Dear Madam,

Confidence interval is the interval within which a statistic is about to vary with certain confidence level. You can compute the confidence interval depending on the probability distribution of your statistic.

Hi Sunita, the confidence interval is sort of the extension of the null hypothesis. So, for example if you take a mean, the 95% confidence interval (CI) tells you that the probability is 95% that the sample mean was obtained from a population with a mean lying within that confidence interval. In the case of a mean coming from a reasonably large sample where a z-statistic can be used to approximate t, you can compute the 95% CI by multiplying the standard error for the mean (usually obtained when you get the mean, although it can be also computed using the standard deviation and the sample size) by 1.96 (z for a p-value of .05) and adding and subtracting the result from the mean. This is roughly the process for many other statistics, such as a regression coefficient, which also normally comes with a standard error. In the case of many statistics like a regression coefficient, we are often interested in the question of whether 0 falls within the confidence interval. This is essentially the same thing we are saying when we say the thing is "significant."

It is about estimating the parameter (which is unknown, possible to know only when you conduct whole population study) using a statistic (function of sample observations). For example, you use sample mean to estimate population mean. Now, when you have only a point estimate in the form of sample mean, you don't know how close to or far from the true value of parameter your estimate is? In other words, you don't have any idea of the amount of error (called sampling error) involved in your estimate. Therefore, you look for an estimate that gives an idea of error or uncertainly involved in your estimate. Answer is interval estimate which is confidence interval (CI). CI gives you an interval within which you are confident to a certain degree that the true value of the parameter lies. For example, if you construct a 95% CI, you are 95% confident that true value of the parameter lies in this interval. Wider is the CI, more error involved in the estimate or less reliable is the estimate. Narrower is the CI, less error involved in the estimate or more reliable is the estimate. FOR COMPUTATION OF CI, CONSULT A STATISTICIAN BECAUSE COMPUTATION OF CI DEPENDS ON WHAT AND HOW ARE YOU ESTIMATING THE PARAMETER.

Imagine you are solving a regression problem. The parameters involved in the regression must be estimated and by constructing the confidence intervals the reliability of the parameter’s measure can be assessed. A confidence interval displays the range where the true parameter confidently lies. It must be remarked that the confidence limits form the upper and lower boundaries of a confidence interval. The upper and lower bounds of a 95% confidence interval are the 95% confidence limits. These limits can also be measured for other confidence levels, for example at 90% or 99% confidence. Note that the confidence level is the probability value (1-α) associated with a confidence interval. It is often expressed as a percentage. For example, say α = 0.05 = 5%, then the confidence level is equal to (1-0.05) = 0.95, i.e., a 95% confidence level.

If you use Matlab, this link will be very helpful: http://de.mathworks.com/help/curvefit/confidence-and-prediction-bounds.html