Population Mean Margin Of Error Formula
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Margin Of Error Calculator
Margin of Error for a Sample Mean Related Book Statistics For Dummies, 2nd Edition By Deborah J. Rumsey When a research question asks margin of error confidence interval calculator you to find a statistical sample mean (or average), you need to report a margin of error, or MOE, for the sample mean. The general formula for the margin of error for the sample mean (assuming a certain margin of error excel condition is met -- see below) is is the population standard deviation, n is the sample size, and z* is the appropriate z*-value for your desired level of confidence (which you can find in 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
How To Find Margin Of Error With Confidence Interval
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. 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 mean: Find the population standard deviation and the sample size, n. The population standard deviation, will be given in the problem. Divide the population standard deviation by the square root of the sample size. gives you the standard error. Multiply by the appropriate z*-value (refer to the above table). For example, the z*-value is 1.96 if you want to be about 95% confident. The condition you need to meet in order to use a z*-value in the margin of error formula for a sample mean is either: 1) The original population has a normal distribution to start with, or 2) The sample size is large enough so the normal distribution can be used (that is, the Central Limit Theorem applies ). In general, the sample size, n, should be above about 30 in order for the Central Limit Theorem to be applicable. Now, if it's 29, don't panic -- 30 is not a magic number, it's just a general rule of thumb. (The population standard deviation must be known either way.) Here's an example
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Margin Of Error Calculator Without Population Size
In a confidence interval, the range 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. http://www.dummies.com/education/math/statistics/how-to-calculate-the-margin-of-error-for-a-sample-mean/ 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 error can be defined by either of the following equations. Margin of error = Critical value x Standard deviation http://stattrek.com/estimation/margin-of-error.aspx?Tutorial=AP 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 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
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