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In statistics we tend use the 'hat' notation to imply a statistic. We designate P to represent the proportion in the population. Because P is unknown and unknowable we use Phat to designate the proportion in the sample. Suppose 30 out of 100 people in my sample support Trump. P = unknown and unknowable.
1 The p-value is not the probability that the null hypothesis is true or the probability that the alternative hypothesis is false. 2  It is not connected to either. 3  In fact, frequentist statistics does not and cannot attach probabilities to hypotheses.ince p-value is used in frequentist inference (and not Bayesian inference), it does not in itself support reasoning about the probabilities of hypotheses but is only as a tool for deciding whether to reject the null hypothesis.