A confidence interval is an estimate of a range of values that includes the true population value for a statistic, such as a mean. In the example below, ten participants were asked to complete a task and the time in seconds was recorded. In this example, alpha is set to 0.05 (a 95% confidence level), the standard deviation is calculated using the Excel STDEV function and the sample size is calculated using the Excel COUNT function. Often times you may want to display your data in graphical form, including the confidence interval.
As the level of confidence decreases, the size of the corresponding interval will decrease. In most practical research, the standard deviation for the population of interest is not known. The probability that an interval estimate will contain the parameter is expressed as the confidence level.A confidence interval is a specific interval estimate of a parameter determined by sample data and a specific confidence level of the estimate.


Let us work out few examples to demonstrate the method of calculating the confidence intervals. The level of confidence you choose will determine how reasonably certain the true population mean is included in the range.
Using the CONFIDENCE function in Excel, we can calculate the confidence interval of the sample data to estimate the range that contains the population mean. The chart below shows the mean of the data set above and graphs the confidence interval 13.02 as an error bar.
Estimates of parameters like mean and proportion which are derived from data collected from samples are often used in statements describing the true parameters of population. A confidence level of 95% means that you can be 95% certain, or wrong 5% of the time, that the sample being analyzed contains the population mean.
For example, a confidence level of 95% has an alpha of 5%, in other words, alpha is equal to 1 minus the confidence level.


There is a general trade off between the confidence level and the range of the confidence interval.
The reliability of a Point estimate as a good estimate is often difficult to find and hence its accuracy is generally questionable, Hence the interval estimates are generally preferred by statisticians over Point estimates.An interval estimate is a range of values to estimate the parameter in question, The interval may or may not contain the parameter. Confidence Interval is an Interval estimate for the parameter which also gives the probability of the true parameter falling in that interval.



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