A Psychology Instructor Gave a Five-Question True-False Quiz to Her $\begin{array}{l|cccccc}\text { Number Correct } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 8 & 30 & 56 & 48 & 26 & 10\end{array}$

Multiple Choice

A psychology instructor gave a five-question true-false quiz to her class of 178 students. The results were as follows.
$\begin{array}{l|cccccc}\text { Number Correct } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 8 & 30 & 56 & 48 & 26 & 10\end{array}$

The instructor thinks that the students may have answered the questions by guessing, so tl probability that any given answer is correct is $0.5$ . Under the null hypothesis, the 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 $\alpha = 0.01$ level?

A) Yes
B) No