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How would one prove that

$\text{Prob}(Z<z_{calc})$ is the $p$-value where $z_{calc}$ is the sample statistics $\sqrt(n)(\bar{x}-\mu_0)/\sigma$. Here, $p$-value is the probability of observing data which are similar to, or more extreme if $H_0$ happens to be true.

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  • $\begingroup$ It is a definition... $\endgroup$
    – V. Vancak
    Feb 22, 2018 at 16:09
  • $\begingroup$ I do not follow. What is a definition of what? Thank you $\endgroup$
    – user122424
    Feb 22, 2018 at 16:26
  • $\begingroup$ $\mathbb{P}(Z < Z_{calc}) = p.value$ is by definition the p.value of one sided test with $Z$ statistics. There is nothing to prove. $\endgroup$
    – V. Vancak
    Feb 22, 2018 at 16:29

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