This is an asymptotic result of an imaginary experiment. It is not a probability that anyone is willing to bet on. Asymptotic results are not relevant to a data set at hand. A p-value for a collected data set is a proportion or percentile–perfectly descriptive of a divergence from a reference point. If you wish to refer to a future experiment of the exact same design, conditional on the observed test statistic, one should quote an interval ie a p value of 0.05 is equivalent to a Z score of 1.96, +/- 1. converting back to the p value scale (one tailed) is 0.17 (1 - 0.83) to 0.002 (1-0.998)
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