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As per statistical literature, there seems to be this understanding that given a p value less than alpha, we are to reject the null hypothesis.
The way I am interpreting this is that is the critical region, as defined by the alpha is the 'False Rejection' (TYPE 1 error) zone and constitutes the error threshold, why then p-value for a sample that is less than the alpha and within the error zone results in rejection of the null hypothesis?
Another line of thought - if the p-value is a way of saying how extreme a test statistic is for our sample data and seems to have a low probability, then how does it constitute evidence against the null hypothesis? Where am I going wrong?