A Psychology Instructor Gave a Five-Question True-False Quiz to Her

Multiple Choice

A psychology instructor gave a five-question true-false quiz to her class of 178 students. ) $$\begin{array} { l | c c c c c c } \text { Number Correct } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 8 & 30 & 56 & 48 & 26 & 10\end{array}$$ The instructor thinks that the students may have answered the questions by guessing, so that the 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) $\mathrm { No }$