Question

(a) a flute instructor examined student progress. she found that playing a longer song does not necessarily mean that a student will have more or fewer wrong notes. what can she 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 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

Explanation:

Step1: Analyze part (a)

The flute - instructor found no relation between song length and number of wrong notes. So, there is no correlation.

Step2: Analyze part (b)

The environmental study shows that more visitors are associated with more trees, so there is a correlation. But we can't be sure of causation without further study.

Step3: Analyze part (c) (not fully shown but based on the trend)

When data shows an association like age and length of stay, there is a correlation, and causation may or may not be present without more study.

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. 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.