AP Statistics 2.3 - Statistics for Two Categorical Variables- MCQs - Exam Style Questions
▶️ Answer/Explanation
We want the joint proportion of all respondents who chose “No” for color consideration and “Safety” as the additional feature.
From the table, that cell count is \(192\). The total number of respondents is \(1{,}092\).
Compute the proportion: \[ \hat{p}=\frac{192}{1{,}092}\approx 0.176\approx 0.18. \] ✅ Answer: (A)
Why the other options are wrong:
(B) \(\frac{376}{1{,}092}\approx 0.34\) — proportion who selected Safety overall (Yes/No/Maybe combined).
(C) \(\frac{192}{534}\approx 0.36\) — conditional proportion among those who said “No.”
(D) \(\frac{534}{1{,}092}\approx 0.49\) — proportion who said “No” regardless of feature.
(E) \(\frac{1{,}092-534}{1{,}092}=\frac{558}{1{,}092}\approx 0.51\) — proportion who did not say “No.”
▶️ Answer/Explanation
1. Determine Sample Sizes:
– Total students = \(200\)
– Male students = \(80\)
– Female students = \(200 – 80 = 120\)
2. Use the Assumption of Independence:
If gender and eye color are independent, the proportion of students with brown eyes should be the same for both males and females.
3. Calculate the Proportion of Brown Eyes:
From the male group, the proportion with brown eyes is: \(\frac{60}{80} = 0.75\).
4. Calculate the Expected Number of Females:
Apply this proportion to the number of female students.
Expected Females with Brown Eyes = (Number of Females) \(\times\) (Proportion with Brown Eyes)
Expected = \(120 \times 0.75 = 90\)
✅ Answer: (D)