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

Essay

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

The instructor thinks that the students may have answered the questions by guessi that the probability that any given answer is correct is $0.5$ . Under the null hypothe number of correct answers has a binomial distribution with 5 trials and success probability $0.5$ .
Perform a chi-square test of this hypothesis. Can you reject $H _ { 0 }$ at the $\alpha = 0.05$ leve