Question

(a) a flute instructor examined student progress. he found that playing a longer song does not necessarily mean that a student will have more or fewer wrong notes. what can he conclude?
○ there is no correlation between song length and number of wrong notes.
○ there is a correlation between song length and number of wrong notes. there may or may not be causation. further studies would have to be done to determine this.
○ there is a correlation between song length and number of wrong notes. there is probably also causation. this is because there is likely an increase in the number of wrong notes with an increase in the song length.
(b) an environmental study was conducted. it reported that, for a park, having more visitors indicates having a larger number of trees. what can be determined?
○ there is no correlation between number of visitors and number of trees.
○ there is a correlation between number of visitors and number of trees. however, there is no causation. this is because there is an increase in the number of trees with an increase in the number of visitors. there may or may not be causation. further studies would have to be done to determine this.
○ there is a correlation between number of visitors and number of trees. there may or may not be causation. further studies would have to be done to determine this.
(c) data was collected at a tennis court. it showed that being older implies that a player will stay for a shorter length of time. what is likely true?
○ there is no correlation between age and length of stay.
○ there is a correlation between age and length of stay. there may or may not be causation. further studies would have to be done to determine this.
○ there is a correlation between age and length of stay. however, there is no causation. this is because there is a decrease in the length of stay with an increase in age.

Explanation:

Correlation does not imply causation. Just because two variables are correlated (e.g., in part (a) song length and wrong notes, in part (b) visitors and trees, in part (c) age and stay length), it doesn't mean one causes the other. Further studies (like controlled experiments) would be needed to determine causation.

Answer:

(a) There is no correlation between song length and number of wrong notes.
(b) There is a correlation between number of visitors and number of trees. However, there is no causation. This is because there is an increase in the number of trees with an increase in the number of visitors. There may or may not be causation. Further studies would have to be done to determine this.
(c) There is a correlation between age and length of stay. There may or may not be causation. Further studies would have to be done to determine this.