Calculating Margin Of Error Without Sample Size
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Calculate Sample Size From Margin Of Error And Standard Deviation
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Sample Size Margin Of Error Formula
Formulas Notation Share with Friends Margin of Error In a confidence interval, the range of values above and below the sample statistic is called the margin of error. For
How Is Margin Of Error Calculated In Polls
example, suppose we wanted to know the percentage of adults that exercise daily. We could devise a sample design to ensure that our sample estimate will not differ from the true population value by more than, say, 5 percent (the margin of error) 90 percent of the time (the confidence level). How to Compute the Margin of Error The margin of determining margin of error error can be defined by either of the following equations. Margin of error = Critical value x Standard deviation of the statistic Margin of error = Critical value x Standard error of the statistic If you know the standard deviation of the statistic, use the first equation to compute the margin of error. Otherwise, use the second equation. Previously, we described how to compute the standard deviation and standard error. How to Find the Critical Value The critical value is a factor used to compute the margin of error. This section describes how to find the critical value, when the sampling distribution of the statistic is normal or nearly normal. The central limit theorem states that the sampling distribution of a statistic will be nearly normal, if the sample size is large enough. As a rough guide, many statisticians say that a sample size of 30 is large enough when the population distribution is bell-shaped. But if the original population is badly skewed, has multiple peaks, and/or has outliers, researchers like the sample size to be even larger. When the sam
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 inbox. Easy! Your margin of error calculator email Submit RELATED ARTICLES How to Calculate the Margin of Error for confidence interval margin of error calculator a Sample… Statistics Essentials For Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for Dummies, 3rd Edition Statistics II for how to find margin of error on ti 84 Dummies Load more EducationMathStatisticsHow to Calculate the Margin of Error for a Sample Proportion How to Calculate the Margin of Error for a Sample Proportion Related Book Statistics For Dummies, 2nd Edition http://stattrek.com/estimation/margin-of-error.aspx 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 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). http://www.dummies.com/education/math/statistics/how-to-calculate-the-margin-of-error-for-a-sample-proportion/ 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. 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 th
larger amount of error than if the respondents are split 50-50 or 45-55. Lower margin of error requires a larger sample size. What confidence level do you need? Typical choices are http://www.raosoft.com/samplesize.html 90%, 95%, or 99% % The confidence level is the amount of uncertainty you can tolerate. https://onlinecourses.science.psu.edu/stat506/node/11 Suppose that you have 20 yes-no questions in your survey. With a confidence level of 95%, you would expect that for one of the questions (1 in 20), the percentage of people who answer yes would be more than the margin of error away from the true answer. The true answer is the percentage you would get if you exhaustively interviewed everyone. margin of Higher confidence level requires a larger sample size. What is the population size? If you don't know, use 20000 How many people are there to choose your random sample from? The sample size doesn't change much for populations larger than 20,000. What is the response distribution? Leave this as 50% % For each question, what do you expect the results will be? If the sample is skewed highly one way or the other,the population probably is, too. margin of error If you don't know, use 50%, which gives the largest sample size. See below under More information if this is confusing. Your recommended sample size is 377
This is the minimum recommended size of your survey. If you create a sample of this many people and get responses from everyone, you're more likely to get a correct answer than you would from a large sample where only a small percentage of the sample responds to your survey. Online surveys with Vovici have completion rates of 66%! Alternate scenarios With a sample size of With a confidence level of Your margin of error would be 9.78% 6.89% 5.62% Your sample size would need to be 267 377 643 Save effort, save time. Conduct your survey online with Vovici. More information If 50% of all the people in a population of 20000 people drink coffee in the morning, and if you were repeat the survey of 377 people ("Did you drink coffee this morning?") many times, then 95% of the time, your survey would find that between 45% and 55% of the people in your sample answered "Yes". The remaining 5% of the time, or for 1 in 20 survey questions, you would expect the survey response to more than the margin of error away from the true answer. When you survey a sample of the population, you don't know that you've founfor estimating proportion Educated guess Conservative estimates Read Textbook Ch. 5.3 Sample Size for Estimating Proportion Using the formula to find sample size for estimating the mean we have: \(n=\dfrac{1}{\dfrac{ d^2}{ z^2_{\alpha/2}\cdot \sigma^2}+\dfrac{1}{N}}\) Now, \(\sigma^2=\dfrac{N}{N-1}\cdot p \cdot (1-p)\)substitutes in and we get: \(n=\dfrac{N \cdot p \cdot (1-p)}{(N-1)\dfrac{d^2}{z^2_{\alpha/2}}+p\cdot(1-p)}\) When the finite population correction can be ignored, the formula is: \(n\approx \dfrac{z^2_{\alpha/2}\cdot p \cdot (1-p)}{d^2}\) Now, for finding sample sizes for proportion, in addition to using an educated guess to estimate p, we can also find a conservative sample size which can guarantee the margin of error is short enough at a specified α . A. Educated guess (estimate p by \(\hat{p}\) ): \(n=\dfrac{N\cdot\hat{p}\cdot(1-\hat{p})}{(N-1)\dfrac{d^2}{z^2_{\alpha/2}}+\hat{p}\cdot(1-\hat{p})}\) Note, \(\hat{p}\) may be different from the true proportion. The sample size may not be large enough for some cases, (i.e., the margin of error not as small as specified). B. Conservative sample size: Since p(1 - p) attains maximum at p = 1/2, a conservative estimate for sample size is: \(n=\dfrac{N\cdot 1/4}{(N-1)\dfrac{d^2}{z^2_{\alpha/2}}+1/4}\) Example To estimate the next president's final approval rating, how many people should be sampled so that the margin of error is 3%, (a popular choice), with 95% confidence? A. Use educated guess: Bush's = 0.22 Since N is very large compared to n, finite population correction is not needed. \begin{align}n &=\dfrac{\hat{p}\cdot(1-\hat{p})\cdot z^2_{\alpha/2}}{d^2}\\&=\dfrac{0.22\cdot0.78\cdot1.96^2}{0.03^2}\\&=732.47\\\end{align} round up to 733 B. Use conservative approach. \begin{align}n &=\dfrac{0.5\cdot0.5\cdot1.96^2}{0.03^2}\\&=1067.11\\\end{align} round up to 1068. H