Formula For Margin Of Error In Estimating Population Proportion
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What Is Population Proportion
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 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 o
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Population Proportion Calculator
calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews margin of error definition Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Margin of Error In a confidence interval, the range how to find margin of error with confidence interval of values above and below the sample statistic is called the margin of error. For example, suppose we wanted to know the percentage of adults that exercise daily. We could devise a sample design to http://www.dummies.com/education/math/statistics/how-to-calculate-the-margin-of-error-for-a-sample-proportion/ 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 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 http://stattrek.com/estimation/margin-of-error.aspx 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 sampling distribution is nearly normal, the critical value can be expressed as a t score or as a z score. When the sample size is smaller, the critical value should only be expressed as a t statistic. To find the critical value, follow these steps. Compute alpha (α): α = 1 - (confidence level / 100) Find the c
formula below provide the sample http://www.r-tutor.com/elementary-statistics/interval-estimation/sampling-size-population-proportion size needed under the requirement of population proportion interval http://onlinestatbook.com/2/estimation/proportion_ci.html estimate at (1 − α) confidence level, margin of error E, and planned proportion estimate p. Here, zα∕2 is the 100(1 − α∕2) percentile of the standard normal distribution. Problem Using a 50% planned margin of proportion estimate, find the sample size needed to achieve 5% margin of error for the female student survey at 95% confidence level. Solution Since there are two tails of the normal distribution, the 95% confidence level would imply the 97.5th percentile of the margin of error normal distribution at the upper tail. Therefore, zα∕2 is given by qnorm(.975). > zstar = qnorm(.975) > p = 0.5 > E = 0.05 > zstar^2 ∗ p ∗ (1−p) / E^2 [1] 384.15 Answer With a planned proportion estimate of 50% at 95% confidence level, it needs a sample size of 385 to achieve a 5% margin of error for the survey of female student proportion. ‹ Interval Estimate of Population Proportion up Hypothesis Testing › Tags: Elementary Statistics with R confidence level interval estimate margin of error normal distribution population proportion sampling size qnorm survey Search this site: R Tutorial eBook R Tutorials R IntroductionBasic Data TypesNumericIntegerComplexLogicalCharacterVectorCombining VectorsVector ArithmeticsVector IndexNumeric Index VectorLogical Index VectorNamed Vector MembersMatrixMatrix ConstructionListNamed List MembersData FrameData Frame Column VectorData Frame Column SliceData Frame Row SliceData ImportElementary Statistics with RQualitative DataFrequency Distribution of Qualitative DataRelative Frequency Distribution of Qualitative DataBar GraphPie ChartCategory StatisticsQuantitative DataFrequency
on the Mean Learning Objectives Estimate the population proportion from sample proportions Apply the correction for continuity Compute a confidence interval A candidate in a two-person election commissions a poll to determine who is ahead. The pollster randomly chooses 500 registered voters and determines that 260 out of the 500 favor the candidate. In other words, 0.52 of the sample favors the candidate. Although this point estimate of the proportion is informative, it is important to also compute a confidence interval. The confidence interval is computed based on the mean and standard deviation of the sampling distribution of a proportion. The formulas for these two parameters are shown below: μp = π Since we do not know the population parameter π, we use the sample proportion p as an estimate. The estimated standard error of p is therefore We start by taking our statistic (p) and creating an interval that ranges (Z.95)(sp) in both directions, where Z.95 is the number of standard deviations extending from the mean of a normal distribution required to contain 0.95 of the area (see the section on the confidence interval for the mean). The value of Z.95 is computed with the normal calculator and is equal to 1.96. We then make a slight adjustment to correct for the fact that the distribution is discrete rather than continuous.
Normal Distribution Calculator sp is calculated as shown below: To correct for the fact that we are approximating a discrete distribution with a continuous distribution (the normal distribution), we subtract 0.5/N from the lower limit and add 0.5/N to the upper limit of the interval. Therefore the confidence interval is Lower limit: 0.52 - (1.96)(0.0223) - 0.001 = 0.475 Upper limit: 0.52 + (1.96)(0.0223) + 0.001 = 0.565 0.475 ≤ π ≤ 0.565 Since the interval extends 0.045 in both directions, the margin of error is 0.045. In terms of percent, between 47.5% and 56.5% of the voters favor the candidate and the margin of error is 4.5%. Keep in mind that the margin of error of 4.5% is the margin of error for the percent favoring the candidate and not t