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# Standard Error Of The Sampling Distribution Of The Sample Proportion

repeatedly randomly drawn from a population, and the proportion of successes in each sample is recorded ($$\widehat{p}$$),the distribution of the sample

## Determine The Mean Of The Sampling Distribution Of P Hat

proportions (i.e., the sampling distirbution) can be approximated by a normal standard deviation of sample proportion distribution given that both $$n \times p \geq 10$$ and $$n \times (1-p) \geq 10$$. This

## Sample Proportion Formula

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

taken, the distribution of $$\hat{p}$$ is said to approximate a normal curve distribution. Alternatively, this can be assumed if BOTH n × p and n × (1 - p) are at least 10. [SPECIAL NOTE: Some textbooks use 15

## P Hat Calculator

instead of 10 believing that 10 is to liberal. We will use 10 for our p hat symbol discussions.] Using this, we can estimate the true population proportion, p, by $$\hat{p}$$ and the true standard deviation of p by

## P Hat Formula

$$s.e.(\hat{p})=\sqrt{\frac {p(1-p)}{n}}$$, where s.e.( $$\hat{p}$$) is interpreted as the standard error of $$\hat{p}$$. Probabilities about the number X of successes in a binomial situation are the same as probabilities about corresponding proportions. In general, if np https://onlinecourses.science.psu.edu/stat200/node/43 ≥ 10 and n(1- p) ≥ 10, the sampling distribution of$$\hat{p}$$ is about normal with mean of p and standard error $$s.e.(\hat{p})=\sqrt{\frac {p(1-p)}{n}}$$. Example. Suppose the proportion of all college students who have used marijuana in the past 6 months is p = .40. For a class of size N = 200, representative of all college students on use of marijuana, what is the chance that the proportion of students who https://onlinecourses.science.psu.edu/stat800/node/35 have used mj in the past 6 months is less than .32 (or 32%)? NOTE: This would imply that 32% of the sample students said "yes" to having used marijuana, or 64 of the 200 said "yes". This means the sample proportion $$\hat{p}$$ is 64/200 or 32%Solution. The mean of the sample proportion$$\hat{p}$$ is p and the standard error of$$\hat{p}$$ is $$s.e.(\hat{p})=\sqrt{\frac {p(1-p)}{n}}$$. For this marijuana example, we are given that p = .4. We then determine $$s.e.(\hat{p})=\sqrt{\frac {p(1-p)}{n}}=\sqrt{\frac{0.4(1-0.4)}{200}}=0.0346$$. So, the sample proportion$$\hat{p}$$ is about normal with mean p = .40 and SE($$\hat{p}$$) = 0.0346.The z-score for .32 is z = (.32 - .40) / 0.0346 = -2.31. Then using Standard Normal Table Prob($$\hat{p}$$ < .32) = Prob(Z <. -2.31) = 0.0104. Question to ponder: If you observed a sample proportion of .32 would you believe a claim that 40% of college students used mj in the past 6 months? Or would you think the proportion is less than .40? ‹ 4: Sampling Distributions up 4.2 - Sampling Distribution of the Sample Mean, x-bar › Printer-friendly version Navigation Start Here! Welcome to STAT 800! Search Course Materials Faculty login (PSU Access Account) Lessons 1: Turning Data Into Information 2: Gathering Data 3: Probability Distributions 4: Sampling Distributions4.1 - Sampling Distributions for Sample P

WorkSocial MediaSoftwareProgrammingWeb Design & DevelopmentBusinessCareersComputers Online Courses B2B Solutions Shop for Books San Francisco, CA Brr, it´s cold outside Search Submit RELATED ARTICLES How to Find the Sampling Distribution of a Sample Proportion Statistics Essentials For Dummies Statistics For Dummies, 2nd Edition http://www.dummies.com/education/math/statistics/how-to-find-the-sampling-distribution-of-a-sample-proportion/ SPSS Statistics for Dummies, 3rd Edition Statistics II for Dummies Load more http://stattrek.com/sampling/sampling-distribution.aspx EducationMathStatisticsHow to Find the Sampling Distribution of a Sample Proportion How to Find the Sampling Distribution of a Sample Proportion Related Book Statistics For Dummies, 2nd Edition By Deborah J. Rumsey If you use a large enough statistical sample size, you can apply the Central Limit Theorem (CLT) to a sample proportion sample proportion for categorical data to find its sampling distribution. The population proportion, p, is the proportion of individuals in the population who have a certain characteristic of interest (for example, the proportion of all Americans who are registered voters, or the proportion of all teenagers who own cellphones). The sample proportion, denoted (pronounced p-hat), is the proportion of individuals in the sample who have that particular of the sampling characteristic; in other words, the number of individuals in the sample who have that characteristic of interest divided by the total sample size (n). For example, if you take a sample of 100 teens and find 60 of them own cellphones, the sample proportion of cellphone-owning teens is The sampling distribution of has the following properties: Its mean, denoted by (pronounced mu sub-p-hat), equals the population proportion, p. Its standard error, denoted by (say sigma sub-p-hat), equals: (Note that because n is in the denominator, the standard error decreases as n increases.) Due to the CLT, its shape is approximately normal, provided that the sample size is large enough. Therefore you can use the normal distribution to find approximate probabilities for The larger the sample size (n) or the closer p is to 0.50, the closer the distribution of the sample proportion is to a normal distribution. If you are interested in the number (rather than the proportion) of individuals in your sample with the characteristic of interest, you use the binomial distribution to find probabilities for your results. How large is large enough for the CLT to work for sample propor

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 review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Sampling Distributions Suppose that we draw all possible samples of size n from a given population. Suppose further that we compute a statistic (e.g., a mean, proportion, standard deviation) for each sample. The probability distribution of this statistic is called a sampling distribution. And the standard deviation of this statistic is called the standard error. Variability of a Sampling Distribution The variability of a sampling distribution is measured by its variance or its standard deviation. The variability of a sampling distribution depends on three factors: N: The number of observations in the population. n: The number of observations in the sample. The way that the random sample is chosen. If the population size is much larger than the sample size, then the sampling distribution has roughly the same standard error, whether we sample with or without replacement. On the other hand, if the sample represents a significant fraction (say, 1/20) of the population size, the standard error will be meaningfully smaller, when we sample without replacement. Sampling Distribution of the Mean Suppose we draw all possible samples of size n from a population of size N. Suppose further that we compute a mean score for each sample. In this way, we create a sampling distribution of the mean. We know the following about the sampling distribution of the mean. The mean of the sampling distribution (μx) is equal t

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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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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 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

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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

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

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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

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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

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