Confidence Interval Margin Of Error Relationship
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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 smaller confidence interval smaller margin of error error decreases. As the variability in the population increases, the margin of error increases. As
Explain What Is Meant By A Margin Of Error For A Confidence Interval
the confidence level increases, the margin of error increases. Incidentally, population variability is not something we can usually control, but more meticulous collection of why does increasing the confidence level result in a larger margin of error 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
How Does Increasing The Confidence Level Affect The Margin Of Error
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 how does margin of error change with confidence level 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 will be needed to shrink your interval to the point where 50% will not be included in a 95% confidence interval centered at the .48 point estimate? Answer: The current interval width is about 6%. So the current margin of error is 3%. We want margin of error = 1.5% or 1.96*sqrt(.48*.52/n) = .015 Solve for n: n = (1.96/.015)^2 * .48*.52 = 4261.6 We'd nee
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Confidence Interval Half Width
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Confidence Interval Margin Of Error Calculator
Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, confidence interval margin of error formula data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top http://inspire.stat.ucla.edu/unit_10/solutions.php How are margins of error related to confidence Intervals? up vote 8 down vote favorite 2 Can somebody tell me the difference between margins of error and confidence intervals? On the Internet I see these two meanings getting used interchangeably. Is it right to say, "Confidence intervals are shown as 1.96 and displayed on the graphs as error margins"? confidence-interval survey polling share|improve this question edited Jan 31 '12 at 19:31 whuber♦ 145k17280540 asked Jan http://stats.stackexchange.com/questions/22021/how-are-margins-of-error-related-to-confidence-intervals 31 '12 at 15:56 Mintuz 143115 1 Useful discussions on this topic can be found by searching our site. –whuber♦ Jan 31 '12 at 19:30 add a comment| 2 Answers 2 active oldest votes up vote 9 down vote accepted The Internet is full of garbage, as all of us know. It helps to find authoritative sources and focus on them to help resolve such issues. A pamphlet published by the American Statistical Association (attributed to Fritz Scheuren and "thoroughly updated circa 1997") defines the margin of error as a 95% confidence interval (p. 64, at right). In light of this, it is surprising that the Wikipedia article on margin of error uses a different definition, even though it references this pamphlet! Wikipedia writes, The margin of error is usually defined as the "radius" (or half the width) of a confidence interval for a particular statistic from a survey. ... When a single, global margin of error is reported for a survey, it refers to the maximum margin of error for all reported percentages using the full sample from the survey. In other words, to Wikipedia the MoE is one-half the maximum width of a set of confidence intervals (which might have coverages differing from 95%). We have discussed this confusion (or, at least, lack of standardization) in comments elsewhere on this site.
test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP calculator review Statistics AP http://stattrek.com/estimation/margin-of-error.aspx study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems https://www.isixsigma.com/tools-templates/sampling-data/margin-error-and-confidence-levels-made-simple/ 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 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 margin of 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 = 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 margin of error 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 smaller, the critical value should only be expressed as a t statistic. To find the critical value, follow these steps. Compute alpha (α): α = 1 - (confidence level / 100) Find the critical probability (p*): p* = 1 - α/2 To express the critical value as a z score, find the z score having a cumulative probabil
Events Submit an Event News Read News Submit News Jobs Visit the Jobs Board Search Jobs Post a Job Marketplace Visit the Marketplace Assessments Case Studies Certification E-books Project Examples Reference Guides Research Templates Training Materials & Aids Videos Newsletters Join71,700 other iSixSigma newsletter subscribers: MONDAY, OCTOBER 03, 2016 Font Size Login Register Six Sigma Tools & Templates Sampling/Data Margin of Error and Confidence Levels Made Simple Tweet Margin of Error and Confidence Levels Made Simple Pamela Hunter 9 A survey is a 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 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 survey were conducted 100 times, the percentage who say service is "very good" will range between 47 and 53 percent most (95 percent) of the time. Survey Sample Size Margin of Error Percent* 2,000 2 1,500 3 1,000 3 900 3 800 3 700 4 600 4 500 4 400 5 300 6 200 7 100 10 50 14 *Assumes a 95% level of confidence Sample Size and the Margin of Error Margin of error – the plus or minus 3 percentage points in the above example – decr