Hypothesis Testing: Neyman Pearson Lemma

**Suppose that Y1,Y2,...,Yn are iid Poisson(lambda)**

**We want to test Ho:lambda=lambda_o vs Ha:lambda=lambda_a (where lambda_a>lambda_o)**

**Using the Neyman Pearson Lemma, find the most powerful test for alpha=0.05**

**(Hint: (Y1+Y2+...+Yn) ~ Possion(n*lambda) )**

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So we need to solve P([L(lambda_o)/L(lambda_a)]<k | Ho is true) = alpha

But I am having some trouble finding the statistic.

L(lambda_o)/L(lambda_a)=(lambda_o)^(y1+...+yn)/(lambda_a)^(y1+...+yn)

How can I proceed from here? I am stuck...

Thanks for any help!