Probability: find decision rule, prob's of Type I, II errors

T

tomato

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Hello, I'm hving some trouble trying to start this homework problem I have. Any help would be so much appreciated!

Here it is:

Peggy is given a jar containing 5 chips and told that either the chips are marked 1,3,5,7, and 9 or they are marked 2,4,6,8, and 10. She is allowed to pick one chip at random. If Peggy sets the null hypothesis as Ho: The chips are marked 1,3,5,7, and 9, what is the most appropriate decision rule that she can devise? Find the corresponding probabilities of Type I and Type II errors.

Thanks in advance!
 
The most appropriate decision rule is easy (odd number or not), but this looks like an exercise in using the Neyman-Pearson Lemma to prove the rule is most appropriate.
 
Neyman-Pearson Lemma isnt in my textbook. Is there any other way I can set up this problem? Thanks again.
 
It appears your textbook is using different words and methods than mine. How does your textbook define a most appropriate decision rule? What tools does your textbook give for verifying that a decision rule is most appropriate?
 
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