Margin Of Error Formula Proportion
Contents |
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 margin of error calculator list for FREE content right to your inbox. Easy! Your email
Margin Of Error Confidence Interval Calculator
Submit RELATED ARTICLES How to Calculate the Margin of Error for a Sample… Statistics Essentials For margin of error excel Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for Dummies, 3rd Edition Statistics II for Dummies Load more EducationMathStatisticsHow to Calculate the Margin of Error for a margin of error definition Sample Proportion How to Calculate the Margin of Error for a Sample Proportion Related Book Statistics For Dummies, 2nd Edition By 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
Sampling Error Formula
conditions 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* 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.
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 how to find margin of error with confidence interval Error for a Population Proportion Example 1000 randomly selected Americans were asked if they believed how to find margin of error on ti 84 the minimum wage should be raised. 600 said yes. Construct a 95% confidence interval for the proportion of Americans who believe that the minimum wage should be raised.
Margin Of Error Sample Size
Solution: We 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 http://www.dummies.com/education/math/statistics/how-to-calculate-the-margin-of-error-for-a-sample-proportion/ of error of .03 , 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 https://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm zc s = E 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 n
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: https://onlinecourses.science.psu.edu/stat500/node/31 The margin of error E is half of the width of the confidence interval. https://www.youtube.com/watch?v=NH40E65TWqg \[E=z_{\alpha/2}\sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}\] 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 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% margin of error 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 usually smaller than the one obtained using the conservative method. This smaller sample size means there is some risk that the resulting confidence interval may be wider than desired. Using the sample size by the conservative method has no such risk. For the next poll of the president's approval rating, we want to get a margin of error of 1
Google. Het beschrijft hoe wij gegevens gebruiken en welke opties je hebt. Je moet dit vandaag nog doen. Navigatie overslaan NLUploadenInloggenZoeken Laden... Kies je taal. Sluiten Meer informatie View this message in English Je gebruikt YouTube in het Nederlands. Je kunt deze voorkeur hieronder wijzigen. Learn more You're viewing YouTube in Dutch. You can change this preference below. Sluiten Ja, nieuwe versie behouden Ongedaan maken Sluiten Deze video is niet beschikbaar. WeergavewachtrijWachtrijWeergavewachtrijWachtrij Alles verwijderenOntkoppelen Laden... Weergavewachtrij Wachtrij __count__/__total__ How to calculate Margin of Error Confidence Interval for a population proportion statisticsfun AbonnerenGeabonneerdAfmelden50.66150K Laden... Laden... Bezig... Toevoegen aan Wil je hier later nog een keer naar kijken? Log in om deze video toe te voegen aan een afspeellijst. Inloggen Delen Meer Rapporteren Wil je een melding indienen over de video? Log in om ongepaste content te melden. Inloggen Transcript Statistieken 43.461 weergaven 202 Vind je dit een leuke video? Log in om je mening te geven. Inloggen 203 4 Vind je dit geen leuke video? Log in om je mening te geven. Inloggen 5 Laden... Laden... Transcript Het interactieve transcript kan niet worden geladen. Laden... Laden... Beoordelingen zijn beschikbaar wanneer de video is verhuurd. Deze functie is momenteel niet beschikbaar. Probeer het later opnieuw. Geüpload op 22 jul. 2011In this tutorial I explain and then calculate, using an example, the margin of error and confidence interval for a population proportion.Like us on: http://www.facebook.com/PartyMoreStud...Link To Playlist on Confidence Intervalshttp://www.youtube.com/course?list=EC...Created by David Longstreet, Professor of the Universe, MyBookSuckshttp://www.linkedin.com/in/davidlongs... Categorie Onderwijs Licentie Stan