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why do we use H0: μ ≥ μ0 in a left tailed test and try to reject H0 rather than using H0: μ ≤ μ0 and trying to prove H0 is true? thanks

kjetil b halvorsen
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shahab shahroodi
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    You seem to have stumbled upon something like non-inferiority testing, but the reason is that we want to disprove $H_0$ in favor of some alternative. We are, in some sense, hoping for the alternative to be true. – Dave Jun 10 '21 at 12:28
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    Some people think absence of evidence (failing to reject $H_0$) is not evidence of absence. – Henry Jun 10 '21 at 13:59
  • Perhaps this discussion is helpful: https://stats.stackexchange.com/questions/23142/when-to-use-fisher-and-neyman-pearson-framework/51823#51823 – Ariel Jun 11 '21 at 02:55

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