# Standard Error For Sample Proportions

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 \(n \times p \geq 10\) and \(n \times sample proportion formula (1-p) \geq 10\). This is known as theRule of Sample Proportions. Note that some textbooks use a minimum of standard error of p hat 15 instead of 10.The mean of the distribution of sample proportions is equal to the population proportion (\(p\)). The standard deviation of the distribution of sample proportions is symbolized by \(SE(\widehat{p})\) and

## Sample Proportion Calculator

equals \( \sqrt{\frac {p(1-p)}{n}}\); this is known as thestandard error of \(\widehat{p}\). The symbol \(\sigma _{\widehat p}\) is also used to signify the standard deviation of the distirbution of sample proportions. Standard Error of the Sample Proportion\[ SE(\widehat{p})= \sqrt{\frac {p(1-p)}{n}}\]If \(p\) is unknown, estimate \(p\) using \(\widehat{p}\)The box below summarizes the rule of sample proportions: Characteristics of the Distribution of Sample ProportionsGiven both \(n \times probability of sample proportion calculator p \geq 10\) and \(n \times (1-p) \geq 10\), the distribution of sample proportions will be approximately normally distributed with a mean of \(\mu_{\widehat{p}}\) and standard deviation of \(SE(\widehat{p})\)Mean \(\mu_{\widehat{p}}=p\)Standard Deviation ("Standard Error")\(SE(\widehat{p})= \sqrt{\frac {p(1-p)}{n}}\) 6.2.1 - Marijuana Example 6.2.2 - Video: Pennsylvania Residency Example 6.2.3 - Military Example ‹ 6.1.2 - Video: Two-Tailed Example, StatKey up 6.2.1 - Marijuana Example › Printer-friendly version Navigation Start Here! Welcome to STAT 200! Search Course Materials Faculty login (PSU Access Account) Lessons Lesson 0: Statistics: The “Big Picture” Lesson 1: Gathering Data Lesson 2: Turning Data Into Information Lesson 3: Probability - 1 Variable Lesson 4: Probability - 2 Variables Lesson 5: Probability Distributions Lesson 6: Sampling Distributions6.1 - Simulation of a Sampling Distribution of a Proportion (Exact Method) 6.2 - Rule of Sample Proportions (Normal Approximation Method)6.2.1 - Marijuana Example 6.2.2 - Video: Pennsylvania Residency Example 6.2.3 - Military Example 6.3 - Simulating a Sampling Distribution of a Sample Mean 6.4 - Central Limit Theorem 6.5 - Probability of a Sample Mean Applications 6.6 - Introduction to the t Distribution 6.7 - Summary Lesson 7: Confidence Intervals Lesson 8: Hypothesis Testing Lesson 9: C

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 sample proportion definition rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books

## Sample Proportion Symbol

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## Standard Error Of Proportion Definition

exam Problems and solutions Formulas Notation Share with Friends What is the Standard Error? The standard error is an estimate of the standard deviation of a statistic. This https://onlinecourses.science.psu.edu/stat200/node/43 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 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 http://stattrek.com/estimation/standard-error.aspx?Tutorial=AP 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 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. Sta

0 otherwise. The standard deviation of any variable involves the sample proportion expression . Let's suppose there are m 1s (and n-m 0s) among the n subjects. Then, and is equal to (1-m/n) for m observations and 0-m/n standard error of for (n-m) observations. When these results are combined, the final result is and the sample variance (square of the SD) of the 0/1 observations is The sample proportion is the mean of n of these observations, so the standard error of the proportion is calculated like the standard error of the mean, that is, the SD of one of them divided by the square root of the sample size or Copyright © 1998 Gerard E. Dallal

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 we take a sample of 40 graduating students, and suppose that 6 out 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 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 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

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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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Sampling Distribution Of Proportions Standard 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 determine the mean of the sampling distribution of p hat distribution given that both n times p geq and n times -p geq standard deviation of sample proportion This is known as theRule of Sample Proportions Note that some textbooks use a minimum of instead of sample proportion formula The mean of the distribution of sample proportions is

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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

standard error for sample proportion

Standard Error For 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 rule Combinations permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP calculator p Standard Error Of Proportion Formula p 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 p Sampling Distribution Of P Hat Calculator p an estimate 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 of sampling distribution of sample proportion

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

Standard Error Of The 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 standard deviation sample proportion sample proportions i e the sampling distirbution can be approximated by a standard error of the sample proportion formula normal distribution given that both n times p geq and n times -p geq p Standard Error Of The Sample Proportion Calculator p This is known as theRule of Sample Proportions Note that some textbooks use a minimum of instead of The mean of the distribution of sample

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Standard Error Sampling Distribution Sample Proportion p repeatedly randomly drawn from a population and the proportion of successes in each determine the mean of the sampling distribution of p hat sample is recorded widehat p the distribution of the sample proportions standard deviation of sample proportion i e the sampling 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 Note that some textbooks use p Sample Proportion Definition p a minimum of instead of The mean of the

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Standard Error Of The Sampling Distribution Of The 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 p Determine The Mean Of The Sampling Distribution Of P Hat p proportions i e the sampling distirbution can be approximated by a normal standard deviation of sample proportion distribution given that both n times p geq and n times -p geq This p Sample Proportion Formula p is known as theRule of Sample Proportions Note that some textbooks use a minimum of instead of The

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Standard Error 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 rule standard error of proportion formula Combinations permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP calculator p Sample Proportion Formula p review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam p Sampling Distribution Of P Hat Calculator p Problems and solutions Formulas Notation Share with Friends What is the Standard Error The standard error is an estimate of the

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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