Is there any evidence that a student has ESP

The p-value for such an experiment as you describe would be slightly less than 0.05 (2-tailed hypothesis test), but all this means is that there is still a 5% probability that the result was due to random chance. And that probability is still far more than there being some magical new power in the universe responsible for the results. Other possibilities are that the result is due in part to intentional or unintentional cheating or sensory leakage due to the methodology of the test.

The p-value is really an abused statistic. Many people take p < 0.05 to mean that the effect is real. That's not what it means at all. The figure of 0.05 is somewhat arbitrary but is the customary value scientists tend to use that indicates that the data _may_ support the hypothesis and is worthy of further exploration. Depending on the experiment, the scientist may choose a higher p-value, or in rarer instances, a lower one.

Now, if you can confirm that the test is rigorous and objective, and this person can average a score of 75% over numerous tests (not just one), the probability of it being due to random chance starts to drop. And then you'll start gathering interest. But no psychic seems to be able to do this.

Are you are using Zener cards?

Since there are twenty-five cards in the deck and five kinds of cards, there is a one in five or 20% chance that any given card is on top of the deck or being viewed by a sender. Of course, these odds change as soon as a card is removed from the deck. The odds for each selection can remain identical only if each card is put back in the deck and the cards are thoroughly reshuffled after each selection. From the point of view of the guesser, however, as long as no feedback is given while going through the deck with a sender, each card has a one in five chance of being the card on top at any given time. A correct "guess" is called a "hit". Anything significantly higher than 20% hits in the long run would indicate that something other than chance is at work. In the short run, higher percentages are expected, on occasion, by chance.

Thus, if a guesser got nine out of twenty-five correct (36%) going through the deck once, that would not necessarily be indicative of anything important. If the guesser got 36% correct over 100 runs through a deck of 25 cards (i.e., 2,500 guesses), that would indicate that something else besides chance is going on. Maybe you're psychic, maybe there is sensory leakage, or maybe you're cheating. (We know, for example, that some of the decks of Zener cards that were printed for Rhine's lab were very thin and translucent, allowing receivers to see through the card to identify which icon the sender was looking at.)