Approximation Formula For Margin Of Error
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Formula For Margin Of Error For Confidence Interval
SPSS Statistics for Dummies, 3rd Edition Statistics II for Dummies Load more EducationMathStatisticsHow to Calculate the Margin of Error for a Sample formula for margin of error in excel 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
Formula For Margin Of Error For Proportions
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). 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 formula for margin of error in statistics 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 of confidence, so z* = 1.96. The number of Americans in the sample who said they approve of the president was
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Formula For Margin Of Error In Estimating Population Proportion
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Formula For Margin Of Error For Means
calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam margin of error formula algebra 2 Problems and solutions 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 http://www.dummies.com/education/math/statistics/how-to-calculate-the-margin-of-error-for-a-sample-proportion/ 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 margin of error) 90 percent of the time (the confidence level). How to Compute the http://stattrek.com/estimation/margin-of-error.aspx 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 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 outlie
a Sample Size Do We Need for a… 3 What Is a Confidence Interval? 4 How to Calculate a Confidence Interval for a… 5 Calculating a Confidence http://statistics.about.com/od/Inferential-Statistics/a/How-To-Calculate-The-Margin-Of-Error.htm Interval for a Mean About.com About Education Statistics . . . Statistics http://www.zweigmedia.com/RealWorld/calctopic1/linearapprox.html Help and Tutorials by Topic Inferential Statistics How to Calculate the Margin of Error What Is the Margin of Error for an Opinion Poll? Share Pin Tweet Submit Stumble Post Share By Courtney Taylor Statistics Expert By Courtney Taylor Many times political polls and other applications of statistics state their margin of results with a margin of error. It is not uncommon to see that an opinion poll states that there is support for an issue or candidate at a certain percentage of respondents, plus and minus a certain percentage. It is this plus and minus term that is the margin of error. But how is the margin of error calculated? For a simple random margin of error sample of a sufficiently large population, the margin or error is really just a restatement of the size of the sample and the level of confidence being used.The Formula for the Margin of ErrorIn what follows we will utilize the formula for the margin of error. We will plan for the worst case possible, in which we have no idea what the true level of support is the issues in our poll. If we did have some idea about this number , possibly through previous polling data, we would end up with a smaller margin of error.The formula we will use is: E = zα/2/(2√ n) continue reading below our video 5 Common Dreams and What They Supposedly Mean The Level of ConfidenceThe first piece of information we need to calculate the margin of error is to determine what level of confidence we desire. This number can be any percentage less than 100%, but the most common levels of confidence are 90%, 95%, and 99%. Of these three the 95% level is used most frequently.If we subtract the level of confidence from one, then we will ob
Finite Math Everything for Finite Math & Calculus Español Note To understand this topic, you will need to be familiar with derivatives, as discussed in Chapter 3 of Calculus Applied to the Real World. If you like, you can review the topic summary material on techniques of differentiation or, for a more detailed study, the on-line tutorials on derivatives of powers, sums, and constant multipes. We start with the observation that if you zoom in to a portion of a smooth curve near a specified point, it becomes indistinguishable from the tangent line at that point. In other words: The values of the function are close to the values of the linear function whose graph is the tangent line. For this reason, the linear function whose graph is the tangent line to $y = f(x)$ at a specified point $(a, f(a))$ is called the linear approximation of $f(x)$ near $x = a.$ Q What is the formula for the linear approximation? A All we need is the equation of the tangent line at a specified point $(a, f(a)).$ Since the tangent line at $(a, f(a))$ has slope $f'(a),$ we can write down its equation using the point-slope formula: $y= y_0 + m(x - x_0)$ $= f(a) + f'(a)(x - a)$ Thus, the the linear approximation to $f(x)$ near $x = a$ is given by $L(x) = f(a) + f'(a)(x - a).$ Q The above argument is based on geometry: the fact that the tangent line is close to the original graph near the point of tangency. Is there an algebriac way of seeing why this is true? A Yes. This links to an algebraic derivation of the linear approximation. Linear Approximation of $f(x)$ Near $x = a$ If $x$ is close to a, then $f(x) \approx f(a) + (x-a)f'(a).$ The right-hand side, $L(x) = f(a) + (x-a)f'(a),$ which is a linear function of $x,$ is called the linear approximation of $f(x)$ near $x = a.$ Example 1 Linear Approximation of the Square Root Let $f(x) = x^{1/2}.$ Find the linear approximation of $f$ near $x = 4$ (at the point $(4, f(4)) = (4, 2)$ on the graph), and use it to approximate $\sqrt{4.1.}$ Solution Since $f'(x) = 1/(2x^{1/2}),$ $f'(4) = 1/(2 \cdot 4^{1/2}) = 1/4.$ so the linear approximation is $L(x) = f(4) + (x-4)f'(4)$ $ = 2 + (x-4)/4$ $ = 0.25x + 1.$ We can use $L(x)$ to approximate the square root of any number close to $4$ very easily without using a calculator. For example, $\sqrt{4.1}$$\approx$$L(4.1) = 0.25(4.1) + 1 = 2.025$ Q $\sqrt{3.82}$$\approx$ Q The Linear approximation of the same function, $f