Margin Of Error In Estimating The Population Mean
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sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends how to find margin of error with confidence interval 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 to know the percentage of
Margin Of Error Sample Size
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 of the following equations. Margin of error sampling error formula statistics = 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 t score or as a z score. When the sample size is smal
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a Sample… Statistics Essentials For Dummies Statistics For Dummies, 2nd Edition SPSS Statistics for Dummies, 3rd Edition Statistics II for confidence interval formula Dummies Load more EducationMathStatisticsHow to Calculate the Margin of Error for a Sample Proportion How to Calculate the Margin of Error for a Sample Proportion Related Book Statistics For Dummies, 2nd Edition http://stattrek.com/estimation/margin-of-error.aspx?Tutorial=AP By Deborah J. Rumsey When you report the results of a statistical survey, you need to include the 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 http://www.dummies.com/education/math/statistics/how-to-calculate-the-margin-of-error-for-a-sample-proportion/ 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. 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 f
Content Standards: S-IC.B.4 Student View Task Background: Researchers have questioned whether the traditional value of 98.6°F is correct for a typical body temperature for healthy adults. Suppose that you plan to estimate mean body temperature by recording the temperatures of the people in a https://www.illustrativemathematics.org/content-standards/tasks/1956 random sample of 10 healthy adults and calculating the sample mean. How accurate can you expect that estimate to be? In this activity, you will develop a margin of error that will help you to answer this question. Let's assume for now that body temperature for healthy adults follows a normal distribution with mean 98.6 degrees and standard deviation 0.7 degrees. Here are the body temperatures for one random sample of 10 healthy adults from this population: 97.73 98.76 98.27 margin of 99.95 98.47 98.49 98.97 98.68 99.27 99.25 What is the mean temperature for this sample? If you were to take a different random sample of size 10, would you expect to get the same value for the sample mean? Explain. Below is a dot plot of the sample mean body temperature for 100 different random samples of size 10 from a population where the mean temperature is 98.6 degrees. How many of the samples had sample margin of error means that were greater than 98.5 degrees and less than 98.7 degrees? Based on the dot plot above, if you were to take a different random sample from the population, would you be surprised if you got a sample mean of 98.8 or greater? Explain why or why not. Which of the following statements is appropriate based on the dot plot of sample means above? Statement 1:Most random samples of size 10 from the population would result in a sample mean that is within 0.1 degrees of the value of the population mean (98.6). Statement 2:Most random samples of size 10 from the population would result in a sample mean that is within 0.3 degrees of the value of the population mean (98.6). Statement 3:Most random samples of size 10 from the population would result in a sample mean that is within 0.5 degrees of the value of the population mean (98.6). The margin of error associated with an estimate of a population mean can be interpreted as the maximum likely difference between the estimate and the actual value of the population mean for a given sample size. Explain why 0.45 degrees would be a reasonable estimate of the margin of error when using the sample mean from a random sample of size 10 to estimate the mean body temperature for the population described above. If you were to use a random sample of size