Question

question 10
1 pts
a study reports a correlation of 0.70 between the number of hours spent commuting per week and the number of hours spent listening to podcasts per week for a random sample of adults. which one of the following is the most appropriate interpretation of this correlation?

• more than half of the variability in hours spent listening to podcasts is explained by hours spent commuting.
• people who commute more often always listen to more podcasts.
• for each additional hour of commute time, podcast listening time increases by over half an hour.
• a natural result of a long commute time is more time to listen to podcasts.
• hours spent listening to podcasts tends to increase as commuting time increases.

Explanation:

1. Analyze the correlation coefficient \( r = 0.70 \):

• The coefficient of determination \( r^{2}=0.70^{2} = 0.49\), so less than half of the variability is explained, eliminating the first option.
• Correlation does not imply causation (eliminates the fourth option about "natural result") or a fixed increase per unit (eliminates the third option about "each additional hour").
• Correlation also does not mean "always" (eliminates the second option).
• A positive correlation (\( r = 0.70>0 \)) means as one variable (commuting time) increases, the other (podcast listening time) tends to increase.

Answer:

Hours spent listening to podcasts tends to increase as commuting time increases.