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

Short Answer

A psychology instructor gave a five-question true-false quiz to her class of 193 students. The results were as follows.

$$\begin{array} { l | c c c c c c } \text { Number Correct } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 6 & 26 & 58 & 59 & 25 & 19\end{array}$$

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 H₀ at the $\alpha$ =0.01 level?