Chapter 12.2, Problem 2E

Refer to Exercise 12.1. Suppose that you allocate n₁ = n₂ observations to each sample. How large must n₁ and n₂ be in order to obtain the same amount of information as that implied by the solution to Exercise 12.1?

12.1 Suppose that you wish to compare the means for two populations and that ${\sigma }_1^2=9$, ${\sigma }_2^2=25$, and n = 90. What allocation of n = 90 to the two samples will result in the maximum amount of information about (μ₁ − μ₂)?