Examples of Confidence intervals for means

Examples of Confidence intervals for means One of the major parts of inferential statistics is the development of ways to calculate confidence intervals. Confidence intervals provide us with a way to estimate a population parameter. Rather than say that the parameter is equal to an exact value, we say that the parameter falls within a range of values.   This range of values is typically an estimate, along with a margin of error that we add and subtract from the estimate. Attached to every interval is a level of confidence. The level of confidence gives a measurement of how often, in the long run, the method used to obtain our confidence interval captures the true population parameter. It is helpful when learning about statistics to see some examples worked out. Below we will look at several examples of confidence intervals about a population mean. We will see that the method we use to construct a confidence interval about a mean depends on further information about our population. Specifically, the approach that we take depends on whether or not we know the population standard deviation or not. Statement of Problems We start with a simple random sample of 25 a particular species of newts and measure their tails. The mean tail length of our sample is 5 cm. If we know that 0.2 cm is the standard deviation of the tail lengths of all newts in the population, then what is a 90% confidence interval for the mean tail length of all newts in the population?If we know that 0.2 cm is the standard deviation of the tail lengths of all newts in the population, then what is a 95% confidence interval for the mean tail length of all newts in the population?If we find that that 0.2 cm is the standard deviation of the tail lengths of the newts in our sample the population, then what is a 90% confidence interval for the mean tail length of all newts in the population?If we find that that 0.2 cm is the standard deviation of the tail lengths of the newts in our sample the population, then what is a 95% confidence interval for the mean tail length of all newts in the population? Discussion of the Problems We begin by analyzing each of these problems. In the first two problems we know the value of the population standard deviation. The difference between these two problems is that the level of confidence is greater in #2 than what it is for #1. In the second two problems the population standard deviation is unknown. For these two problems we will estimate this parameter with the sample standard deviation. As we saw in the first two problems, here we also have different levels of confidence. Solutions We will calculate solutions for each of the above problems. Since we know the population standard deviation, we will use a table of z-scores. The value of z that corresponds to a 90% confidence interval is 1.645. By using the formula for the margin of error we have a confidence interval of 5 – 1.645(0.2/5) to 5 1.645(0.2/5). (The 5 in the denominator here is because we have taken the square root of 25). After carrying out the arithmetic we have 4.934 cm to 5.066 cm as a confidence interval for the population mean.Since we know the population standard deviation, we will use a table of z-scores. The value of z that corresponds to a 95% confidence interval is 1.96. By using the formula for the margin of error we have a confidence interval of 5 – 1.96(0.2/5) to 5 1.96(0.2/5). After carrying out the arithmetic we have 4.922 cm to 5.078 cm as a confidence interval for the population mean.Here we do not know the population standard deviation, only the sample standard deviation. Thus we will use a table of t-scores. When we use a tabl e of t scores we need to know how many degrees of freedom we have. In this case there are 24 degrees of freedom, which is one less than sample size of 25. The value of t that corresponds to a 90% confidence interval is 1.71. By using the formula for the margin of error we have a confidence interval of 5 – 1.71(0.2/5) to 5 1.71(0.2/5). After carrying out the arithmetic we have 4.932 cm to 5.068 cm as a confidence interval for the population mean. Here we do not know the population standard deviation, only the sample standard deviation. Thus we will again use a table of t-scores. There are 24 degrees of freedom, which is one less than sample size of 25. The value of t that corresponds to a 95% confidence interval is 2.06. By using the formula for the margin of error we have a confidence interval of 5 – 2.06(0.2/5) to 5 2.06(0.2/5). After carrying out the arithmetic we have 4.912 cm to 5.082 cm as a confidence interval for the population mean. Discussion of the Solutions There are a few things to note in comparing these solutions. The first is that in each case as our level of confidence increased, the greater the value of z or t that we ended up with. The reason for this is that in order to be more confident that we did indeed capture the population mean in our confidence interval, we need a wider interval. The other feature to note is that for a particular confidence interval, those that use t are wider than those with z. The reason for this is that a t distribution has greater variability in its tails than a standard normal distribution. The key to correct solutions of these types of problems is that if we know the population standard deviation we use a table of z-scores. If we do not know the population standard deviation then we use a table of t scores.

The Value of Self-Reflection for Success in Teaching

The Value of Self-Reflection for Success in Teaching In a profession as challenging as teaching, honest self-reflection is key. That means that we must regularly examine what has worked and what hasnt worked in the classroom, despite how painful it can sometimes be to look in the mirror. Once you self-reflect you then need to take your answers and turn them into positive, resolute statements that give you concrete goals on which to focus immediately. Be honest, work hard, and watch your teaching transform for the better! Ask Yourself These Tough Questions - And Be Honest! Where did I fail as a teacher in the past? Where did I succeed?What is my top teaching goal for the coming year?What can I do to make my teaching more fun while adding to my students learning and enjoyment?What can I do to be more proactive in my professional development?What resentments do I need to resolve in order to move forward more optimistically and with a fresh mind?What types of students do I tend to ignore or do I need to spend more time serving?Which lessons or units am I only continuing to perform out of habit or laziness?Am I being a cooperative member of my grade level team?Are there any aspects of the profession that I am ignoring out of fear of change or lack of knowledge? (i.e. technology)How can I increase valuable parental involvement?Have I done enough to foster a productive relationship with my administrator?Do I still enjoy teaching? If not, what can I do to increase my enjoyment in my chosen profession?Do I bring additional stress upon myself? If so, how can I decrease or eliminate it? How have my beliefs about learning and pedagogy changed over the years?What minor and/or major changes can I make to my academic program in order to directly increase my students learning? What Happens If You Refuse to Self-Reflect Put earnest effort and pure intention into your self-reflection. You dont want to be one of those stagnant teachers that drably presents the same ineffective and outdated lessons year after year. The unexamined teaching career can lead to becoming just a glorified babysitter, stuck in a rut and no longer enjoying your job! Times change, perspectives change, and you must change in order to adapt and remain relevant in the ever-changing world of education. Often its difficult to get motivated to change when you have tenure and cant be fired but thats precisely why you must undertake this effort on your own. Think about it while youre driving or doing the dishes. It doesnt matter where you self-reflect, only that you do it earnestly and energetically. Examine Your Teaching - Any Time of Year One of the best things about teaching is that every school year offers a fresh start. Make the most of this new beginning - any time of year! - and move ahead with the confidence that you are mindful and motivated to be the best teacher you can be! Edited By: Janelle Cox

Ecology of Organisms Lab Report Example | Topics and Well Written Essays - 250 words

Ecology of Organisms - Lab Report Example Different pH levels affected the germination and growth rates of the radish seeds. This experiment was examining the effects of different pH level on germination of radish seeds. Water with a pH of 6, vinegar pH 3 and baking soda pH 10.5 were used. From the results, pH 3 radish never grew at a slow rate radish on pH 10.5 grew at a slower fairly rate and pH 6.5 grew the fastest. In vinegar, only 10% of the seeds germinated 40% in baking soda and 100% in water. Extremely low pH affected seed germination and maximum growth recorded at a neutral pH. In general, the lower the pH of the environment, the harder for radish seeds to germinate and to survive. It would be appropriate to conclude that plant species with a narrow range of pH are in trouble. Most plants germinate and grow best in a pH range of 7 to 9. The higher and lower pH levels, especially of 3 and 11, drastically reduce growth of plants and crops. Acid rain is a problem since it reduces the pH levels of soil to below 5. From the above experimental results, it suggests that acid rain may drastically reduce crops and plants

Why did Slavery Come to be the Dominant Labor System in the Southern Essay

Why did Slavery Come to be the Dominant Labor System in the Southern Colonies - Essay Example The workforce in the agricultural sector in the southern colonies was mainly comprised of Europeans servants who worked on indenture basis. Although the Europeans still offered labor, African slaves were the better choice for planters because they were cheap to maintain and more productive. By mid 17th century there was a massive shift towards slave labor in the south since demand for food was rising with expanding markets. At this time Africans had started to be shipped and be sold as slaves to Americans. The climate and soil in the south were more favorable for agriculture than those of the north. This made the sound to be heavily dependent on labor for development of plantations. The south as stated above was an ideal region for agriculture all year round and crops like tobacco and rice thrived well. These crops are labor intensive and the lands were quite vast. Therefore, a huge potential of the southern lands remained untapped considering that there were many waterways where cro ps could be transported to overseas markets. As these farms grew labor shortages became intense and by the end of the 17th century more than 500 Africans had been bought as slaves to meet the demand (Schneider and Schneider 48). This trend was soon followed by withdrawal of indentured European servants since many had saved enough to buy their own land and start farming. America was quite big and unexploited by then and the Europeans found no reason not to venture into far away lands. The Bacon’s Rebellion also saw many planters release white servants as they proved to be a danger to political stability. In this regards an alternative had to be sought to counter the exodus of the white servants. By mid 18th century a total of 235,000 Africans were in America and 85% of them worked in the southern colonies of Virginia, Georgia, North and South Carolina (73). African slaves however came to be fully exploited after failed trials were made on Native Americans (Rodriguez 106). Many of them died from European diseases while many others ran away since they knew the land better than the Europeans. This left the planters no choice but to take in African slaves. This followed a massive expansion of plantations in Georgia and South Carolina which translated to increased production levels of rice and tobacco. These slaves did a great deal of work which the white servants had refused to do for example draining of swamps. West Africans came in handy especially in rice growing plantations since they were familiar with the kind of work required as their mother lands grew rice. Slaves worked for 15 hours on a daily basis especially during the harvest season (Norton and Sheriff 27). One overseer was required to supervise a minimum of 20 slaves doing back-breaking work and when a slave lazed around, the overseer was supposed to whip them. The fact that slaves were cheap to buy and maintain saw planters buy them in masses so as to plant and cultivate more. As earlier indica ted slaves used to work for many hours per day which translated to bumper harvests and therefore booming plantation business. Many plantation owners like the Byrd family from Virginia turned to be quite wealthy (58). Such families came together to form elite classes of planters in the southern states who ensured that slave trade remained because it was a lifeline to their wealth. Southern colonies had vast fertile lands for agriculture where Europeans worked as servants on indenture basis. The vastness and the need to grow crops on large scale raised the need to have more workers. Slave trade was on the rise by mid 17th century and it saw many planters buy African slaves to work in

Planning to Live Your Life Your Way Essay Example for Free

Planning to Live Your Life Your Way Essay Goal setting is a formal process for personal planning. By setting goals on a routine basis you decide what you want to achieve, and then move step by-step towards the achievement of these goals. The process of setting goals and targets allows you to choose where you want to go in life. By knowing precisely what you want to achieve, you know what you have to concentrate on to do it. You also know what is merely a distraction. Goal setting is a standard technique used by top-level athletes, successful business-people and achievers in all fields. It gives you long-term vision and short-term motivation. It focuses your acquisition of knowledge and helps you to organize your resources. By setting sharp, clearly defined goals, you can measure and take pride in the achievement of those goals. You can see forward progress in what might previously have seemed a long pointless grind. By setting goals, you will also raise your self-confidence, as you recognize your ability and competence in achieving the goals that you have set. The process of achieving goals and seeing this achievement gives you confidence that you will be able to achieve higher and more difficult goals. Goals are set on a number of different levels: First you decide what you want to do with your life and what large-scale goals you want to achieve. Second, you break these down into the smaller and smaller targets that you must hit so that you reach your lifetime goals. Finally, once you have your plan, you start working towards achieving it. Starting to Set Personal Goals This section explains how to set personal goals. It starts with your lifetime goals, and then works through a series of lower level plans culminating in a daily to-do list. By setting up this structure of plans you can break even the biggest life goal down into a number of small tasks that you need to do each day to reach the lifetime goals. Your Lifetime Goals The first step in setting personal goals is to consider what you want to achieve in your lifetime, as setting Lifetime goals gives you the overall perspective that shapes all other aspects of your decision making. How to Start to Achieve Your LifetimeGoals Once you have set your lifetime goals, set a 25 year plan of smaller goals that you should complete if you are to reach your lifetime plan. Then set a 5 year plan, 1 year plan, 6 month plan, and 1 month plan of progressively smaller goals that you should reach to achieve your lifetime goals. Each of these should be based on the previous plan. Finally set a daily to-do list of things that you should do today to work towards your lifetime goals. At an early stage these goals may be to read books and gather information on the achievement of your goals. This will help you to improve the quality and realism of your goal setting. Finally review your plans, and make sure that they fit the way in which you want to live your life.

Islam and Christianity :: Religion Religious Chirstian Islamic Essays

Islam and Christianity There are hundreds of religions in this world. Of them two are the most prominent. Islam and Christianity. It is averaged that there are 750 million people practicing Islam, and another 1 billion practicing Christianity. The start of Islam is actually derived form Christianity, history books indicates that one night in the year 610, the first of many revelations came to Muhammad from God by way of the angel Gabriel (In Christianity this is the same Angel which brings the news of Jesus' birth, Jesus of course is the founder of Christianity). The message Muhammad received told him that there was but one God (Identical to the inception of the Ten Commandments), not many gods, as most Arabs believed. This God was creator of the world (In Christianity, it's documented in Genesis Chapter 1 verse 1, In the beginning God created the heavens and the earth), and He would one day judge mankind (This is also true in Christianity: "The Lord will judge his people." Hebrews 10:30). Both of these re ligions share almost the same framework, but they also differ in many ways. The word Islam means "surrender" or "submission," submission to the will of Allah, the one God. Muslims are those who have submitted themselves. The basic creed of Islam is brief: There is no God but Allah, and Muhammad is the Prophet of Allah. Islam teaches that there is one God, the creator and sustainer of the universe. This God, Allah, is compassionate and just. Because He is compassionate, He calls all people to believe in Him and worship Him. Because He is also just, on the Last Day He will judge every person according to his deeds. On the Last Day, all the dead will be resurrected and either rewarded with heaven or punished with hell. In Christianity one of the Ten Commandments states that "I am the Lord you God.....you shall have no other gods before me", also identical to Islam God is considered the creator of the universe, and he is also just. On the last day, or judgment day, the same holds true as in Islam in the Christian beliefs, the dead will be resurrected and either rewarded with heaven or punished with hell. Mankind is regarded as the crown of creation, entrusted by God with management of the whole created order. In Christianity this was Adam, who had dominion over all the animals and beasts of the earth.

Negative Images of African Americans in the Media

Mass media is a powerful force in American pop culture. Images seen on billboards, television, magazines, and the big screen create lasting impressions. Sometimes these impressions have a negative impact. Mass media can be very detrimental to society if it is not criticized. Many groups of Americans are negatively affected by the images and content of mass media. African Americans are at the top of this list. Images of African Americans in television, music, and film are often less than stellar.Black men are often portrayed as drug pushers, pimps, thugs, and dead beat dads, while black women are portrayed as poor, lazy, and promiscuous. This needs to stop! That is a given! Question is, how are these negative images going to be stopped? Several steps should be taken in order to prevent these negative images in the media. The origins of these images need to be examined, and modern racism and prejudice need to be exposed. There may be some accuracy to the negative images of African Amer icans in the media, but that is no excuse.The media should focus more on uplifting people. African Americans have historically had a disadvantage when compared to their white counterparts. This should not be exploited for entertainment purposes. African Americans are often placed in roles that portray them as poorly educated. This dates all the way to minstrel shows! This is still a problem today! Americans are more comfortable laughing at blacks as appose to understanding blacks. The main problem with images of African Americans is that they are one dimensional.African Americans are diverse and come from a variety of backgrounds. If an African American is portrayed as a druggie or a convict, then there should be some reasoning behind this. People don't become drug addicts for the fun of it; they become drug addicts because they want to numb themselves from the pain and suffering of their everyday lives. Black men and women don't become criminals because they are horrible people. Th ey become criminals because they are taught that they have no other option!African Americans have to stand up for themselves and fight against the media. That is the only way things will change. While doing this, they may have to criticize other African Americans. This should be done with love. Black rappers, singers, and actors should be held with some responsibility. Black leaders like Oprah Winfrey and Bill Cosby have spoken out about this. Rappers, including Ludacris and 50 Cent have been criticized for their lyrics.It is unclear if they are rapping about their experiences in order to expose their struggles, or if they are exploiting the black struggle with their lyrics. Violence, sexuality, and the lack of education are unfortunately a part of African American society. The media should show this. Rappers and singers should perform songs about this. Black actors should play roles that depict this. Black actors, singers, and rappers should not exploit these disadvantages. Instead they should use their craft to create solutions to these problems. Drugs and violence should not be glamorized!