A statistics instructor gave a four-question true–false quiz to his class of 150 students. The results were as follows.

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 H0 at the α = 0.05 level?

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Number correct Observed 0 012 3 4 2 13 29 71 35