Difference Between Standard Error Of The Mean And Confidence Interval
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normal distribution calculator to find the value of z to use for a confidence interval Compute a confidence interval on the mean when σ is known Determine whether to use a t distribution or a normal distribution Compute a confidence interval on the mean when σ central limit theorem confidence interval is estimated View Multimedia Version When you compute a confidence interval on the mean, you null hypothesis confidence interval compute the mean of a sample in order to estimate the mean of the population. Clearly, if you already knew the population mean, coefficient of variation confidence interval there would be no need for a confidence interval. However, to explain how confidence intervals are constructed, we are going to work backwards and begin by assuming characteristics of the population. Then we will show how sample data http://www.healthknowledge.org.uk/e-learning/statistical-methods/practitioners/standard-error-confidence-intervals can be used to construct a confidence interval. Assume that the weights of 10-year-old children are normally distributed with a mean of 90 and a standard deviation of 36. What is the sampling distribution of the mean for a sample size of 9? Recall from the section on the sampling distribution of the mean that the mean of the sampling distribution is μ and the standard error of the mean is For the present example, the http://onlinestatbook.com/2/estimation/mean.html sampling distribution of the mean has a mean of 90 and a standard deviation of 36/3 = 12. Note that the standard deviation of a sampling distribution is its standard error. Figure 1 shows this distribution. The shaded area represents the middle 95% of the distribution and stretches from 66.48 to 113.52. These limits were computed by adding and subtracting 1.96 standard deviations to/from the mean of 90 as follows: 90 - (1.96)(12) = 66.48 90 + (1.96)(12) = 113.52 The value of 1.96 is based on the fact that 95% of the area of a normal distribution is within 1.96 standard deviations of the mean; 12 is the standard error of the mean. Figure 1. The sampling distribution of the mean for N=9. The middle 95% of the distribution is shaded. Figure 1 shows that 95% of the means are no more than 23.52 units (1.96 standard deviations) from the mean of 90. Now consider the probability that a sample mean computed in a random sample is within 23.52 units of the population mean of 90. Since 95% of the distribution is within 23.52 of 90, the probability that the mean from any given sample will be within 23.52 of 90 is 0.95. This means that if we repeatedly compute the mean (M) from a sample, and create an interval ranging from M - 23.
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the http://stats.stackexchange.com/questions/151541/confidence-intervals-vs-standard-deviation workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags http://onlinelibrary.wiley.com/doi/10.1002/9781444311723.oth2/pdf Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; confidence interval 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 Confidence intervals vs. standard deviation up vote 1 down vote favorite The 95% confidence interval gives you a range. The 2 sigma of a standard deviation also gives you a difference between standard range of ~95%. Can someone shed some light on how they are different? confidence-interval standard-deviation share|improve this question edited May 9 '15 at 11:54 Andy 11.7k114671 asked May 9 '15 at 11:43 Berry 6112 add a comment| 2 Answers 2 active oldest votes up vote 4 down vote There are two things here : The "2 sigma rule" where sigma refers to standard deviation is a way to construct tolerance intervals for normally distributed data, not confidence intervals (see this link to learn about the difference). Said shortly, tolerance intervals refer to the distribution inside the population, whereas confidence intervals refer to a degree of certainty regarding an estimation. In case you meant standard error instead of standard deviation (which is what I understood at first), then the "2 sigma rule" gives a 95% confidence interval if your data are normally distributed (for example, if the conditions of the Central Limit Theorem apply and your sample size is great enough). share|improve this answer edited May 9 '15 at 15:57 answered May 9 '15 at 12:23 Antoine R
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