Margin Of Error Statistics Definition
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Margin Of Error Example
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Margin Of Error Excel
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Margin Of Error Confidence Interval Calculator
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Acceptable Margin Of Error
Formulas Notation Share with Friends Margin of Error In a confidence interval, the range of values above and below the sample statistic margin of error synonym is called the margin of error. For example, suppose we wanted to know the percentage of adults that exercise daily. We could devise a sample design to ensure that our sample estimate will not differ from the true http://stattrek.com/statistics/dictionary.aspx?definition=margin%20of%20error population value by more than, say, 5 percent (the margin of error) 90 percent of the time (the confidence level). How to Compute the Margin of Error The margin of error can be defined by either of the following equations. Margin of error = Critical value x Standard deviation of the statistic Margin of error = Critical value x Standard error of the statistic If you know the standard deviation of the statistic, use the first equation http://stattrek.com/estimation/margin-of-error.aspx to compute the margin of error. Otherwise, use the second equation. Previously, we described how to compute the standard deviation and standard error. How to Find the Critical Value The critical value is a factor used to compute the margin of error. This section describes how to find the critical value, when the sampling distribution of the statistic is normal or nearly normal. The central limit theorem states that the sampling distribution of a statistic will be nearly normal, if the sample size is large enough. As a rough guide, many statisticians say that a sample size of 30 is large enough when the population distribution is bell-shaped. But if the original population is badly skewed, has multiple peaks, and/or has outliers, researchers like the sample size to be even larger. When the sampling distribution is nearly normal, the critical value can be expressed as a t score or as a z score. When the sample size is smaller, the critical value should only be expressed as a t statistic. To find the critical value, follow these steps. Compute alpha (α): α = 1 - (confidence level / 100) Find the critical probability (p*): p* = 1 - α/2 To express the critical value as a z score, find the z score having a cumulative probability equal to the critical probability (p*). To express the critical val
WorkSocial MediaSoftwareProgrammingWeb Design & DevelopmentBusinessCareersComputers Online Courses B2B Solutions Shop for Books San Francisco, CA Brr, it´s cold outside Search Submit Learn more with dummies Enter your email to join our http://www.dummies.com/education/math/statistics/how-to-interpret-the-margin-of-error-in-statistics/ mailing list for FREE content right to your inbox. Easy! Your https://www.math.lsu.edu/~madden/M1100/week12goals.html email Submit RELATED ARTICLES How to Interpret the Margin of Error in Statistics Statistics Essentials For Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for Dummies, 3rd Edition Statistics II for Dummies Load more EducationMathStatisticsHow to Interpret the Margin of Error in Statistics margin of How to Interpret the Margin of Error in Statistics Related Book Statistics For Dummies, 2nd Edition By Deborah J. Rumsey You've probably heard or seen results like this: "This statistical survey had a margin of error of plus or minus 3 percentage points." What does this mean? Most surveys are based on information collected margin of error from a sample of individuals, not the entire population (as a census would be). A certain amount of error is bound to occur -- not in the sense of calculation error (although there may be some of that, too) but in the sense of sampling error, which is the error that occurs simply because the researchers aren't asking everyone. The margin of error is supposed to measure the maximum amount by which the sample results are expected to differ from those of the actual population. Because the results of most survey questions can be reported in terms of percentages, the margin of error most often appears as a percentage, as well. How do you interpret a margin of error? Suppose you know that 51% of people sampled say that they plan to vote for Ms. Calculation in the upcoming election. Now, projecting these results to the whole voting population, you would have to add and subtract the margin of erro
information about a sample. One very vivid application is currently in the news: polls attempt to determine the way a population will vote by examining the voting patterns within a sample. The idea of generalizing from a sample to a population is not hard to grasp in a loose and informal way, since we do this all the time. After a few vivits to a store, for example, we notice that the produce is not fresh. So we assume that the store generally has bad produce. This is a generalization from a sample (the vegetables we have examined) to a population (all the vegetables the store sells). But there are many ways to go wrong or to misunderstand the meaning of the data obtained from a sample. How do statisticians conceive of the process of drawing a conclusion about a population from a sample? How do they describe the information that is earned from a sample and quantify how informative it is? How much data do we need in order to reach a conclusion that is secure enough to print in a newpaper? Or on which to base medical decisions? These are the questions that we will address this week. The simplest example arises when one uses a sample to infer a population proportion. We can give a fairly complete account of the mathematical ideas that are used in this situation, based on the binomial distribution. My aim is to enable you to understand the internal mathematical "clockwork" of how the statistical theory works. Assignment: Read: Chapter 8, sections 1, 2 and 3. For the time being, do not worry about pasages that contain references to the "normal distribution" of the "Central Limit Theorem" . (Last sentence on page 328, last paragraph on p. 330, first paragraph on p. 332.) Also, do not worry for the time being about the examples in section 3.2. Review questions: pages 335 and 351. Problems: p. 336: 1--8, 11, 12, 13, 14. p. 351: 1--12, 13, 16, 21, 22. In-class: p. 337: 20. EXTRA CREDIT: Find an article in the New York Times that describes a poll. The New York Times provides readers with a very careful explanantion of margin of error and level of confidence; find their explanation either in an issue of the paper or on the paper's web site, and report on it. Compare with the information provided by other papers. Vocabulary: Parameters and statistics: population mean: the average value of a variable, where the reference class is a population of interest. E.g. the average high of all persons owning a Louisiana driver's license. This is a parameter. sample mean: the average value of a variable, where the reference class is a sample from the population. This is a statistic. It is also a variable that has as its refernce class all possibl