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# Chi-Squared Goodness of Fit Test

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Problem
More than one teacher has given the following advice: choose answer C when blindly guessing among four answers in a multiple choice test, since C is more often the correct answer than either A, B, or D.
Suppose that we take a random sample of multiple-choice test answers (the correct answers from the instructor's answer sheet) from introductory college courses and obtain the information summarized in the first row of numbers in Table 1 below. These numbers are the observed frequencies for each of the categories A, B, C, and D for our sample of correct answers. The second row of numbers in Table 1 contains the frequencies expected for a sample of correct answers if a correct answer is equally likely to be A, B, C, or D. The bottom row of numbers in Table 1 contains the values

= (Observed frequency - Expected frequency)2

Expected frequency
for each of the correct answer categories A, B, C, and D.
Fill in the missing values of Table 1. Then, using the level of significance, perform a test of the hypothesis that each of A, B, C, and D is equally likely to be the correct answer on tests in these introductory college courses. Then complete Table 2.
Round your responses for the expected frequencies in Table 1 to at least two decimal places. Round your responses in Table 1 to at least three decimal places. Round your responses in Table 2 as specified.