Computing Standard Error Proportion
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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 standard error of proportion definition a normal distribution given that both \(n \times p \geq 10\) and \(n
Sample Proportion Formula
\times (1-p) \geq 10\). 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 \(n
Confidence Interval For Proportion Calculator
\times p \geq 10\) 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 (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
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 population proportion calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews confidence interval of proportion Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Confidence Interval: Proportion (Large Sample) This lesson describes how
Confidence Interval For Proportion Formula
to construct a confidence interval for a sample proportion, p, when the sample size is large. Estimation Requirements The approach described in this lesson is valid whenever the following conditions are met: The sampling method https://onlinecourses.science.psu.edu/stat200/node/43 is simple random sampling. The sample is sufficiently large. As a rule of thumb, a sample is considered "sufficiently large" if it includes at least 10 successes and 10 failures. Note the implications of the second condition. If the population proportion were close to 0.5, the sample size required to produce at least 10 successes and at least 10 failures would probably be close to 20. But if the population http://stattrek.com/estimation/confidence-interval-proportion.aspx?Tutorial=Stat proportion were extreme (i.e., close to 0 or 1), a much larger sample would probably be needed to produce at least 10 successes and 10 failures. For example, imagine that the probability of success were 0.1, and the sample were selected using simple random sampling. In this situation, a sample size close to 100 might be needed to get 10 successes. The Variability of the Sample Proportion To construct a confidence interval for a sample proportion, we need to know the variability of the sample proportion. This means we need to know how to compute the standard deviation and/or the standard error of the sampling distribution. Suppose k possible samples of size n can be selected from the population. The standard deviation of the sampling distribution is the "average" deviation between the k sample proportions and the true population proportion, P. The standard deviation of the sample proportion σp is: σp = sqrt[ P * ( 1 - P ) / n ] * sqrt[ ( N - n ) / ( N - 1 ) ] where P is the population proportion, n is the sample size, and N is the population size. When the population size is much larger (at least 20 times larger) than the sample si
0 otherwise. The standard deviation of any variable involves the standard error 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