Margin Error Confidence Interval T Distribution
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Margin Of Error Formula Statistics
Wizard Graphing Scientific Financial Calculator books AP calculator review Statistics AP study margin of error calculator guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation how to find margin of error with confidence interval 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 example, suppose we wanted
Confidence Interval Formula
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 error can be defined by either
Confidence Interval Calculator
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 sampling distribution is nearly normal, the critical value can be expressed as a
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 margin of error formula for sample size practical applications, we replace the population standard deviation in (7.2) by
95 Confidence Interval Z Score
S, the standard deviation of the sample. However, this substitution changes the coverage probability . Fortunately, there is a simple 90 confidence interval 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 http://stattrek.com/estimation/margin-of-error.aspx?Tutorial=AP 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. 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 http://www.stat.wmich.edu/s216/book/node79.html 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 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
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