Calculating Standard Error Of P Hat
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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 instead of 10 believing standard error of p hat equation that 10 is to liberal. We will use 10 for our discussions.] Using this, we standard error of p hat formula can estimate the true population proportion, p, by \(\hat{p}\) and the true standard deviation of p by \(s.e.(\hat{p})=\sqrt{\frac {p(1-p)}{n}}\), where s.e.( \(\hat{p}\)) is calculating standard error in excel 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 ≥ 10 and n(1- p) ≥ 10,
Calculating Standard Error Of Proportion
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 have used mj in the past 6 months is less than calculating standard error stata .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 Proportion, p-hat 4.2 - Sampling Distribution of the Sample Mean, x-bar 4.3 - Review of Sampling Distributions 5: Confidence Intervals 6: Hypothesis Testin
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Calculating Standard Error Of Estimate
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Calculating Standard Error Of Measurement
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 & Levels Blog Safety Tips https://onlinecourses.science.psu.edu/stat800/node/35 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 No Sorry, something has gone wrong. Trending Now https://answers.yahoo.com/question/index?qid=20100313103237AAiMbs5 Dow Jones Debra Messing Gloria Naylor Atlanta Falcons Tim Tebow Life Insurance Quotes Witney Carson Toyota RAV4 Reverse Mortgage Buffalo Bills 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 Submit Cancel Report Abuse I think this question violates the Community Guidelines Chat or rant, adult content, spam, insulting
distribution of a sample proportion compute probabilities of a sample proportion The Sample Proportion Consider these recent headlines: Hispanics See Their Situation in U.S. Deteriorating Half (50%) of all Latinos https://faculty.elgin.edu/dkernler/statistics/ch08/8-2.html say that the situation of Latinos in this country is worse now than it was a year ago, according to a new nationwide survey of 2,015 Hispanic adults conducted by the Pew Hispanic Center. (Source: Pew Research) Automatic enrollment http://stattrek.com/sampling/sampling-distribution.aspx in 401(k) doesn't take care of everything Never got around to signing up for the company retirement plan? The boss may have done it for you. Forty-two percent of employers with 401(k) plans automatically enroll new or existing standard error employees in the plans, nearly double the 23 percent from 2006, according to estimates from the 2008 401(k) Benchmarking Survey by the International Foundation of Employee Benefit Plans and Deloitte Consulting. The survey polled 436 employers with workforces of all sizes. (Source: Chicago Tribune) Stem cell, marijuana proposals lead in Mich. poll A recent poll shows voter support leading opposition for ballot proposals to loosen Michigan's restrictions on embryonic stem cell research and allow medical use calculating standard error of marijuana. The EPIC-MRA poll conducted for The Detroit News and television stations WXYZ, WILX, WOOD and WJRT found 50 percent of likely Michigan voters support the stem cell proposal, 32 percent against and 18 percent undecided. (Source: Associated Press) These three articles all have something in common - they're referring to sample proportions - 50% of all Latinos, 42% of employers, and 50% of likely Michigan voters, respectively, in the three articles above. Proportions are the number with that certain characteristics divided by the sample size. In general, if we let x = the number with the specific characteristic, then the sample proportion, , (read "p-hat") is given by: Where is an estimate for the population proportion, p. Let's focus for a bit on x, the number with that characteristic. If we rephrase that a bit, and consider an individual having that characteristic as a "success", we can see that x follows the binomial distribution. From Section 6.2, we know that the distribution of a binomial random variable becomes bell-shaped as n increases. The three histograms below demonstrate the effect of the sample size on the distribution shape. n=10, p=0.8 n=20, p=0.8 n=50, p=0.8 As the number of trials in a binomial experiment increases, the probability distribution becomes bell-shaped. As a rule of thumb, if np(1-p)≥10, the distribution will be approximately bell-shaped. With our new
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 to the mean of the population (μ). And the standard error of the sampling distribution (σx) is determined by the standard deviation of the population (σ), the population size (N), and the sample size (n). These relationships are shown in the equations below: μx = μ and σx = [ σ / sqrt(n) ] * sqrt[ (N - n ) / (N - 1) ] In the standard error formula, the factor sqrt[ (N - n ) / (N - 1) ] is called the finit