Proportion Margin Of Error
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a Sample Proportion How to Calculate the Margin of Error for a Sample Proportion Related Book Statistics For Dummies, 2nd Edition By margin of error confidence interval calculator Deborah J. Rumsey When you report the results of a statistical survey, you need to include the margin of error. The general formula for the margin of error for a sample proportion (if certain conditions
Margin Of Error Excel
are met) is where is the sample proportion, n is the sample size, and z* is the appropriate z*-value for your desired level of confidence (from the following table). z*-Values for Selected (Percentage) Confidence Levels Percentage Confidence z*-Value 80 1.28 90 1.645 95 1.96 98 2.33 99 2.58 Note that these values are taken from the standard normal (Z-) distribution. The area between each z* value and the negative of that z* margin of error definition value is the confidence percentage (approximately). For example, the area between z*=1.28 and z=-1.28 is approximately 0.80. Hence this chart can be expanded to other confidence percentages as well. The chart shows only the confidence percentages most commonly used. Here are the steps for calculating the margin of error for a sample proportion: Find the sample size, n, and the sample proportion. The sample proportion is the number in the sample with the characteristic of interest, divided by n. Multiply the sample proportion by Divide the result by n. Take the square root of the calculated value. You now have the standard error, Multiply the result by the appropriate z*-value for the confidence level desired. Refer to the above table for the appropriate z*-value. If the confidence level is 95%, the z*-value is 1.96. Here's an example: Suppose that the Gallup Organization's latest poll sampled 1,000 people from the United States, and the results show that 520 people (52%) think the president is doing a good job, compared to 48% who don't think so. First, assume you want a 95% level of confidence, so z* = 1.96. The number of Americans in the sample who said they approve of the president was found to be 520. This means that the sample proport
zc s x We can make a similar construction for a confidence interval for a population proportion. Instead of x, we can use p and instead of s, we use , hence, we can write the confidence interval for a large sample proportion as Confidence Interval Margin of Error for a
How To Find Margin Of Error With Confidence Interval
Population Proportion Example 1000 randomly selected Americans were asked if they believed the minimum wage should
Sampling Error Formula
be raised. 600 said yes. Construct a 95% confidence interval for the proportion of Americans who believe that the minimum wage should be raised. Solution: We how to find margin of error on ti 84 have p = 600/1000 = .6 zc = 1.96 and n = 1000 We calculate: Hence we can conclude that between 57 and 63 percent of all Americans agree with the proposal. In other words, with a margin of error of .03 , http://www.dummies.com/education/math/statistics/how-to-calculate-the-margin-of-error-for-a-sample-proportion/ 60% agree. Calculating n for Estimating a Mean Example Suppose that you were interested in the average number of units that students take at a two year college to get an AA degree. Suppose you wanted to find a 95% confidence interval with a margin of error of .5 for m knowing s = 10. How many people should we ask? Solution Solving for n in Margin of Error = E = zc s/ we have E = zcs zc s = E https://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm Squaring both sides, we get We use the formula: Example A Subaru dealer wants to find out the age of their customers (for advertising purposes). They want the margin of error to be 3 years old. If they want a 90% confidence interval, how many people do they need to know about? Solution: We have E = 3, zc = 1.65 but there is no way of finding sigma exactly. They use the following reasoning: most car customers are between 16 and 68 years old hence the range is Range = 68 - 16 = 52 The range covers about four standard deviations hence one standard deviation is about s @ 52/4 = 13 We can now calculate n: Hence the dealer should survey at least 52 people. Finding n to Estimate a Proportion Example Suppose that you are in charge to see if dropping a computer will damage it. You want to find the proportion of computers that break. If you want a 90% confidence interval for this proportion, with a margin of error of 4%, How many computers should you drop? Solution The formula states that Squaring both sides, we get that zc2 p(1 - p) E2 = n Multiplying by n, we get nE2 = zc2[p(1 - p)] This is the formula for finding n. Since we do not know p, we use .5 ( A conservative estimate) We round 425.4 up for greater accuracy We will need to drop at least 426 computers. This could get expensive. Handout of more examples and exerc
by over 573 bloggers. There are many ways to follow us - By e-mail: https://www.r-bloggers.com/margin-of-error-and-comparing-proportions-in-the-same-sample/ On Facebook: If you are an R blogger yourself you are invited to add your own R content feed to this site (Non-English R bloggers should add themselves- https://onlinecourses.science.psu.edu/stat500/node/31 here) Jobs for R-usersStatistical Analyst @ Rostock, Mecklenburg-Vorpommern, GermanyData EngineerData Scientist – Post-Graduate Programme @ Nottingham, EnglandDirector, Real World Informatics & Analytics Data Science @ Northbrook, Illinois, U.S.Junior statistician/demographer margin of for UNICEF Popular Searches web scraping heatmap twitter maps time series animation boxplot shiny hadoop ggplot2 how to import image file to R trading finance latex eclipse rstudio excel SQL ggplot quantmod knitr googlevis PCA market research rattle regression map tutorial coplot rcmdr Recent Posts Election 2016: Tracking Emotions with R and Python Data science for executives margin of error and managers The Worlds Economic Data, Shiny Apps and all you want to know about Propensity Score Matching! August Package Picks Slack all the things! Warsaw R-Ladies Notes from the Kölner R meeting, 14 October 2016 anytime 0.0.4: New features and fixes 2016-13 ‘DOM’ Version 0.3 Building a package automatically The new R Graph Gallery Network Analysis Part 3 Exercises Annotated Facets with ggplot2 Paper published: mlr - Machine Learning in R a grim knight [cont’d] Other sites SAS blogs Jobs for R-users Margin of error, and comparing proportions in the same sample October 15, 2010By arthur charpentier (This article was first published on Freakonometrics - Tag - R-english, and kindly contributed to R-bloggers) I recently tried to answer a simple question, asked by @adelaigue. Actually, I thought that the answer would be obvious… but it is a little bit more compexe than what I thought. In a recent pool about elections in Brazil, it was mentionned in a French newspapper that"Mme Rousseff, 62 ans, de 46,8% des inte
version Unit Summary Margin of Error Determining the Required Sample Size Cautions About Sample Size Calculations Reading AssignmentAn Introduction to Statistical Methods and Data Analysis, (See Course Schedule). Margin of Error Note: The margin of error E is half of the width of the confidence interval. \[E=z_{\alpha/2}\sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}\] Confidence and precision (we call wider intervals as having poorer precision): Note that the higher the confidence level, the wider the width (or equivalently, half width) of the interval and thus the poorer the precision. One television poll stated that the recent approval rating of the president is 72%; the margin of error of the poll is plus or minus 3%. [For most newspapers and magazine polls, it is understood that the margin of error is calculated for a 95% confidence interval (if not stated otherwise). A 3% margin of error is a popular choice.] If we want the margin of error smaller (i.e., narrower intervals), we can increase the sample size. Or, if you calculate a 90% confidence interval instead of a 95% confidence interval, the margin of error will also be smaller. However, when one reports it, remember to state that the confidence interval is only 90% because otherwise people will assume a 95% confidence. Determining the Required Sample Size If the desired margin of error E is specified and the desired confidence level is specified, the required sample size to meet the requirement can be calculated by two methods: a. Educated Guess \[n=\frac {(z_{\alpha/2})^2 \cdot \hat{p}_g \cdot (1-\hat{p}_g)}{E^2}\] Where \(\hat{p}_g\) is an educated guess for the parameter π. b. Conservative Method \[n=\frac {(z_{\alpha/2})^2 \cdot \frac{1}{2} \cdot \frac{1}{2}}{E^2}\] This formula can be obtained from part (a) using the fact that: For 0 ≤ p ≤ 1, p (1 - p) achieves its largest value at \(p=\frac{1}{2}\). The sample size obtained from using the educated guess is u