A negative value of r is reported between the number of minutes spent exercising per week and the number of hours spent commuting per week for a random sample of adults. What is the most appropriate conclusion to reach based on this information?

Question

A negative value of r is reported between the number of minutes spent exercising per week and the number of hours spent commuting per week for a random sample of adults.  What is the most appropriate conclusion to reach based on this information?

BlackTom AI · Accepted Answer

A negative correlation coefficient r indicates a negative linear association: as one variable increases, the other tends to decrease.

1) Relevant concepts:
- The sample correlation r measures direction (sign) and strength (magnitude) of a linear relationship between two quantitative variables. r ranges from −1 to 1.
- Correlation describes association, not causation. It does not provide a rate of change (slope) in original units.
- The proportion of variability explained is r^2 (so you need the numeric value of r to assess how much variability is explained).

2) Step-by-step reasoning:
- We are told r is negative between minutes exercising/week and hours commuting/week. The negative sign tells us the direction: higher commute hours are associated with fewer exercise minutes.
- Because only the sign (negative) is reported and no numeric r is given, the only safe conclusion concerns direction (tendency), not magnitude, causation, or the exact amount of change.
- The sample being random supports generalizability to the population but does not permit causal inferences without experimental design or additional information.

3) (No numerical calculations are required because r’s numeric value is not provided.)

4) Why the correct answer is correct:
- “Minutes spent exercising per week tends to decrease as commute time increases” exactly states the negative association in plain-language, which is the appropriate inference from a negative r.

5) Why the other options are incorrect:
- “Less than half of the variability…” requires knowing r^2; without a numeric r you cannot determine whether r^2 < 0.5.
- “People who commute more do not prioritize exercise” attributes motive/intent and implies causation; correlation cannot support this.
- “For each additional hour of commute time, minutes spent exercising per week decreases” asserts a specific rate (slope) in units; correlation alone does not provide that number.
- “A natural result of a long commute is less time to exercise.” This is a causal statement; correlation does not prove causation.

Conclusion: The best-supported conclusion is: Minutes spent exercising per week tends to decrease as commute time increases. This matches the provided answer.

A negative value of r is reported between the number of minutes spent exercising per week and the number of hours spent commuting per week for a random sample of adults. What is the most appropriate conclusion to reach based on this information?单项选择题

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