# Standard Error For Sample Proportion

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## Standard Error Of Proportion Formula

review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary sample proportion formula AP practice exam Problems and solutions Formulas Notation Share with Friends What is the Standard Error? The standard error is

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an estimate of the standard deviation of a statistic. This lesson shows how to compute the standard error, based on sample data. The standard error is important because it is used to compute other measures, like standard deviation of sample proportion confidence intervals and margins of error. Notation The following notation is helpful, when we talk about the standard deviation and the standard error. Population parameter Sample statistic N: Number of observations in the population n: Number of observations in the sample Ni: Number of observations in population i ni: Number of observations in sample i P: Proportion of successes in population p: Proportion of successes in sample Pi: Proportion of successes sample proportion calculator in population i pi: Proportion of successes in sample i μ: Population mean x: Sample estimate of population mean μi: Mean of population i xi: Sample estimate of μi σ: Population standard deviation s: Sample estimate of σ σp: Standard deviation of p SEp: Standard error of p σx: Standard deviation of x SEx: Standard error of x Standard Deviation of Sample Estimates Statisticians use sample statistics to estimate population parameters. Naturally, the value of a statistic may vary from one sample to the next. The variability of a statistic is measured by its standard deviation. The table below shows formulas for computing the standard deviation of statistics from simple random samples. These formulas are valid when the population size is much larger (at least 20 times larger) than the sample size. Statistic Standard Deviation Sample mean, x σx = σ / sqrt( n ) Sample proportion, p σp = sqrt [ P(1 - P) / n ] Difference between means, x1 - x2 σx1-x2 = sqrt [ σ21 / n1 + σ22 / n2 ] Difference between proportions, p1 - p2 σp1-p2 = sqrt [ P1(1-P1) / n1 + P2(1-P2) / n2 ] Note: In order to compute the standard deviation of a sample statistic, you must know the va

test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books

## Population Proportion

AP calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book standard error of p hat reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends What is the Standard Error? The

## Probability Of Sample Proportion Calculator

standard error is an estimate of the standard deviation of a statistic. This lesson shows how to compute the standard error, based on sample data. The standard error is important because it is used to http://stattrek.com/estimation/standard-error.aspx?Tutorial=AP compute other measures, like confidence intervals and margins of error. Notation The following notation is helpful, when we talk about the standard deviation and the standard error. Population parameter Sample statistic N: Number of observations in the population n: Number of observations in the sample Ni: Number of observations in population i ni: Number of observations in sample i P: Proportion of successes in population p: Proportion of successes http://stattrek.com/estimation/standard-error.aspx?Tutorial=AP in sample Pi: Proportion of successes in population i pi: Proportion of successes in sample i μ: Population mean x: Sample estimate of population mean μi: Mean of population i xi: Sample estimate of μi σ: Population standard deviation s: Sample estimate of σ σp: Standard deviation of p SEp: Standard error of p σx: Standard deviation of x SEx: Standard error of x Standard Deviation of Sample Estimates Statisticians use sample statistics to estimate population parameters. Naturally, the value of a statistic may vary from one sample to the next. The variability of a statistic is measured by its standard deviation. The table below shows formulas for computing the standard deviation of statistics from simple random samples. These formulas are valid when the population size is much larger (at least 20 times larger) than the sample size. Statistic Standard Deviation Sample mean, x σx = σ / sqrt( n ) Sample proportion, p σp = sqrt [ P(1 - P) / n ] Difference between means, x1 - x2 σx1-x2 = sqrt [ σ21 / n1 + σ22 / n2 ] Difference between proportions, p1 - p2 σp1-p2 = sqrt [ P1(1-P1) / n1 + P2(1-P2) / n2 ] Note: In order to compute

population parameters like p are typically unknown and estimated from the data. Consider estimating the proportion p of the current WMU graduating class who plan to go to graduate school. Suppose http://www.stat.wmich.edu/s216/book/node70.html we take a sample of 40 graduating students, and suppose that 6 out http://web9.uits.uconn.edu/lundquis/stats/stderr.html of the 40 are planning to go to graduate school. Then our estimate is of the graduating class plan to go to graduate school. Now is based on a sample, and unless we got really lucky, chances are the .15 estimate missed. By how much? On the average, a random variable misses the mean by sample proportion one SD. From the previous section, the SD of equals . It follows that the expected size of the miss is . This last term is called the standard error of estimation of the sample proportion, or simply standard error (SE) of the proportion . However, since we do not know p, we cannot calculate this SE. In a situation like this, statisticians replace p with when calculating the standard error of SE. The resulting quantity is called the estimated standard error of the sample proportion . In practice, however, the word ``estimated'' is dropped and the estimated SE is simply called the SE . Exercise 4. a. If 6 out of 40 students plan to go to graduate school, the proportion of all students who plan to go to graduate school is estimated as ________. The standard error of this estimate is ________. b. If 54 out of 360 students plan to go to graduate school, the proportion of all students who plan to go to graduate school is estimated as ________. The standard error of this estimate is ________. Exercise 4 shows the effect of of increasing the sample size on the SE of the sample proportion. Multiplying the sample size by a factor of 9 (from 40 to 360) makes the SE decrease by a factor of 3. In the formula for the SE of , the sample size appears (i) in the denominator, and (ii) inside a squareroot. Therefore, multiplying the sample size by a certain factor divides the SE of by the squareroot of that factor Next: Exercises Up: Sampling Distribution of the Previous: The Sampling Distribution of 2003-09-08

NOT the scatter of particular scores; it's the scatter of the MEANS of all the samples (of a given size "n") you could take of those scores. A proportion is just the mean of a discrete variable (yes-or-no, success-or-failure, 0-or-1, etc.) -- usually one with only two categories, but the math can be extended if you want. So standard error of the mean and standard error of a proportion are the same thing but for different kinds of variables, and with different formulas involved. Let me assume you know what a sample's standard deviation is and how to calculate it. In words instead of symbols (cause I can't type them), the variance is "(sum of [(x - mean)squared]) / n" (or if you're estimating the population s.d., you divide by (n - 1) instead, as you probably know -- let's forget that for now). And the standard deviation is the square root of that. Standard error of the mean says, take a random sample of size n -- say you take a measure on 10 people. Then take another random sample of size n (ten more people). Then another. Keep doing it. For every sample you take you can find the mean of those ten scores. Every sample mean will be a little different, but they'll all be dancing around the true mean in the population. Like, you might measure the average pregancy duration for ten women and find it's 38.5 weeks, and in another group of ten it might be 39.2 weeks, and in another maybe it's 40.1 weeks. If you keep taking those samples forever, you know the mean of ALL the sample means is going to be 39 weeks, because that's the average human gestation period. (Isn't it?) So the mean of all the sample means is equal to the population mean. You could also find the standard deviation of all those sample means, but that's NOT equal to the population standard deviation. Cause think about it, the mean of a sample tends to be closer to the population mean than just one particular point would be, otherwise we'd just ask one person our questions instead of getting an average from a bunch of people to represent the population. So this standard deviation of all the sample means will b

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Sample Proportion Standard Error p repeatedly randomly drawn from a population and the proportion of successes in each sample is recorded widehat p the distribution sample proportion formula of the sample proportions i e the sampling distirbution can be standard error of proportion formula approximated by a normal distribution given that both n times p geq and n times standard error of p hat -p geq This is known as theRule of Sample Proportions Note that some textbooks use a minimum of instead of The mean of the p Population Proportion p distribution of sample proportions is equal to the

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Sample Proportion Error p repeatedly randomly drawn from a population and the proportion of successes in each sample is recorded widehat p the distribution of the sample proportions i e the sampling distirbution can be approximated by a normal sample proportion formula distribution given that both n times p geq and n times -p p Standard Error Of Proportion Formula p geq This is known as theRule of Sample Proportions Note that some textbooks use a minimum of p Sampling Distribution Of P Hat Calculator p instead of The mean of the distribution of sample proportions is equal to the

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Sample Standard Error For Proportion p test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations permutations Factorial Event counter p Standard Error Of Proportion Formula p Wizard Graphing Scientific Financial Calculator books AP calculator review Statistics AP study guides sample proportion formula Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share standard error of p hat with Friends What is the Standard Error The standard error is an estimate of the standard deviation

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Standard Error Binomial Distribution Proportion p repeatedly randomly drawn from a population and the proportion of successes in each sample is recorded widehat p the distribution of the sample proportions i e the sampling distirbution can be approximated p Standard Deviation Of Sample Proportion p by a normal distribution given that both n times p geq and determine the mean of the sampling distribution of p hat n times -p geq This is known as theRule of Sample Proportions Note that some textbooks use a p Sample Proportion Formula p minimum of instead of The mean of the distribution of

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Standard Error Of A Sample Proportion p test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes standard error of proportion formula rule Combinations permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP p Sample Proportion Formula p calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice standard error of p hat exam Problems and solutions Formulas Notation Share with Friends What is the Standard Error The standard error is an estimate of the standard

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Standard Error For The Sampling Distribution Of Proportion p repeatedly randomly drawn from a population and the proportion of successes in each sample is p Standard Deviation Of Sample Proportion p recorded widehat p the distribution of the sample proportions i e the sampling sample proportion formula distirbution can be approximated by a normal distribution given that both n times p sample proportion definition geq and n times -p geq This is known as theRule of Sample Proportions Note that some textbooks use a minimum of p Sample Proportion Calculator p instead of The mean of the distribution of sample

standard error for sample proportions

Standard Error For Sample Proportions p repeatedly randomly drawn from a population and the proportion of successes in each sample is recorded widehat p the distribution of the sample proportions i e the sampling distirbution can be approximated by a standard error of proportion formula normal distribution given that both n times p geq and n times sample proportion formula -p geq This is known as theRule of Sample Proportions Note that some textbooks use a minimum of standard error of p hat instead of The mean of the distribution of sample proportions is equal to the population proportion p

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Standard Error Of Sampling Distribution Of Sample Proportion p repeatedly randomly drawn from a population and the proportion of successes in each sample is recorded widehat p the distribution of the sample proportions i e the sampling standard deviation of sample proportion distirbution can be approximated by a normal distribution given that both n p Sample Proportion Formula p times p geq and n times -p geq This is known as theRule of Sample Proportions sample proportion definition Note that some textbooks use a minimum of instead of The mean of the distribution of sample proportions is equal to the

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Standard Error Of Sample Proportion Formula p repeatedly randomly drawn from a population and the proportion of successes in each sample is recorded widehat p the distribution of the sample proportions i e the sampling distirbution can be approximated by a normal distribution given that sampling distribution of p hat calculator both n times p geq and n times -p geq This p Standard Error Of Proportion Definition p is known as theRule of Sample Proportions Note that some textbooks use a minimum of instead of The mean of population proportion the distribution of sample proportions is equal to the

standard error of sampling proportion

Standard Error Of Sampling Proportion p repeatedly randomly drawn from a population and the proportion of successes in each sample is recorded widehat p the distribution of the sample proportions i e standard error of proportion formula the sampling distirbution can be approximated by a normal distribution given p Sample Proportion Formula p that both n times p geq and n times -p geq This is known as standard error of p hat theRule of Sample Proportions Note that some textbooks use a minimum of instead of The mean of the distribution of sample proportions is equal to the population

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Standard Error Of Proportion Example p repeatedly randomly drawn from a population and the proportion of successes in each sample sample proportion formula is recorded widehat p the distribution of the sample proportions i e the p Standard Error Of Proportion Formula p sampling distirbution can be approximated by a normal distribution given that both n times standard error of p hat p geq and n times -p geq This is known as theRule of Sample Proportions Note that some textbooks use a minimum p Sample Proportion Calculator p of instead of The mean of the distribution of sample proportions

standard error of the sampling distribution of a sample proportion

Standard Error Of The Sampling Distribution Of A Sample Proportion p repeatedly randomly drawn from a population and the proportion of successes in each sample is recorded widehat p the distribution of the sample proportions i e the sampling p Standard Deviation Of Sample Proportion p distirbution can be approximated by a normal distribution given that both n sample proportion formula times p geq and n times -p geq This is known as theRule of Sample Proportions sample proportion definition Note that some textbooks use a minimum of instead of The mean of the distribution of sample proportions is equal

standard error of the sample proportion

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standard error of sample proportion

Standard Error Of Sample Proportion p repeatedly randomly drawn from a population and the proportion of successes in each p Standard Error Of Proportion Formula p sample is recorded widehat p the distribution of the sample proportions sample proportion formula i e the sampling distirbution can be approximated by a normal distribution given that both n p Sampling Distribution Of P Hat Calculator p times p geq and n times -p geq This is known as theRule of Sample Proportions Note that some textbooks use standard error of proportion definition a minimum of instead of The mean of the distribution

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What Is The Standard Error Of The Sample Proportion p repeatedly randomly drawn from a population and the proportion of successes in each sample standard error of proportion formula is recorded widehat p the distribution of the sample proportions i e p Sample Proportion Formula p the sampling distirbution can be approximated by a normal distribution given that both n p Standard Error Of P Hat p times p geq and n times -p geq This is known as theRule of Sample Proportions Note that some textbooks use a p Sample Proportion Calculator p minimum of instead of The mean