The sample mean is a point estimate of the population mean µ. This estimate is based on a single sample and another random sample from the same population would almost assuredly result in a different point estimate. We need to know how much these point estimates vary in repeated sampling from the population in order to assess the efficacy of our estimate.
The interval estimate of µ includes a measure of the variability of the point estimate as encapsulated in the error term. It is computed as the sample mean ± t x se, where t is the 1 - (alphs/2) quantile of the t distribution with n - 1 degrees of freedom and se (the standard error) is s/sqrt(n).
Example #1 uses data from an Australian school to set confidence intervals on the perceived width of a classroom in meters.
Exercise #3 uses measured pulse rates on Peruvian Indians to construct a confidence interval on the mean pulse rate.
Exercise #4 uses daily revenues from parking meters to constructs a confidence interval on the expected income.