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valuable assessment tool in which a sample is selected and information from the sample can then be generalized to a larger population. Surveying has been likened to taste-testing soup – a few spoonfuls tell what the whole pot tastes like. The key to the validity of any survey is randomness. Just as the soup must be stirred in order for margin of error confidence interval ti 83 the few spoonfuls to represent the whole pot, when sampling a population, the group must be stirred before respondents are selected. It is critical that respondents be chosen randomly so that the survey results can be generalized to the whole population. How well the sample represents the population is gauged by two important statistics – the survey's margin of error and confidence level. They tell us how well the spoonfuls represent the entire pot. For example, a survey may have a margin of error of plus or minus 3 percent at a 95 percent level of confidence. These terms simply mean that if the survey were conducted 100 times, the data would be within a certain number of percentage points above or below the percentage reported in 95 of the 100 surveys. In other words, Company X surveys customers and finds that 50 percent of the respondents say its customer service is "very good." The confidence level is cited as 95 percent plus or minus 3 percent. This information means that if the sur

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Notation 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, https://www.isixsigma.com/tools-templates/sampling-data/margin-error-and-confidence-levels-made-simple/ 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 Margin of Error The margin of error can http://stattrek.com/estimation/margin-of-error.aspx 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 outliers, researchers like the sample size to be even larger. When the sampling distribution is ne

Confidence Intervals and Margin of Error statisticsfun SubscribeSubscribedUnsubscribe49,94349K Loading... Loading... Working... Add to Want to watch this again later? Sign in to add this video to a playlist. Sign in Share More Report https://www.youtube.com/watch?v=dNfpsVLaaEE Need to report the video? Sign in to report inappropriate content. Sign http://inspire.stat.ucla.edu/unit_10/solutions.php in Transcript Statistics 154,276 views 783 Like this video? Sign in to make your opinion count. Sign in 784 16 Don't like this video? Sign in to make your opinion count. Sign in 17 Loading... Loading... Transcript The interactive transcript could not be loaded. Loading... Loading... Rating is available when the margin of video has been rented. This feature is not available right now. Please try again later. Uploaded on Jul 12, 2011Tutorial on how to calculate the confidence interval and margin of error (interval estimate). Include an example and some discussion on the bell curve and z scores.Like MyBookSucks on: http://www.facebook.com/PartyMoreStud...Related Videos:Z scores and Normal Tableshttp://www.youtube.com/watch?v=q5fwCl... How to Normalized Tables Used for Z scoreshttp://www.youtube.com/watch?v=dWu0KL...Playlist t margin of error tests for independent and dependent means.http://www.youtube.com/playlist?list=...Created by David Longstreet, Professor of the Universe, MyBookSuckshttp://www.linkedin.com/in/davidlongs... Category Education License Standard YouTube License Show more Show less Loading... Advertisement Autoplay When autoplay is enabled, a suggested video will automatically play next. Up next How to calculate sample size and margin of error - Duration: 6:46. statisticsfun 64,488 views 6:46 Statistics 101: To z or to t, That is the Question - Duration: 38:17. Brandon Foltz 76,145 views 38:17 Statistics 101:Confidence Intervals for the Variance - Duration: 40:41. Brandon Foltz 16,172 views 40:41 Margin of Error Example - Duration: 11:04. drenniemath 36,919 views 11:04 Statistics 101: Confidence Intervals, Population Deviation Known - Duration: 44:07. Brandon Foltz 107,687 views 44:07 Introduction to Confidence Intervals - Duration: 6:42. jbstatistics 80,684 views 6:42 Understanding Confidence Intervals: Statistics Help - Duration: 4:03. Statistics Learning Centre 328,221 views 4:03 95% Confidence Interval - Duration: 9:03. mathwithmrbarnes 314,903 views 9:03 Statistics Lecture 7.2: Finding Confidence Intervals for the Population Proportion - Duration: 2:24:10. Professor Leonard 42,089 views 2:24:10 Statistics 101: Confidence Intervals, Population Deviation Unknown - Part 1 - Duration: 27:15. Brandon Foltz 55,628 views 27:15 z-t

a confidence interval estimate of a population mean: sample size, variability in the population, and confidence level. For each of these quantities separately, explain briefly what happens to the margin of error as that quantity increases. Answer: As sample size increases, the margin of error decreases. As the variability in the population increases, the margin of error increases. As the confidence level increases, the margin of error increases. Incidentally, population variability is not something we can usually control, but more meticulous collection of data can reduce the variability in our measurements. The third of these--the relationship between confidence level and margin of error seems contradictory to many students because they are confusing accuracy (confidence level) and precision (margin of error). If you want to be surer of hitting a target with a spotlight, then you make your spotlight bigger. 2. A survey of 1000 Californians finds reports that 48% are excited by the annual visit of INSPIRE participants to their fair state. Construct a 95% confidence interval on the true proportion of Californians who are excited to be visited by these Statistics teachers. Answer: We first check that the sample size is large enough to apply the normal approximation. The true value of p is unknown, so we can't check that np > 10 and n(1-p) > 10, but we can check this for p-hat, our estimate of p. 1000*.48 = 480 > 10 and 1000*.52 > 10. This means the normal approximation will be good, and we can apply them to calculate a confidence interval for p. .48 +/- 1.96*sqrt(.48*.52/1000) .48 +/- .03096552 (that mysterious 3% margin of error!) (.45, .51) is a 95% CI for the true proportion of all Californians who are excited about the Stats teachers' visit. 3. Since your interval contains values above 50% and therefore does finds that it is plausible that more than half of the state feels this way, there remains a big question mark in your mind. Suppose you decide that you want to refine your estimate of the population proportion and cut the width of your interval in half. Will doubling your sample size do this? How large a sample will be needed to cut your interval width in half? How large a sample w

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