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AP Statistics 2.1 Introducing Statistics: Are Variables Related?- MCQs - Exam Style Questions

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Question

In a recent survey, 60 randomly selected married couples from the same town were asked to rate the overall quality of living in their town on a scale from 1 (very poor) to 10 (excellent) on twenty different attributes such as accessibility to major highways, availability of entertainment, services provided by tax dollars, etc. For each couple, the husband’s individual ratings on the twenty attributes were averaged to produce an overall quality rating, and that process was repeated for the wife. Each point on the scatterplot below displays the overall rating of one of the 60 couples with the husband’s rating represented by the horizontal axis and the wife’s rating represented by the vertical axis.
Based on the scatterplot, which of the following statements is true?
(A) Husbands tended to rate the quality of living higher than their wives did.
(B) More overall ratings of 7 or less were assigned by husbands than by wives.
(C) The range in the husbands’ overall ratings is greater than the range in the wives’ overall ratings.
(D) The difference in overall ratings between a husband and wife was not more than 3 for any couple.
(E) For each couple, the overall rating assigned by the husband was the same as the overall rating assigned by the wife.
▶️ Answer/Explanation
Detailed solution

1. Analyze the Scatterplot with a Line of Equality:
Imagine a line where the wife’s rating equals the husband’s rating (the line \(y=x\)).
– Points **on** this line represent couples who gave the same rating.
– Points **below** this line represent couples where the husband’s rating (x-axis) was higher than the wife’s rating (y-axis).
– Points **above** this line represent couples where the wife’s rating was higher than the husband’s.

2. Observe the Pattern:
By visually inspecting the scatterplot, it is clear that there are significantly more points below the line \(y=x\) than above it. This shows a clear pattern or tendency.

3. Evaluate the Statement:
The fact that most points are below the line of equality directly supports the statement that “Husbands **tended to** rate the quality of living higher than their wives did.” The phrase “tended to” correctly describes this overall pattern rather than a rule that applies to every single couple.
✅ Answer: (A)

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