Chapter 12.2, Problem 4E

Refer to Exercise 12.3. How many observations are needed for a 95% confidence interval to be 2 units in length if n₁ = n₂?

12.3 Suppose, as in Exercise 12.1, that two populations have respective variances ${\sigma }_1^2=9$, and ${\sigma }_2^2=25$. Find the smallest sample size and the corresponding sample allocation that will yield a 95% confidence interval for μ₁ − μ₂ that is 2 units in length.