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AP Statistics 8.7 Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data- MCQs - Exam Style Questions

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Question

A survey was conducted in which both men and women were asked a question about a current issue. Possible responses to this question were “in favor of,” “not in favor of,” or “no opinion.” A chi-square test is to be used to determine whether the response to this question is independent of gender. The number of degrees of freedom for the chi-square test in this situation is
(A) 6
(B) 5
(C) 3
(D) 2
(E) 1
▶️ Answer/Explanation
Detailed solution

1. Identify Table Dimensions:
Gender: 2 categories (men, women)
Response: 3 categories (in favor, not in favor, no opinion)

2. Apply Chi-square Formula:
Degrees of freedom = \((r-1)(c-1)\) where \(r\) = rows, \(c\) = columns
Here: \((2-1)(3-1) = (1)(2) = 2\)

✅ Answer: (D) 2

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