Margin Of Error T Table
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Margin Of Error Excel
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 ensure that our sample estimate will not differ from the true population value by more than, say, 5 percent (the how to find margin of error with confidence interval 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 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 st
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Margin Of Error Calculator Without Population Size
to Calculate the Margin of Error for a Sample… Statistics Essentials For Dummies Statistics For Dummies, 2nd
Margin Of Error Formula For Sample Size
Edition SPSS Statistics for Dummies, 3rd Edition Statistics II for Dummies Load more EducationMathStatisticsHow to Calculate the Margin of Error for a Sample Mean How to Calculate the Margin http://stattrek.com/estimation/margin-of-error.aspx?Tutorial=AP of Error for a Sample Mean Related Book Statistics For Dummies, 2nd Edition By Deborah J. Rumsey When a research question asks 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 http://www.dummies.com/education/math/statistics/how-to-calculate-the-margin-of-error-for-a-sample-mean/ certain 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 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
population standard deviation is usually unknown (if we knew it, we would likely also know the population average , and have no need for an interval estimate.) In practical applications, we replace the population standard deviation in (7.2) by S, the standard deviation http://www.stat.wmich.edu/s216/book/node79.html of the sample. However, this substitution changes the coverage probability . Fortunately, there is a simple adjustment that allows us to maintain the desired coverage level : replace the normal distribution critical value z by the slightly larger t-distribution critical value t. The resulting confidence interval is the primary result of this section. where t is a critical value determined from the tn-1 distribution in such a way that there is area between t and -t. margin of The value n-1 is called degrees of freedom, or df for short. It is a parameter of the t-curve in the sense that changing the value of n-1 changes the shape of the t-curve, though usually not by much. Here are appropriate t critical values for selected and n-1. The t critical values are always larger than the z, and get progressively closer as n-1 gets larger (they are equal at ). For a 95% confidence margin of error interval, the t values are 2.06, 2.03, 2.01, 1.98, and 1.96 for respective sample sizes n= 26,36, 51, 101, and 501. Recall that the term in equation (7.5) is the (estimated) standard error of the mean. With .68 chance, misses by less than this amount. To generalize, misses by less than with certainty. Thus, the term is called the margin of error with confidence level . If , then t is close to 2.0. For this reason, the 95% margin of error is often written as . When working with a random sample, the exact critical value t is read from a table or calculator, and depends on the sample size. However, for sample size calculations (see next section), the approximate critical value 2.0 is typically used. Example: Given the following GPA for 6 students: 2.80, 3.20, 3.75, 3.10, 2.95, 3.40 a. Calculate a 95% confidence interval for the population mean GPA. b. If the confidence level is increased from 95% to 99% , will the length of the confidence interval increase, decrease, or remain the same? c. If the confidence level is kept at 95% but the sample size is quadrupled to n=24 (i) do you expect the sample mean to increase, decrease, or remain approximately the same? (ii) do you expect the sample SD S to increase, decrease, or remain approximately the same? (iii) do you expect the length of the confidence interval to increase,