1.23 Inference for Poisson parameters can often be based on connections with binomial and multinomial distributions. Show how to test Ho: = for

1.23 Inference for Poisson parameters can often be based on connections with binomial and multinomial distributions. Show how to test Ho: μ₁ = μ₂ for two populations based on independent Poisson counts (y1, y2), using a corresponding binomial test.

[Hint: Condition on n = y1 + y2 and identify π = μ₁/(μ₁ + μ2).] How can you construct a confidence interval for μι/μ2 based on one for π?