Chapter 8.5, Problem 6P

Critical Thinking Consider use of a Student’s t distribution to test the difference of means for independent populations using random samples of sizes n₁ and n₂.

1. (a) Which process gives the larger degrees of freedom, Satterthwaite’s approximation or using the smaller of n₁ − 1 and n₂ + 1? Which method is more conservative? What do we mean by “conservative”? Note that computer programs and other technologies commonly use Satterthwaite’s approximation.
2. (b) Using the same hypotheses and sample data, is the P-value smaller for larger degrees of freedom? How might a larger P-value impact the significance of a test?