# Question

Suppose we are testing the hypotheses

H0 : 1 2

H1 : 1 2

where 12 and 22 are known. Resources are limited, and consequently the total sample size n1 + n2 = N. How should we allocate the N observations between the two populations to obtain the most powerful test?

H0 : 1 2

H1 : 1 2

where 12 and 22 are known. Resources are limited, and consequently the total sample size n1 + n2 = N. How should we allocate the N observations between the two populations to obtain the most powerful test?

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