Question

An academic publishing company that specializes in 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 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 to two decimal places.

Answer Choice	# of Times Correct
A	55
B	86
C	23
D	93
E	84

Answer 1

The formula for chi-Square test Statistic is

Here

O: Observed Frequency

E : Expected Frequency

Since we have 5 ansswer choices and proportion of each choice is equal so proportion (P) = 1 / 5 = 0.2

Expected frequency = n * p

Here n= Sum of observed Frequency =341

E= 341 x 0.2 = 68.2 for All choices

Let's make a table

Test Statistic = 49.84