Question: Josh and Kendra each calculated a 90% confidence interval for the difference of means using a Students t distribution for random samples of size n1

Josh and Kendra each calculated a 90% confidence interval for the difference of means using a Student’s t for random samples of size n1 = 20 and n2 = 31. Kendra followed the convention of using the smaller sample size to compute d.f. = 19. Josh used his calculator and Satterthwaite’s approximation and obtained d.f. ≈ 36.3. Which confidence interval is shorter? Which confidence interval is more conservative in the sense that the margin of error is larger?

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