A psychology instructor gave a five-question true-false quiz to her class of 201 students. The results were as follows.

$\begin{array} { l | c c c c c c } \text { Number Correct } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 10 & 40 & 56 & 64 & 25 & 6\end{array}$

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?

Question

A psychology instructor gave a five-question true-false quiz to her class of 201 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 } & 10 & 40 & 56 & 64 & 25 & 6\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?

Quizplus · Accepted Answer

The chi-square test for goodness of fit would compare the observed frequencies of correct answers to the expected frequencies under the null hypothesis that students are guessing (each question has a 0.5 probability of being answered correctly). To reject the null hypothesis at the $\alpha = 0.01$ level, the calculated chi-square statistic must exceed the critical value from the chi-square distribution table for the appropriate degrees of freedom. Without calculating the chi-square statistic and comparing it to the critical value, we cannot definitively conclude whether to reject the null hypothesis at the $\alpha = 0.01$ level based solely on the provided information.

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