Identifying Best Critical Regions

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What is the Neyman-Pearson Lemma, and how can we put it to work?
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  1. Equitable Equations
  2. statistical inference
  3. best critical regions
  4. statistical power
  5. neyman-pearson lemma
  6. stats
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I didn't understand the concept of k what it would be, can you solve by letting k equals to some value

SyedMuhammadIqbal-cd