Special note concerning the degrees of freedom for the sampling distribution of the difference of
two means : In most situations, a conservative , and usually acceptable, approach for determining the
required number of degrees of freedom is to let the number of degrees of freedom equal n 1 – 1 or n 2 – 1,
whichever is smaller. We will abbreviate this as df = min{n 1 – 1, n 2 – 1}. This is “conservative” in the
sense that it will give a smaller number of degrees of freedom than other methods, which translates to a
larger margin of error. It will be easiest to use a calculator to do the interval, and report the degrees of
freedom given by the calculator.
When the confidence interval is constructed by calculator or computer (that’s the “computed by
software” notation in the chart), the degrees of freedom will be computed using the following expression:
You don’t need to, and probably don’t want to do this computation by hand, but you could! Note that
this technique usually results in a noninteger number of degrees of freedom.
In practice, since most people will be constructing a two-sample confidence interval using a