In an extrasensory perception experiment carried out in a live television interview, the interviewee who claimed to have extrasensory powers was required to identify the pattern on each of 10 cards, which had been randomly assigned with one of five different patterns. The cards were visible only to the audience who were asked to “transmit” the patterns to the interviewee. When the interviewee failed to identify any of the cards correctly, she claimed that this was clear proof of the existence of ESP, since there was a strong mind in the audience who was willing her to get the answers wrong.
State the hypotheses implied by the interviewee’s conclusion and carry out a 5% test on this basis.
State precisely the hypotheses that the interviewer could have specified before the experiment to prevent the interviewee from “cheating” in this way, and determine the number of cards that would have to be identified correctly to demonstrate the existence of ESP at the 5% level.
I took $Ho:p=0.2$ and $H1:p \neq 0.2.$ I have computed $ P(X=0).$ It comes to $0.107.$
How to proceed after this? Also, how do I solve part 2?