A statistics instructor gave a four-question true-false quiz to his class of 81 students. The results were as follows. Number correct 0 1 2 3 4 Observed 2 19 29 23 8 Send data to Excel The instructor thinks that the students may have answered the questions by guessing, so that the probability that any given answer is correct is 0.5 . Under this null hypothesis, the number of correct answers has a binomial distribution with 4 trials and success probability 0.5 . Perform a chi-square test of this hypothesis. Can you reject Ho at the a = 0.01 level? Use the P-value method with the TI-84 Plus calculator. Part: 0 / 4 Part 1 of 4 (a) State the null and alternate hypotheses. Ho: The number of correct answers has a binomial distribution with 4 trials X 5 and success probability 0.5 . H: The number of correct answers does not have v a binomial distribution with 4 trials and success probability 0.5. Part: 1 / 4 Part 2 of 4 (b) Find the P-value. Round the answer to at least four decimal places. The P-value is