MHB How Do You Determine the Correct Quantile for One-Sided Hypothesis Tests?

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In one-sided hypothesis tests, determining the correct quantile involves referencing the standard Normal Table at a specified significance level. The discussion focuses on finding the appropriate quantile for a greater-than hypothesis test. Participants are prompted to evaluate various statements regarding quantiles and their significance. The conversation indicates a need for clarity on which option is correct based on the standard normal distribution. Understanding these quantiles is crucial for accurate hypothesis testing.
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Consider a one-sided (greater than) hypothesis tests. For a given level of significance we can find the quantile which satisfies

From the standard Normal Table, find the approximate quantiles for and and indicate which of the following statements is correct.Select one:




Is it the second option?

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Standard normal table
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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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