A publisher of academic testing software is interested in whether the system that
generates the questions and answers does so in a way that ensures that the distribution of
correct answers is uniform across all answer choices. If some answer choices are more
likely to be chosen than others, unethical test preparation companies could use the
uneven distribution of answers to give their clients an unfair “edge.”
The test has 5 answer choices per question (A, B, C, D, or E). Let p1 be the proportion of
correct answer choices that are A’s, p2 be the proportion of correct answer choices that
are B’s, and so on. The publisher wishes to conduct a chi-squared goodness-of-fit test.
What are the null and alternative hypotheses for the test?