Bonus Question (5 points): Psychic is defined as relating to or denoting faculties or phenomena that are apparently inexplicable by natural laws, especially involving telepathy or clairvoyance. One psychologist would like to investigate this "Psychic" phenomena. He assumed that if a person is "psychic", he or she would be able to guess the color coat of the M&Ms chocolate correctly when he or she was blindfolded. If a person is not "psychic", he or she would guess the color coat of the M&Ms no more than just by randomly guessing. He conducted an experiment using 20 participants. Each participant pick 12 M&M chocolate from the bag without seeing them, and guess what color they were. He recorded the number of each participants 'correct guess. Here is the data from his experiment. 2, 2,3, 4, 5, 1, O, 2, 2,0, 3, 2, 0,1,3, 1, 4, 4, 3, and 3 (n=20) (1) Suppose there are six different colors for each pack of M&M chocolate. What is the probability for participants to guess the color correctly for each M&M chocolate? (2) Each participant pick 12 MaM chocolates from the bag. What is the test value (if the participants were not "psychic" and guess the color just by random)? (3) What kind of data analysis method would be appropriate for analyzing the data? (4) Using SPSS to conduct the data analysis. What is the result? (provide your output at the end of this question.)