An interval estimate is constructed by adding and subtracting the margin of error from the point estimate. So to compute an interval estimate of the population mean, add and subtract the margin of error from the sample mean. When constructing an interval estimate, it is important to choose a confidence level, such as 95%. The confidence coefficient is the decimal form of the confidence level, so .95. An interval estimate constructed at a confidence level of 95% is called a 95% confidence interval. For confidence intervals of population mean: $\sigma$ known, use the standard normal, or z, distribution.
For confidence intervals of the population mean: $\sigma$ unknown , the main difference is that instead of using the z distribution, the t distribution is used. The t distribution is a family of probability distributions, with each individual t distribution depending on the degrees of freedom. Degrees of freedom refers to the number of independent pieces of information that go into computing the sample standard deviation. There are n-1 independent pieces of information because we know that the sum of the deviation about the mean is always equal to zero. Thus, we use n-1 degrees of freedom when computing confidence intervals for the population mean when the population standard deviation is unkown.