The degrees of freedom associated with the two-sample t-test is an issue that appears to be troubling a number of teachers. Past communications have indicated reasonable courses of action, as reviewed below.
1. It is not wise, as a general rule, to pool the variances and use the sum of the two sets of degrees of freedom, n1 + n2 - 2. [This, however, is what is presented in most introductory textbooks.]
2. The easy but conservative "fix" is to use the smaller of the two degrees of freedom from the individual samples, min[(n1-1),(n2-1)]. This procedure will fail to find real differences in means more often than it should, but it will not get you into trouble by finding too many significant differences where they do not exist.
3. The "best" solution in some sense is to adjust the degrees of freedom according to the sample sizes and the sample variances. This is the approximation built into the TI-83 and many software packages. It may give fractional degrees of freedom, but that is not a problem for the computer.
Now, about the exam. We would not expect students to calculate option 3 unless they had the routine available in their calculator. Therefore, we will allow the conservative option 2. This can be accounted for in the grading of the free response questions. The multiple choice questions have been reviewed very carefully to avoid the situation in which the correct answer depends on the particular choice of degree-of-freedom rule. In short, any correct statistical procedure will be accepted.
This prompts a further note on communication. The student should communicate clearly which rule is being used and what numerical value for degrees of freedom is being used in the analysis.