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A Psychology Instructor Gave a Five-Question True-False Quiz to Her  Number Correct 012345 Observed 4275571274\begin{array}{l|cccccc}\text { Number Correct } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 4 & 27 & 55 & 71 & 27 & 4\end{array}

Question 49

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A psychology instructor gave a five-question true-false quiz to her class of 188 students. The results were as follows.
 Number Correct 012345 Observed 4275571274\begin{array}{l|cccccc}\text { Number Correct } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 4 & 27 & 55 & 71 & 27 & 4\end{array}

The instructor thinks that the students may have answered the questions by guessi that the probability that any given answer is correct is 0.50.5 . Under the null hypothe number of correct answers has a binomial distribution with 5 trials and success probability 0.50.5 .
Perform a chi-square test of this hypothesis. Can you reject H0H _ { 0 } at the α=0.05\alpha = 0.05 leve

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