Confidence intervals are all similar to one another in a few ways. Two-sided confidence intervals all have the same form: Estimate  ± Margin of Error Similarities in confidence intervals also extend to the steps used to calculate confidence intervals. We will examine how to determine a two-sided confidence interval for a population mean when the population standard deviation is unknown. An underlying assumption is that we are sampling from a normally distributed population. Process for Confidence Interval for Mean With an Unknown Sigma We will work through a list of steps required to find our desired confidence interval. Although all of the steps are important, the first one is particularly so: Check Conditions: Begin by making sure that the conditions for our confidence interval have been met. We assume that the value of the population standard deviation, denoted by the Greek letter sigma ÏÆ', is unknown and that we are working with a normal distribution. We can relax the assumption that we have a normal distribution as long as our sample is large enough and has no outliers or extreme skewness.Calculate Estimate: We estimate our population parameter, in this case, the population mean, by use of a statistic, in this case, the sample mean. This involves forming a simple random sample from our population. Sometimes we can suppose that our sample is a simple random sample, even if it does not meet the strict definition.Critical Value: We obtain the critical value t* that correspond with our confidence level. These values are found by consulting a table of t-scores or by using the software. If we use a table, we will need to know the number of degrees of freedom. The number of degrees of freedom is one less than the number of individuals in our sample.Margin of Error: Calculate the margin of error t*s /√n, where n is the size of the simple random sample that we formed and s is the sample standard deviation, which we obtain from our statistical sample.Conclude: Finish by putting together the estimate and margin of error. This can be expressed as either Estimate  ± Margin of Error or as Estimate — Margin of Error to Estimate Margin of Error. In the statement of our confidence interval it is important to indicate the level of confidence. This is just as much a part of our confidence interval as numbers for the estimate and margin of error. Example To see how we can construct a confidence interval, we will work through an example. Suppose we know that the heights of a specific species of pea plants are normally distributed. A simple random sample of 30 pea plants has a mean height of 12 inches with a sample standard deviation of 2 inches. What is a 90% confidence interval for the mean height for the entire population of pea plants? We will work through the steps that were outlined above: Check Conditions: The conditions have been met as the population standard deviation is unknown and we are dealing with a normal distribution.Calculate Estimate: We have been told that we have a simple random sample of 30 pea plants. The mean height for this sample is 12 inches, so this is our estimate.Critical Value: Our sample has a size of 30, and so there are 29 degrees of freedom. The critical value for confidence level of 90% is given by t* 1.699.Margin of Error: Now we use the margin of error formula and obtain a margin of error of t*s /√n (1.699)(2) /√(30) 0.620.Conclude: We conclude by putting everything together. A 90% confidence interval for the population’s mean height score is 12  ± 0.62 inches. Alternatively, we could state this confidence interval as 11.38 inches to 12.62 inches. Practical Considerations Confidence intervals of the above type are more realistic than other types that can be encountered in a statistics course. It is very rare to know the population standard deviation but not know the population mean. Here we assume that we do not know either of these population parameters.

Mucha Is a Powerful Executive Essay - 563 Words

Mary Doe is the Vice President, Chief Communications Officer, responsible for global communications at The Walt Disney Company, which includes acting as chief spokesperson and overseeing communication strategy and media relations for the company, its business segments and its philanthropic and environmental initiatives. Prior to join The Walt Disney, Mary Doe served as a communications director to the New York State Governor George Pataki and for the United States Senator Alfonse D’Amato. A member of the Arthur Page Society and The Seminar, in 2012 Ms. Mary Doe received the prestigious Matrix Award from New York Women in Communications, Inc. Also, named as one of the 100 Most Important In-House Communicators in the World by The Holmes†¦show more content†¦Under her directions, all executives were pushed to challenge all-comers and scrapped the posture in which queries were often dismissed with a flat â€Å"no comment† response. She was quick on unleashing her â€Å"inner pit bull† on critics and reporters ((Disney Case Study – Corporate Spokesperson, â€Å"2004, Running Disney’s Word Machine,† Page 9). She even went against the proxy advisor glass, Lewis Co by publicly stating it as â€Å"an upstart company that is trying to grab publicity.† She is tough even with the top management at Disney and known for difficult relationship with Fred Dicker, a New York Post Editor who described her as the â€Å"Jack Kevorkian of Public Information.†(Disney Case Study – Corporate Spokesperson, â€Å"2004, Running Disney’s Word Machine,† Page 10.) No doubt she is a successful professional and a powerful woman who has created some enemies along the way such as the journalist who may not have adored Mary Doe throughout the way. In my opinion, her approach is effective to keep Disney out of negative publicity as Disney is still considered as the best-known companies in the world. Her experience has saved the company during crisis management and has helped theShow MoreRelatedDisney Company s Operations And Board Of Directors3617 Words   |  15 Pagesbillion (Mucha Singer, 2013). In 2013, this segment comprised approximately 45% of revenues and 64% of income. In fiscal years 2014 and 2013, revenues and income for the Media Networks segment increased 4% and 7%, respectively (Mucha Singer, 2014). Additionally, according to the first quarter segment operating results for fiscal 2015 and 2014, the data illustrate that the Media Networks revenues for the quarter increased 11% to around $5.9 billion and income increased 3% to $1.5 b illion (Mucha SingerRead MoreWho Made Rizal Our Foremost National Hero, and Why?5235 Words   |  21 Pagessocieties, trade names that bear his name; in the number of persons, both Filipinos foreigners, who were named Rizal or Rizalina because of their parents’ admiration for the Great Malayan; in the number of laws, Executive Orders Proclamations of the Chief Executive, bulletins, memoranda, circulars of both the bureaus of public private schools. Who is the Filipino writer thinker whose teachings noble thoughts have been frequently invoked quoted by authors public speakersRead MoreMarketing Management130471 Words   |  522 Pagesacquiring control over the levels of state power. Property no more rules, even indirectly, these days. Nor does labour in the †peasant and workers† states. It is the â€Å"knowledge† group comprising not only politicians and bureaucrats but also business executives, company directors, factory mangers, scientists eng ineers, technocrats, bankers, journalists, intellectuals lawyers, doctors, teachers and many other belonging to liberal profession and â€Å"services† sector, that does so. That group or class constitutes

Transformational Leadership In Health Care â€Myassignmenthelp.Com

Question: Discuss About The Transformational Leadership In Health Care? Answer: Introduction Leadership contributes to the successful growth of the organisation. The challenges opportunities are managed with the able leadership of the organisation. The leadership also contributes to the growth of the human resources of the organisation. The enhancement of skill, the growth of the culture of the organisation consistent learning is possible with the able leadership. It is a fact that the growth of the organisation depends on the vital contribution of the leaders the followers of it. The strategies of the management for the growth of the organisation are successfully implemented with the help of leaders and their ability to lead the people of the organisation. There are different styles of leadership used by the leaders to bring effective work environment. Concept and theories of leadership There are different theories of leadership that focus on the traits and attributes for a leader to become successful. Theory of Great Man states that leadership traits are intrinsic. The leaders are born leaders. A true leader rises when he or she confronts the correct situation. Trait theory of leadership focuses on the qualities of the leadership like intelligence, responsibilities, creativity values(Barr Dowding, 2016). The theory makes an analysis of the mental, physical social traits of the leader. The Behavioural theory focuses on the behaviour of the leader. It studies how a leader is able to behave when he or she deals with the task the people in an organisation. Contingency theory of leadership advocates that there are different ways to lead the people and these ways are based on the situation. The effects of the leader are found when the leader takes decisions differently in different situations. Transactional leadership theory advocates that there is always a need of developing a mutual reinforcing atmosphere. The focus of the theory is on the beneficial relationship between the leaders the followers(Drucker, 2014). The theory advocates that a leader follows both reward and punishment to manage the people in the organisation. The transformational leadership style advocates that the leader sets an example and motivates followers. The leader interacts with people in the organisation and leads them to work successfully. Style, attribute behaviour of different leadership style It is very important to define the importance of the effective leadership. The effective leadership does not focus on holding the authority in the organisation. A true leader always makes an assessment of all the works and the decision that he or she takes in the course of his or her work(Drucker, 2017). It is very important for a leader to see that the decisions taken by him or her are aligned with the objectives of the organisation. For the successful growth of the leadership, it is always important for a person to have a good personality. A good leader interacts with the followers of the organisation and the manner of interacting with the followers also determines the ability of an individual to lead the team(Fassin, et al., 2011). People from different thinking, cultures and well managed by a good leader. The leader becomes very creative and manages the people with appropriate ability in order to become successful in the workplace. An autocratic leader wants the followers to work as per the instruction is given to them. The autocratic leader wants to manage the employees of the organisation as per the decision made by him or her. The leader makes the people follow him or her and does not allow the employees to make an opinion on his style of decision-making. A democratic leader is different from an autocratic leader. The leader allows the followers to take part in the decision-making process and contributes to their opinion and skills. The contribution of the employees is found in the strategic development of the organisation. A transactional leader leads the people of the organisation through his or her involvement in the activities of the organisation. The leader follows reward and punishment policy to motivate people to work in the workplace. The transformational leader is an inspirational leader and the leader sets the example before the followers to get motivated. The employees of the organisation are inspired by the leader. The employees get motivated and the transformational leader develops the ability of the people in the organisation. The transformational leader becomes visionary, good in communication, responsible, competent and has the problem-solving ability. The leader believes in self-esteem and discipline(Gentile, 2012). The empathy skill of the leader enhances values of the team performance. The goals of the organisation are achieved when the transformational leader leads the people in the correct direction. Importance of leadership qualities for managers The leader possess different qualities and these qualities help the leader to lead people in the correct direction for the fulfilment of the goals and objectives of the organisation(Gellis, 2001). The following are the different qualities that are used by the leader of the organisation to manage the challenges and opportunities to achieve the strategic objectives of the organisation. Vision The leader of an organisation is a man of vision. The vision of the organisation is set by the leader aligning his or her vision. The strategy that has been formulated by the leader is followed by the people in the organisation(Hughes Wearing, 2007). The most important activities of a leader are to communicate the strategic plan to the people in the organisation so that people remain aware of that. Good Communication skill A good leader communicates with the people appropriately. The people of the organisation are communicated the aim of the organisation and the ways the people should work to achieve the goals of the organisation(Luu, et al., 2008). The communication helps the people to get motivated and to use their skills for the development of the organisation. Motivation Motivating people in the correct direction is an ability of the leader. The leader sometimes takes the help of reward and punishment to motivate the people to perform their duties and responsibilities. The people perform well when they are motivated well. Interpersonal skill The leader of the organisation always tries to build cooperation and coordination among the people of the organisation. The leader tries to establish the healthy relationship among the employees. The people perform well when they work together as a team. Thus developing interpersonal skill is an important quality of the leader. Problem-solving quality The leader possesses problem-solving attitude. In the organisation, we come across many types of issues and problems. These issues are required to be solved unless the success of the organisation is not possible. The leader manages the issues with his problem-solving skills. Decision-making ability A good leader is a good decision maker. The leader takes an appropriate decision at the time of need. The leader involves people in the organisation to contribute their skills and experiences(Sanborn, 2016). The aim of the leader is to take the good decision so that the goals of the organisation will be achieved. Application of leadership in practice in teams in an organisation The leader of the organisation should be very sensible and sensitive. The development of a team and the performance of the team depend on the way leader lead the people. The leader knows the ability of the team members and encourages them to perform best of their abilities.The leader leads a team like a transformational leader. The leader builds trust and friendship among the people so that the team will work effectively(Velsor, et al., 2010). The leader remains very transparent and takes the decision as per the need of the organisation. The leader focuses on the best utilisation of the skills and experience of the team members. The leader knows that the combined efforts of the people in the organisation can only bring success in the organisation. The team building attitude is very important for the leader. The leader of the organisation always focuses on establishing the good culture in the organisation. The leader establishes the culture of the organisation that aligns with the set of beliefs, values and faith of the people in the organisation. The employees of the organisation accept the culture of the organisation when they feel that the culture of the organisation helps them to work independently and they have the freedom to use their skills and expertise in the workplace(Luu, et al., 2008). It is important for the leader of the organisation to focuses on good culture for the organisation. The practice of good leadership is found in the organisation when the leader of the organisation acts sensibly during the change in the organisation. The strategic plan is formulated by the organisation and the plan is changed as per the organisation needs. The people in the organisation do not accept the change if they are not satisfied with the change initiative. They need to know the cause of the change and how the change will contribute to the growth of the organisation(Reich, 2000). The leader of the organisation uses the skills to motivate people. The leader makes the people know the need of the change for the growth of the organisation. This motivates people to accept the change. Assessment of my leadership skills and the areas I need to improve I have earned that a good leader works on a certain philosophy. The leader follows the philosophy and works effectively. I understand that a leader requires knowing the different leadership styles so that he or she can use them in different situations. As a leader I understand that I will behave like a democratic leader, a visionary leader, a transaction leader or a transformational leader and all these styles will be used as per the demand of the situation. I understand that I need to be a transformational leader as it is very important to manage people in different situations. The complex situations will be easily handled by me if I develop my problem-solving ability. I will be able to take the appropriate decision when I will know understand the perceptions and expectations of the people in the organisation. A true leader should also motivate the employees by fulfilling their individual needs. A satisfied worker gives his or her complete efforts for the growth of the organisation. Thus as a leader, I must try to satisfy my fellow workers so that the objectives of my organisation will be accomplished. As a student, I have learnt about the need of developing leadership skills to manage people in the organisation. The knowledge I get about the leadership skills will be helpful to utilise in the working place. It is also very important to know how to manage the people in the diverse culture. I have learnt that I need to be very empathetic to my followers and I will try to motivate people to achieve their goals. The areas I feel very important for me to develop are the development of the interpersonal skills, decision-making skills and problem-solving skills. All these three skills are very important for the leader of the organisation. I will develop all these qualities in order become a successful leader. Conclusion Leadership is an ability to inspire the people to work for the achievement of the goals of the organisation. A true leader motivates people to work and contribute their expertise to the development of the organisation. The appropriate decision of the leader keeps the people work without any worries and anxiety. The good culture also helps the employees to be very productive in the workplace. The problem-solving attitudes and interpersonal skills are very important for the leader. I understand that in order to be very successful in my workplace as a leader I need to develop my skills and should know how and where I should use the different styles of leadership. I must act like a visionary leader and lead the people in the correct direction. I will focus on establishing good work culture among the team members and motivate all to work collectively. This will help me to be a successful leader. References Barr, J. Dowding, L., 2016. Leadership in Health Care, 3rd Edition. London: SAGE Publication. Drucker, P., 2014. Leadership vs. Management. [Online] Available at: https://www.diffen.com/difference/Leadership_vs_Management [Accessed 21 09 2017]. Drucker, P., 2017. Managerial Point of view. [Online] Available at: http;//solaas.com.ar/harald/en/liderazgo2 [Accessed 21 09 2017]. Fassin, Y., Van, R. A. Buelens, M., 2011. Small business owner-managers perceptions of business ethics and CSR-related concepts. J Bus Ethics, 98(3), pp. 425-453. Gellis, Z. D., 2001. Social work perceptions of transformational and transactional leadership in health care. Social Work Research, vol.25. no. 1, pp. 17-25. Gentile, M. C., 2012. Values-driven leadership development: Where we have been and where we could could go. Organisation management Journal, pp. 188-196. Hughes, M. Wearing, M., 2007. Organsiations and Management in Socila Work. Los Angels: sage. Kouzes, J. Posner, B., 2008. The Leadership Challenge: The Leadership Practcies Inventory. San Francisco: CA: Jossey- Bass. Luu, V. T., Kim, S. Y. Huynh, T. A., 2008. Improving project management performance of large contractors using. International Journal of Project Management,, 256(7), pp. 758-769. Mintzberg, H., 2009. Managing. San Francisco: Berrett-Koehler. Qureshi, T. M. Warraich, A. S., 2009. Significance of project management performance assessment. International Journal of Project Management, Volume 27, pp. 378-388. Reich, R., 2000. The future of sucess: Working and living in the new economy. New York: Alfred Knopf. Sanborn, M., 2016. 9 Difference Between Managers and Leaders. [Online] Available at: https://www.marksanborn.com/blog/9-differences-between-managers-and-leaders/# [Accessed 21 09 2017]. Velsor, V., McCuley Ruderman, 2010. Developing of Leaders. In: The Center for Creative Leadership handbook of leadership development. San Francisco,: Jossey Bass.