Margin Of Error Binomial
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Margin Of Error Formula
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; margin of error calculator 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 How to calculate margin of error for a binomial quality margin of error definition control experiment where only successes are observed (including FPC)? up vote 4 down vote favorite 1 Wikipedia's Margin of Error entry says that a random sample of size 400 will give a margin of error, at a 95% confidence level, of 0.98/20 or 0.049 - just under 5% given an infinite population size. This means that if I polled 400 US citizens (randomly selected) and asked them "Obama or Romney?", the resulting proportion would be accurate with a 95% confidence
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level, to a margin of error below 5%. However, can I use this same calculation in testing that a software program will be able to deal with roughly all inputs? For example: I have an infinite population of users, I need to be sure (95% confident, given 5% error) that my software will be able to come up with a nickname for all of them based on their name and a simple algorithm. If I randomly select 400 users, and the nickname algorithm works perfectly for all 400 users, can I assume (with 95% confidence, given 5% error) that my algorithm holds for the entire population? Is this the incorrect way to calculate margin of error for this type of problem? statistical-significance confidence-interval measurement-error quality-control share|improve this question edited May 5 '12 at 5:44 Peter Ellis 13k12266 asked May 5 '12 at 3:21 Sam Porch 14515 First, the margin of error given in the wiki article was based on a binary outcome with a 50/50 chance of success, which would have the maximal margin of error - so the margin of error is at most 0.049 - this same logic applies for any binary outcome, not just poll results. Second, are you asking that if you sampled 400 people and the algorithm worked for all 400 people, can you conclude that the algorithm would work for 100% of the population? That seems to be a different quest
Unit Summary Introduction to Inferences Estimation Properties of 'Good' Estimators General Format and Interpretation of a Confidence Interval Inferences on the Binomial Parameter p Confidence Interval for Binomial Parameter, p Assumptions to be Checked When Using the Z-interval for Estimating Binomial calculate confidence interval Parameter The Derivation of the Confidence Interval When Conditions are NOT satisfied More on the confidence interval formula Interpretation of a Confidence Interval Reading AssignmentAn Introduction to Statistical Methods and Data Analysis, (see Course Schedule). Introduction to Inferences The
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real power of statistics comes from applying the concepts of probability to situations where you have data. The results, called statistical inference, give you probability statements about the population of interest based on that set of data. There http://stats.stackexchange.com/questions/27817/how-to-calculate-margin-of-error-for-a-binomial-quality-control-experiment-where are two types of statistical inferences: 1. Estimation Use information from the sample to estimate (or predict) the parameter of interest. Using the result of a poll about the president's current approval rating to estimate (or predict) his or her true current approval rating nationwide. 2. Statistical Test Use information from the sample to determine whether a certain statement about the parameter of interest is true. Think about the following, then click on the icon https://onlinecourses.science.psu.edu/stat500/node/30 to the left to display an answer. Give an example about statistical test: The democrats claim that President Barack Obama's current approval rating is more than 85%. We want to determine whether that statement is supported by the poll data. Estimation We begin our discussion on inference with estimation. Two common estimation methods are point estimates (e.g. sample proportion or sample mean), and confidence intervals. The latter is a new concept which be the focus of this lesson. Such intervals are built around point estimates which is why understanding point estimates is important to understanding confidence intervals. Properties of 'Good' Estimators In determining what makes a good estimator, there are two key features. 1. The center of the sampling distribution for the estimate is the same as that of the population. When this property is true, the estimate is said to be unbiased. The most often-used measure of the center is the mean. 2. Smallest standard error when compared to other estimators. For example, in the normal distribution the mean and median are essentially the same. However, the standard error of the median is about 1.25 times that of the standard error of the mean. We know the standar error of the mean is \(\sigma / \sqrt{N}\). Therefore in a normal distribution, the SE(median) is about 1.25 times \(\sigma / \sqrt{N}\)
units and are then classified according to two levels ofa categorical variable, a binomial sampling emerges. Consider the High-risk Drinking Example where we have high-risk drinkers versus non-high-risk drinkers. https://onlinecourses.science.psu.edu/stat504/node/58 In this study there was a fixed number of trials (e.g., fixed number of students surveyed, n=1315) where the researcher counted the number of "successes" and the number of "failures" that occur. We can let X be the number of "successes" that is the number of students who are the high-risk drinkers. We can use the binomial probability distribution (i.e., binomial model), margin of to describe this particular variable. Binomial distributions arecharacterized by two parameters: n, which is fixed - this could be the number of trials or the total sample size if we think in terms of sampling, and π, which usually denotes a probability of "success". In our example this would be the probability that someone is a high-risk drinker in the population of margin of error Penn State students. Please note that some textbooks will use π to denote the population parameter and p to denote the sample estimate, whereas some may use p for the population parameters as well. We may do both; don't be confused by this, just make sure to read carefully the specification. Once you know n and π, the probability of success, you know the mean and variance of the binomial distribution, and you know everything about that binomial distribution. Below are the probability density function, mean and variance of the binomial variable. \(f(x)=\dfrac{n!}{x!(n-x)!}π^x(1-π)^{n-x}\qquad \text{for }x=0,1,2,\ldots,n\) Mean E (X) = nπ Variance Var (X) = nπ (1 - π) Binomial Model (distribution) Assumptions Fixed n: the total number of trials/events, (or total sample size) is fixed. Each event has two possible outcomes, referred to as "successes" or "failures", (e.g., each student can be either a heavy drinker or a non-heavy drinker; heavy drinker being a success here). Independent and Identical Events/Trials: Identical trials means that probability of success is the same for each trial. Independent means that the outcome of one trial does not affe
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