AP Statistics 3.6 Selecting an Experimental Design- MCQs - Exam Style Questions
▶️ Answer/Explanation
Size is a potential confounder (student believes larger rabbits may respond differently).
Best practice is to control for size by forming matched pairs of similar size, then randomly assign one rabbit in each pair to medicine and the other to no medicine (paired comparison).
This design reduces variability due to size and isolates the treatment effect; the veterinarian’s evaluation is blinded, which helps reduce bias.
(A) random pairing ignores size → poor control of confounding.
(C) and (D) systematically mix size with treatment → confounding the treatment with size.
(E) completely randomized design ignores known size differences → less precise than matched pairs.
✅ Answer: (B)
Best practice is to control for size by forming matched pairs of similar size, then randomly assign one rabbit in each pair to medicine and the other to no medicine (paired comparison).
This design reduces variability due to size and isolates the treatment effect; the veterinarian’s evaluation is blinded, which helps reduce bias.
(A) random pairing ignores size → poor control of confounding.
(C) and (D) systematically mix size with treatment → confounding the treatment with size.
(E) completely randomized design ignores known size differences → less precise than matched pairs.
✅ Answer: (B)
▶️ Answer/Explanation
Detailed solution
Let $X$ be the actual mass and $Y$ be the displayed mass.
1. The Calculation:
The relationship is defined by a precise formula:
$Y = X – 0.75$
2. Analysis of the Formula:
– This is the equation of a perfect straight line.
– Because it’s a perfect line, the correlation must be exactly $1$ or $-1$.
– As the actual mass ($X$) increases, the displayed mass ($Y$) also increases. This means the relationship is positive.
A perfect positive relationship has a correlation of 1.
✅ Answer: (E)