Question:

Let \[{{X}_{1}},{{X}_{2}},{{X}_{3}},{{X}_{4}}\] be a random sample from a Poisson distribution with parameter \[\lambda \] and let \[Y={{X}_{1}}+{{X}_{2}}+{{X}_{3}}+{{X}_{4}}\] . You decide to test \[\lambda \] =1.60 versus \[\lambda \] <1.60 using the following decision rule:

Reject \[\lambda \] =1.60 in favor of \[\lambda \] <1.60 when \[Y\le \] 2.

1. Find the type I error, \[\alpha \] .
2. Find the type II error , \[\beta \] , when \[\lambda \] =1.70.

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