H0 and H1 should always be phrased so that H0 is "not H1". In the above case that would be H1 "The psychic is not just lucky". Rejecting the data based on hypo

H0 and H1 should always be phrased so that H0 is "not H1". In the above case that would be H1 "The psychic is not just lucky". Rejecting the data based on hypothesis testing is a misapplication of the technique. That doesn't mean that data is always right but it's just another hypothesis about the data itself, e.g. H0 "data is fine", H1 "data is not fine".