MHB Help with Problem: Seeking Solutions

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The discussion centers on seeking assistance for a specific problem, with an emphasis on providing details about attempted solutions. Participants encourage sharing previous efforts to better understand the issue at hand. This approach aims to facilitate more effective guidance from others in the forum. Clear communication of the problem and past attempts is crucial for receiving relevant help. Engaging with the community in this manner increases the likelihood of finding a resolution.
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Can some help me with this problem? Thanks!
 

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Can you show what you've tried so our helpers have a better idea where you are stuck or where you may be going wrong?
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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