Edward C. answered 04/13/16
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Think about how the p-value is calculated. The p-value is computed assuming that H0 is true, and is simply the probability that the observed outcome would take a value as extreme or more extreme than what was actually observed in the sample data. The smaller the p-value is, the stronger the evidence against H0 provided by the data. If the p-value is high (in particular, if it is higher than the level of significance) then the data does not provide strong evidence against H0 and H0 cannot be rejected.