A publisher of academic testing software is interested in wh

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 even 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). Letting p1 be the proportion of correct answer choices that are A\'s, p2 be the proportion of answer choices that are B\'s, and so on. A random sample of 200 questions was selected and the correct answer noted for each one. The publisher wishes to conduct a chi-squared goodness-of-fit test. What is the value of the chi-square distribution that marks the rejection region for a 0.05 level test? Help me work out the problem in steps

Solution

Here, the number of degrees of freedom is

df = k - 1

where k = the number of categories.

As there are 5 choices, k = 5. Thus,

df = 4.

At 0.05 level and df = 4, the critical chi^2 value, by table/technology,

chi^2 (crit) = 9.487729037 [ANSWER]