Calculate The Standard Error Of P Hat
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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 a
Standard Error Of P Hat Equation
normal distribution given that both \(n \times p \geq 10\) and \(n \times standard error of p hat formula (1-p) \geq 10\). This is known as theRule of Sample Proportions. Note that some textbooks use a minimum of 15
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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 equals \( how to calculate standard error in r \sqrt{\frac {p(1-p)}{n}}\); 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 \(n \times p \geq how to calculate standard error without standard deviation 10\) 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: Comparing Two Groups Lesson 10:
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Indonesia Italy Malaysia Mexico New Zealand Philippines Quebec Singapore Taiwan Hong Kong Spain Thailand UK & Ireland Vietnam Espanol About About Answers Community Guidelines Leaderboard Knowledge Partners Points & https://onlinecourses.science.psu.edu/stat200/node/43 Levels Blog Safety Tips Science & Mathematics Mathematics Next Statistics - how to calculate standard error and confidence interval? after examining 400 IT workers , 100 individuals were found to b having WRS(work related stress) calculate the standard error proportion and confidence interval 1 following 2 answers 2 Report Abuse Are you sure you want to delete this answer? Yes https://answers.yahoo.com/question/index?qid=20100313103237AAiMbs5 No Sorry, something has gone wrong. Trending Now Blake Shelton Evan Peters Kanye West Illinois Lottery Cheap Airline Tickets Reverse Mortgage Andrea Tantaros Hillary Clinton Oakland Raiders Auto Insurance Quotes Answers Best Answer: Estimated p = 100 / 400 = 0.25 Variance of proportion = p*(1-p)/n = 0.25(0.75)/400 =0.0004688 S.D. of p is sqrt[0.000469] = 0.0217 (standard error of proportion) Confidence interval: phat-zval*sd = 0.25 - (1.96)(0.021651) phat-zval*sd = 0.25 + (1.96)(0.021651) 95 % Confidence interval is ( 0.2076 , 0.2924 ) Source(s): cidyah · 7 years ago 1 Thumbs up 0 Thumbs down Comment Add a comment Submit · just now Report Abuse Just fiddle the statistics to suit yourself - my government does berniece · 4 months ago 0 Thumbs up 0 Thumbs down Comment Add a comment Submit · just now Report Abuse Add your answer Statistics - how to calculate standard error and confidence interval? after examining 400 IT workers , 100 individuals were found to b having WRS(work related stress) calculate the standard error proportion and confidence interval Add your answer Source S
WorkSocial MediaSoftwareProgrammingWeb Design & DevelopmentBusinessCareersComputers Online Courses B2B Solutions Shop for Books San Francisco, CA Brr, it´s cold outside Search Submit Learn more with dummies Enter your email to join our mailing list for FREE content right to your http://www.dummies.com/education/math/statistics/how-to-find-the-sampling-distribution-of-a-sample-proportion/ inbox. Easy! Your email Submit RELATED ARTICLES How to Find the Sampling Distribution of a Sample Proportion Statistics Essentials For Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for Dummies, http://www.stat.wmich.edu/s216/book/node70.html 3rd Edition Statistics II for Dummies Load more EducationMathStatisticsHow to Find the Sampling Distribution of a Sample Proportion How to Find the Sampling Distribution of a Sample Proportion Related Book Statistics standard error 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 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 calculate standard error 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 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 interest
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