Maximum Statistical Error
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the sample does not include all members of the population, statistics on the sample, such as means and quantiles, generally differ from the characteristics of the entire population, which are known as parameters. For
Margin Of Error Formula
example, if one measures the height of a thousand individuals from a country of margin of error calculator one million, the average height of the thousand is typically not the same as the average height of all one million
Margin Of Error Definition
people in the country. Since sampling is typically done to determine the characteristics of a whole population, the difference between the sample and population values is considered a sampling error.[1] Exact measurement of sampling margin of error excel error is generally not feasible since the true population values are unknown; however, sampling error can often be estimated by probabilistic modeling of the sample. Contents 1 Description 1.1 Random sampling 1.2 Bias problems 1.3 Non-sampling error 2 See also 3 Citations 4 References 5 External links Description[edit] Random sampling[edit] Main article: Random sampling In statistics, sampling error is the error caused by observing a sample instead of margin of error in polls the whole population.[1] The sampling error is the difference between a sample statistic used to estimate a population parameter and the actual but unknown value of the parameter (Burns & Grove, 2009). An estimate of a quantity of interest, such as an average or percentage, will generally be subject to sample-to-sample variation.[1] These variations in the possible sample values of a statistic can theoretically be expressed as sampling errors, although in practice the exact sampling error is typically unknown. Sampling error also refers more broadly to this phenomenon of random sampling variation. Random sampling, and its derived terms such as sampling error, imply specific procedures for gathering and analyzing data that are rigorously applied as a method for arriving at results considered representative of a given population as a whole. Despite a common misunderstanding, "random" does not mean the same thing as "chance" as this idea is often used in describing situations of uncertainty, nor is it the same as projections based on an assessed probability or frequency. Sampling always refers to a procedure of gathering data from a small aggregation of individuals that is purportedly representative of a larger grouping which must in principle be capable of being measured as a totality. Ra
was out of range. Must be non-negative and less than the size of the collection. Parameter name: index Enter YOUR Problem About Mobile Examples Glossary Affiliates Careers Press Privacy
Acceptable Margin Of Error
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here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring http://math.stackexchange.com/questions/328031/statistics-maximum-error-of-05-with-90-confidence developers or posting ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Statistics: Maximum error of .05 with 90% confidence up margin of vote 0 down vote favorite 1 What size sample is required to have a maximum error of .05 with 90% confidence for the proportion of students who will vote? Please help. statistics share|cite|improve this question edited Mar 12 '13 at 2:08 azimut 14.4k94085 asked Mar 12 '13 at 1:58 Shaily 707 1 Can you show some of your own work and change the title to something more descriptive? –Tyler Mar 12 '13 at 2:03 By margin of error .05, do you mean .05 students or .05 the measured amount? –Joe Z. Mar 12 '13 at 12:41 add a comment| 1 Answer 1 active oldest votes up vote 0 down vote accepted Let $p$ be the probability that a student votes, and let $X$ be the number of students in the group of $n$ who vote. Then $X$ has binomial distribution, with mean $np$, and variance $np(1-p)$. Let $Y=\frac{X}{n}$. Then $Y$ is the sample proportion of the students who vote. It is standard that $Y$ has mean $p$ and variance $\frac{p(1-p)}{n}$. We don't know $p$, so let's be pessimistic. The largest value of $p(1-p)$ occurs when $p=\frac{1}{2}$. This value is $\frac{1}{4}$. (Actually, $p(1-p)$ remains remarkably close to $\frac{1}{4}$ even for $p$ not very close to $\frac{1}{2}$.) So let us assume that $Y$ has variance $\frac{1}{4n}$, and therefore standard deviation $\frac{1}{2\sqrt{n}}$. The sample size will be fairly large, so $Y$ can be approximated by a normal distribution with mean $p$ and standard deviation $\frac{1}{2\sqrt{n}}$. We want, with probability $0.90$, to have $$|Y-p|\lt 0.05.$$ Note that $0.05$ is $(0.05)(2\sqrt{n})$ "standard deviation units." Look at the place in the table of the standard normal that has $0.05$ in the right tail, that is, the place $z$ such that $\Pr(Z\le z)=0.95$. We want $0.05$ in the right tail, because if we want the same amount in the right and left tail, that amount should