They are related but they are NOT the same.
Confidence intervals represent a specific probability that the "true" mean of a data set falls within a given range. The given range is based off of the experimental mean.
Statistical estimates cannot be exact: there is a degree of uncertainty associated with any statistical estimate. A confidence interval is a range such that the estimated value belongs to the confidence interval with the stated probability.
See: http://en.wikipedia.org/wiki/Confidence_interval Includes a worked out example for the confidence interval of the mean of a distribution. In general, confidence intervals are calculated from the sampling distribution of a statistic. If "n" independent random variables are summed (as in the calculation of a mean), then their sampling distribution will be the t distribution with n-1 degrees of freedom.
Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.
confidence intervals
, the desired probabilistic level at which the obtained interval will contain the population parameter.
Esa I. Uusipaikka has written: 'Confidence intervals in generalized regression models' -- subject(s): Regression analysis, Linear models (Mathematics), Statistics, Confidence intervals
They are related but they are NOT the same.
Confidence intervals represent a specific probability that the "true" mean of a data set falls within a given range. The given range is based off of the experimental mean.
No. For instance, when you calculate a 95% confidence interval for a parameter this should be taken to mean that, if you were to repeat the entire procedure of sampling from the population and calculating the confidence interval many times then the collection of confidence intervals would include the given parameter 95% of the time. And sometimes the confidence intervals would not include the given parameter.
If you are a good business man then they don't.
An open interval centered about the point estimate, .
Length
In a study using 9 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is
The standard deviation associated with a statistic and its sampling distribution.
The confidence intervals will increase. How much it will increase depends on whether the underlying probability model is additive or multiplicative.