Question:
Suppose that you wish to test the hypothesis $H_{0}:\mu_{1}=\mu_{2}$ versus $H_{1}:\mu_{1}\neq \mu_{2}$,where both variances $\sigma^2_{1}$ and $\sigma^2_{2}$ are know ,A tatal of $n_{1}+n_{2}=N$ observations can be taken.How should these observations be allocated to the two populations to maximize the probability that $H_{0}$ will be rejected if $H_{1}$ is true and $\mu_{1}-\mu_{2}=\Delta\neq 0?$
This is my homework,and I can't find this solution, and I have to turn it in in on Wednesday,so I hope someone can help ,If help me to answer,
I would be very grateful to you
because this homewor is very important to me!
maybe this problem is not easy?
Thank you very much!