please show work A publisher of academic testing software is interested in wheth

Question

please show work

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 p_1 be the proportion of correct answer choices that are A's, P_2 be the proportion of answer choices that are B's, and so on. The publisher wishes to conduct a chi-squared goodness-of-fit test. The distribution of answer choices from a random sample of questions from the software's "test bank" is shown below. Calculate the value of the test statistic. Take all calculations to two (2) decimal places.

Explanation / Answer

here for equal proportion each choice has probability =1/5

hence applying chi square goodness of fit:

hence test stat =31.96

observed Expected Chi square Probability O E=total*p =(O-E)^2/E A 1/5 81.00 65.80 3.51 B 1/5 27.00 65.80 22.88 C 1/5 74.00 65.80 1.02 D 1/5 64.00 65.80 0.05 E 1/5 83.00 65.80 4.50 329 329 31.9574

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